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US20170128940A1 - Inertial droplet generation and particle encapsulation - Google Patents

Inertial droplet generation and particle encapsulation Download PDF

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Publication number
US20170128940A1
US20170128940A1 US15/347,709 US201615347709A US2017128940A1 US 20170128940 A1 US20170128940 A1 US 20170128940A1 US 201615347709 A US201615347709 A US 201615347709A US 2017128940 A1 US2017128940 A1 US 2017128940A1
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Prior art keywords
bead
beads
cell
channel
fluid
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Abandoned
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US15/347,709
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English (en)
Inventor
Hamed Amini
Arash Jamshidi
Tarun Kumar Khurana
Foad Mashayekhi
Yir-Shyuan Wu
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Illumina Inc
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Illumina Inc
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Priority to US15/347,709 priority Critical patent/US20170128940A1/en
Assigned to ILLUMINA, INC. reassignment ILLUMINA, INC. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: JAMSHIDI, ARASH, AMINI, Hamed, MASHAYEKHI, FOAD, KHURANA, TARUN KUMAR, WU, Yir-Shyuan
Publication of US20170128940A1 publication Critical patent/US20170128940A1/en
Priority to US16/691,405 priority patent/US11123733B2/en
Abandoned legal-status Critical Current

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01F—MIXING, e.g. DISSOLVING, EMULSIFYING OR DISPERSING
    • B01F23/00—Mixing according to the phases to be mixed, e.g. dispersing or emulsifying
    • B01F23/40—Mixing liquids with liquids; Emulsifying
    • B01F23/41—Emulsifying
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01F—MIXING, e.g. DISSOLVING, EMULSIFYING OR DISPERSING
    • B01F33/00—Other mixers; Mixing plants; Combinations of mixers
    • B01F33/30—Micromixers
    • B01F33/301—Micromixers using specific means for arranging the streams to be mixed, e.g. channel geometries or dispositions
    • B01F33/3011—Micromixers using specific means for arranging the streams to be mixed, e.g. channel geometries or dispositions using a sheathing stream of a fluid surrounding a central stream of a different fluid, e.g. for reducing the cross-section of the central stream or to produce droplets from the central stream
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
    • B01L3/00—Containers or dishes for laboratory use, e.g. laboratory glassware; Droppers
    • B01L3/50—Containers for the purpose of retaining a material to be analysed, e.g. test tubes
    • B01L3/502—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures
    • B01L3/5027—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip
    • B01L3/502761—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip specially adapted for handling suspended solids or molecules independently from the bulk fluid flow, e.g. for trapping or sorting beads, for physically stretching molecules
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
    • B01L3/00—Containers or dishes for laboratory use, e.g. laboratory glassware; Droppers
    • B01L3/50—Containers for the purpose of retaining a material to be analysed, e.g. test tubes
    • B01L3/502—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures
    • B01L3/5027—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip
    • B01L3/502769—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip characterised by multiphase flow arrangements
    • B01L3/502776—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip characterised by multiphase flow arrangements specially adapted for focusing or laminating flows
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
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    • B01L3/50—Containers for the purpose of retaining a material to be analysed, e.g. test tubes
    • B01L3/502—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures
    • B01L3/5027—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip
    • B01L3/502769—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip characterised by multiphase flow arrangements
    • B01L3/502784—Containers for the purpose of retaining a material to be analysed, e.g. test tubes with fluid transport, e.g. in multi-compartment structures by integrated microfluidic structures, i.e. dimensions of channels and chambers are such that surface tension forces are important, e.g. lab-on-a-chip characterised by multiphase flow arrangements specially adapted for droplet or plug flow, e.g. digital microfluidics
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
    • B01J2219/00—Chemical, physical or physico-chemical processes in general; Their relevant apparatus
    • B01J2219/00274—Sequential or parallel reactions; Apparatus and devices for combinatorial chemistry or for making arrays; Chemical library technology
    • B01J2219/00277—Apparatus
    • B01J2219/00457—Dispensing or evacuation of the solid phase support
    • B01J2219/00459—Beads
    • B01J2219/00468—Beads by manipulation of individual beads
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
    • B01J2219/00—Chemical, physical or physico-chemical processes in general; Their relevant apparatus
    • B01J2219/00274—Sequential or parallel reactions; Apparatus and devices for combinatorial chemistry or for making arrays; Chemical library technology
    • B01J2219/00277—Apparatus
    • B01J2219/00497—Features relating to the solid phase supports
    • B01J2219/005—Beads
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
    • B01J2219/00—Chemical, physical or physico-chemical processes in general; Their relevant apparatus
    • B01J2219/00274—Sequential or parallel reactions; Apparatus and devices for combinatorial chemistry or for making arrays; Chemical library technology
    • B01J2219/00718—Type of compounds synthesised
    • B01J2219/0072—Organic compounds
    • B01J2219/00722—Nucleotides
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
    • B01L2200/00—Solutions for specific problems relating to chemical or physical laboratory apparatus
    • B01L2200/06—Fluid handling related problems
    • B01L2200/0636—Focussing flows, e.g. to laminate flows
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
    • B01L2200/00—Solutions for specific problems relating to chemical or physical laboratory apparatus
    • B01L2200/06—Fluid handling related problems
    • B01L2200/0647—Handling flowable solids, e.g. microscopic beads, cells, particles
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
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    • B01L2200/06—Fluid handling related problems
    • B01L2200/0647—Handling flowable solids, e.g. microscopic beads, cells, particles
    • B01L2200/0652—Sorting or classification of particles or molecules
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
    • B01L2300/00—Additional constructional details
    • B01L2300/08—Geometry, shape and general structure
    • B01L2300/0809—Geometry, shape and general structure rectangular shaped
    • B01L2300/0816—Cards, e.g. flat sample carriers usually with flow in two horizontal directions
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
    • B01L2300/00—Additional constructional details
    • B01L2300/08—Geometry, shape and general structure
    • B01L2300/0848—Specific forms of parts of containers
    • B01L2300/0858—Side walls
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
    • B01L2300/00—Additional constructional details
    • B01L2300/08—Geometry, shape and general structure
    • B01L2300/0861—Configuration of multiple channels and/or chambers in a single devices
    • B01L2300/0867—Multiple inlets and one sample wells, e.g. mixing, dilution
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01L—CHEMICAL OR PHYSICAL LABORATORY APPARATUS FOR GENERAL USE
    • B01L2300/00—Additional constructional details
    • B01L2300/08—Geometry, shape and general structure
    • B01L2300/0861—Configuration of multiple channels and/or chambers in a single devices
    • B01L2300/0883—Serpentine channels

Definitions

  • the invention relates to the fields of microfluidics and encapsulation of particles such as beads, nucleic acid fragments, and cells into droplets for performing biological and chemical reactions.
  • Microfluidic devices may be used to move fluids through narrow channels to perform certain diagnostic or other reactions. These devices can include inlets for receiving one or more fluids and outlets for transferring fluids to external devices or systems.
  • the invention features methods of generating liquid droplets containing two or more types of particles.
  • the methods include focusing a bead fluid having beads suspended therein into a first ordered stream of beads within a first microchannel; focusing a cell fluid having cells suspended therein into a second ordered stream of cells within a second microchannel; and merging the first ordered stream with the second ordered stream to form a plurality of droplets having a predetermined number of cells and beads within each droplet.
  • the first microchannel has a minimum cross-sectional dimension D and the beads have a cross-sectional dimension that is at least about 0.1 D.
  • the cells have a cross-sectional dimension that is at least about 0.1 D.
  • Merging of the first ordered stream and the second ordered stream includes contacting with a third fluid immiscible in the first fluid and the second fluid. Focusing the beads includes passing the beads through a first inertial focusing portion of the first microchannel. Focusing the cells includes passing the cells through a second inertial focusing portion of the second microchannel.
  • the beads include nucleotide fragments.
  • the nucleotide fragments include a tag or barcode region, an index region, and a capture region.
  • the tag or barcode region of each nucleotide fragment can be at least about six nucleotides in length.
  • the index region of each nucleotide fragment can be at least about four nucleotides in length.
  • the capture region includes poly-T nucleotides and can be at least about ten nucleotides in length.
  • the predetermined number of cells is one and the predetermined number of beads is one.
  • the Reynolds number (R e ) of each of the beads is at least about 1, with the Reynolds number of a bead defined as
  • ⁇ is the density of the bead fluid
  • U m is the maximum flow speed of the bead fluid
  • H is the hydraulic diameter of the bead fluid
  • ⁇ is the dynamic viscosity of the bead fluid.
  • the Reynolds number of each of the cells is at least about 1, with the Reynolds number of a cell defined as
  • ⁇ is the density of the cell fluid
  • U m is the maximum flow speed of the cell fluid
  • H is the hydraulic diameter of the cell fluid
  • ⁇ is the dynamic viscosity of the cell fluid
  • the proportion of the plurality of droplets containing k 1 beads and k 2 cells is greater than ( ⁇ 1 k1 exp( ⁇ 1 )/( k 1 !)) ( ⁇ 2 k2 exp( ⁇ 2 )/(k 2 !)), where ⁇ 1 is the average number of the beads per droplet and ⁇ 2 is the average number of the cells per droplet.
  • the flow rate of the first ordered stream is at least about 10 ⁇ L/min, or is about 10 to 100 ⁇ L/min, or is about 40 to 70 ⁇ L/min, or is about 45 to 65 ⁇ L/min, or is about 50 to 60 ⁇ L/min, or is about 50 L/min, or is about 60 ⁇ /min.
  • the flow rate of the second ordered stream is at least about 10 ⁇ L/min, or is about 10 to 100 ⁇ L/min, or is about 40 to 70 ⁇ L/min, or is about 45 to 65 ⁇ L/min, or is about 50 to 60 ⁇ L/min, or is about 50 ⁇ L/min, or is about 60 ⁇ L/min.
  • a droplet generation system includes a first inlet connected to a first inertial focusing microchannel disposed in a substrate; a first flow source configured to drive a bead fluid containing beads through the first inertial focusing microchannel; a second inlet connected to a second inertial focusing microchannel disposed in the substrate, where the first inertial focusing microchannel is connected to the second inertial focusing microchannel for forming the bead fluid and the cell fluid into a plurality of droplets; a second flow source configured to drive a cell fluid containing cells through the second inertial focusing microchannel.
  • one or more particle channels may have a curved region to decrease the focusing length required and to decrease the device foot-print.
  • one or all channels for a first particle type A (such as beads) may have a curved region to decrease the focusing length required and to decrease the device foot-print.
  • one or all channels for a second particle type B (such as cells) may have a curved region to decrease the focusing length required and to decrease the device foot-print.
  • the curved regions may be symmetrically curved. In some embodiments, the curved regions may be asymmetrically curved, such as S-shaped, sinusoidal, or sigmoidal shaped, or continuously curved in a spiral pattern.
  • the curved regions of some or all of the channels are sinusoidal. In some embodiments, the curved regions of some or all of the channels are spiral shaped. In some embodiments, the bead channels, or the cell channels, or both the bead and cell channels comprise spiral shaped regions. In some embodiments, the bead channels, or the cell channels, or both the bead and cell channels comprise sinusoidal regions. In some embodiments, the bead channels comprise spiral regions and the cell channels comprise sinusoidal regions.
  • the bead channel 104 may have an expansion/contraction region which enables the adjustment of the spacing between beads inside the channel.
  • one or both of the cell channels 108 , 110 may have an expansion/contraction region which enables the adjustment of the spacing between cells inside the channel.
  • the first inertial focusing microchannel includes a side wall having an irregular shape (e.g., a discontinuity in the linear nature of the side wall).
  • the second inertial focusing microchannel includes a side wall having an irregular shape.
  • the irregular shape includes a first irregularity protruding from a baseline surface away from a longitudinal axis of the inertial focusing microchannel with the irregular shape. In some instances, the irregularity narrows the microchannel with respect to the longitudinal axis and in other instances the irregularity expands the microchannel with respect to the longitudinal axis.
  • each irregular shape is independently selected from the group consisting of trapezoidal, triangular, rounded, and rectangular. In some embodiments, the group further includes elliptical or unsymmetrical shapes.
  • the microchannel includes a plurality of irregular shapes along a portion of the microchannel. The irregular shapes may be of the same shape or different shapes.
  • one or both of the first inertial focusing microchannel and the second inertial focusing microchannel have an expansion/contraction region having a side wall, where the side wall has a stepped surface. In some embodiments, at least one of the first inertial focusing microchannel and the second inertial focusing microchannel has an expansion/contraction region having a side wall, where the side wall has a curved surface. In some embodiments, at least one of the first inertial focusing microchannel and the second inertial focusing microchannel has a curved region having a Dean number of up to about 30. In some embodiments, one of the first inertial focusing microchannel and the second inertial focusing microchannel has a side wall with a stepped surface. In other embodiments, both inertial focusing microchannels have side walls with stepped surfaces.
  • FIG. 1 is a perspective view of one embodiment of a system for the separation, ordering, and focusing of cells and beads within microchannels prior to droplet generation.
  • FIGS. 2A-D are schematic drawings showing bead focusing through different sized bead channels.
  • FIG. 2A shows beads flowing through a square channel.
  • FIG. 2B shows beads flowing through a rectangular channel having a cross-sectional dimension or flow rate that allows two beads to flow adjacent one another.
  • FIG. 2C shows beads flowing through a rectangular channel having a cross-sectional dimension or flow rate that focuses the beads so that the beads flow in a single file line within the bead channel due to presence of bead-present and bead-absent co-flows.
  • FIG. 2D is a top schematic view of an inertial focusing bead channel having a dual-inlet co-flow configuration.
  • FIG. 3 is a perspective view of an alternate embodiment of a system using curving channels for the separation, ordering, and focusing of cells and beads within microchannels.
  • FIGS. 4A-B are schematic drawings of embodiments of flow channels configured to provide an inertial ordering process.
  • FIG. 4A is a schematic drawing of the inertial ordering processing with an asymmetrical curving channel.
  • FIG. 4B is a schematic drawing showing the use of an expansion/contraction region within the flow channels to tune the spacing between ordered beads inside the channel.
  • FIGS. 5A-F show different embodiments of microchannel configurations for the ordering and focusing of cells and beads within microchannels.
  • FIG. 6 illustrates a microchannel configuration that allows high efficiency formation of single-cell/single-bead droplets.
  • FIG. 7 illustrates a microchannel configuration that allows high efficiency formation of single-cell/single-bead droplets using a dual-inlet co-flow system for cells.
  • FIG. 8 illustrates the use of an embodiment of the system for single cell sequencing.
  • FIG. 9 is an image of a device according to embodiments which shows the focusing of 30 ⁇ m diameter beads to the four focusing positions in a square channel within a length of 1.2-3 cm from the bead fluid inlet.
  • FIG. 10 is an image of a device according to embodiments that shows focusing and ordering of 40 ⁇ m diameter polystyrene beads in a rectangular straight microchannel prior to droplet formation.
  • FIG. 11 is an image of a device according to embodiments that shows focusing and ordering of 30 to 40 ⁇ m PMMA beads in a rectangular straight microchannel prior to droplet formation.
  • FIGS. 12A-12B show the focusing and ordering of 30 to 40 ⁇ m sepharose gel beads in a straight rectangular microchannel prior to droplet formation.
  • FIG. 12A shows the image taken from the instrument.
  • FIG. 12B depicts the same image as FIG. 12A , except that the contrast level has been adjusted to allow for easier visualization of the sepharose gel beads.
  • FIGS. 13A-13B show the focusing and ordering of 30 to 40 ⁇ m sepharose gel beads in a spiral rectangular microchannel prior to droplet formation.
  • FIG. 13A shows the image taken from the instrument.
  • FIG. 13B depicts the same image as FIG. 13A , except the contrast level has been adjusted to allow for easier visualization of the sepharose gel beads.
  • FIGS. 14A-14B depict two embodiments of systems comprising spiral channels.
  • FIG. 14A shows a system with two adjacent spiral channels and one channel comprising a sinusoidal curve.
  • FIG. 14B shows a system with two spiral channels on opposite ends of the system, surrounding two concentric channels comprising sinusoidal regions.
  • FIGS. 15A-15B depict the configuration of a microfluidic system with respect to the width of the channels after the convergence of two inlet channels.
  • FIG. 15A shows two cell channels feeding into a bead channel (width b) and resulting in a single channel of width m. Two oil inlet channels then converge, yielding a single channel with width d.
  • FIG. 15B shows a variation of the configuration shown in FIG. 15A in which channel widths m and d are increased relative to channel width b.
  • FIG. 16 depicts an embodiment of a microfluidic system in which intra-channel structures or constrictions that can de-clump a pool of clumped beads to yield ordered beads.
  • Embodiments relate to the fields of microfluidics and includes devices and methods for encapsulation of particles, such as beads, nucleic acid fragments, and cells into droplets.
  • Various embodiments described below use laminar flow of a fluid, such as an oil, through microfluidic channels to result in the continuous and accurate self-ordering of particles suspended within the fluid.
  • embodiments include microfluidic devices having a variety of specific channel geometries that can be configured to advantage of the self-ordering liquid flows to create continuous streams of ordered particles constrained in three spatial dimensions. Particles order laterally within the y-z plane (or cross-sectional plane) of a fluidic channel and can also order longitudinally along the direction of fluid flow (i.e., the x direction). An additional dimension of rotational ordering can occur for asymmetrically shaped particles.
  • a microchannel device is designed to mix a single cell with a single bead in one droplet.
  • Each bead applied to the microchannel device bears one or more nucleotide fragments, and each nucleotide fragment comprises a unique DNA tag.
  • the DNA tag may be a barcode or other DNA sequence having the same nucleotide sequence on all fragments bound to a single bead.
  • the DNA tag may alternatively be an index sequence which has a different nucleotide sequence for each fragment on a single bead.
  • the tag may also include a capture region that can be used to capture the tag by hybridization to other DNA sequences.
  • the capture region may comprise a poly-T tail in some embodiments.
  • each bead is uniquely tagged in comparison to all other beads being used in the device.
  • lysis buffer for example, the lysis buffer is present in the droplet when encapsulation occurs, or is added to the droplet after encapsulation
  • the cell is lysed, and each polyadenylated mRNA in the cell becomes bound to the poly-T tail of the capture region on the bead with which it is encapsulated.
  • cDNA strands are formed having the original mRNA sequences along with the unique tag from the bead that was encapsulated with the cell. This results in all of the mRNA from a single cell being labeled with a unique tag sequence from the bead.
  • This procedure allows later sequencing reactions to be performed in bulk, with cDNA samples from many cells being sequenced, but each having a unique tag so that they can be sorted from one another. The index is used to correct for amplification errors and avoid multiple-counting of a single molecule.
  • the mRNA expression of individual cells can be determined by sequencing the cDNA and determining which mRNA population was present in each cell, and the expression level of that mRNA.
  • the microchannel device is configured to separate, order, and focus streams of beads to focusing positions within a channel flow field that result in the creation of droplets each with a predetermined number of beads and cells.
  • the focusing can be based, at least in part, on inertial lift forces. In square channels, this can lead, for example, to four streams of focused particles spaced an equal distance apart from a center of each of the four square faces. For rectangular geometries, this four-fold symmetry can be reduced to a two-fold symmetry, with streams of particles spaced apart from each of two opposed faces of the channel.
  • a dual-inlet co-flow system serves to create a first focused, ordered stream of particles A and a second focused, ordered stream of particles B, where particles A and B are of different types.
  • the system serves to create a single focused bead stream and a single focused cell stream (e.g., the A particles are beads and the B particles are cells).
  • the two streams of particles are merged in the system to create a single stream comprising the particles A and B, such as beads and cells.
  • the merged stream of particles is then contacted with an oil or other immiscible fluid to create a droplet containing the two particle types.
  • a third fluid stream is introduced that serves to encapsulate the two types of particles.
  • the third fluid stream comprises a carrier fluid that is immiscible or partially immiscible with the first and second stream fluids and/or the combined first/second stream fluid.
  • Embodiments include microchannel devices that encapsulate a selected number of A and B particles in a droplet.
  • the device may be configured to encapsulate no more than one A particle and no more than one B particle in a single droplet, or up to one A particle and one B particle in a single droplet, or one A particle and one B particle in a single droplet.
  • Configurations of fewer, or more, A particles and fewer, or more, B particles in a single droplet are also contemplated, including but not limited to two A particles and one B particle, or one A particle and two B particles.
  • Embodiments also relate to microchannel devices that place a selected number of beads and cells into a droplet.
  • the device may be configured to encapsulate no more than one bead and no more than one cell in a single droplet, or up to one bead and one cell in a single droplet, or one bead and one cell in a single droplet. Configurations of fewer or more beads and fewer or more cells in a single droplet are also contemplated, including but not limited to two beads and one cell, or one bead and two cells.
  • the device may be configured to encapsulate one bead and one cell within a single droplet.
  • the capture efficiency of the cells can be improved to the same order of magnitude.
  • embodiments that employ focusing, such as inertial focusing as described below, for both beads and cells may overcome both Poisson distributions, one for beads and one for cells, in double-Poisson statistics, thus achieving more than 100 ⁇ improvement in throughput.
  • Embodiments may be operated continuously and at high volumetric flow rates with cascading outputs yet still produce droplets having the desired numbers of beads and cells per droplet.
  • Systems and methods may relate to inertial microfluidic technology for high-throughput and precise microscale control of cell and particle motion. These systems and methods may be suitable for applications in any type of nucleic acid sequence analysis, including long-read DNA sequencing, paired-end sequencing, and single cell sequencing.
  • the generation of droplets each with, for example, one bead and one cell enable the continuous analysis and sequencing of single cells.
  • the microfluidic system 100 generally includes three inlets: a bead inlet 102 that connects to a bead channel 104 , a cell inlet 106 that connects to two cell channels 108 , 110 on the two sides of the bead channel 104 , and an oil inlet 112 that connects to two oil channels 114 , 116 which are the outermost channels of the system 100 and are next to the cell channels 108 , 110 and spaced laterally away from the bead channel 104 .
  • the microfluidic system 100 generally has one system outlet 118 .
  • the microfluidic system 100 can be provided on a microfabricated chip 120 with the various channels formed in the chip 120 .
  • the bead inlet 102 is configured for introducing beads 122 suspended in a bead fluid 124 into the microfluidic system 100 .
  • the beads 122 can be of any density made up of various materials.
  • the bead channel 104 formed in the chip 120 can have numerous configurations which will be described in detail below. In general, the bead channel 104 can have a specified geometry designed to separate, order, and focus the beads 122 to pre-determined lateral positions in the channel when entering a droplet generation junction 126 . These lateral locations correspond to similar flow velocities in the velocity profile of the bead fluid 124 such that, once focused, the beads 122 move at more or less similar speeds and maintain their spacing and generally do not cross each other.
  • the bead channel 104 may be straight as shown.
  • the bead channels used in the microfluidic systems can have various geometries and cross-sections as detailed below for focusing beads of a predetermined size suspended within a fluid. For example, bead channel 104 may
  • the size of the bead channel 104 is related to the size of the beads 122 intended to be used within the channel. For example, as mentioned below, 80-125 ⁇ m diameter bead channels were successfully used for separating, ordering, and focusing beads that were 30-50 ⁇ m in size. The closer the size of the channel was to the bead size, the faster and more efficient the separating, focusing, and ordering was found to be.
  • the cell channels 108 , 110 have long serpentine regions 109 , 111 respectively.
  • the oil channels 114 , 116 also have long serpentine regions 115 , 117 respectively. These long serpentine regions act as fluidic resistances to ensure equal distribution of fluid flow on both branches of the corresponding channel.
  • the bead channel 104 may have a curved region to decrease the focusing length required and to decrease the device foot-print. In some embodiments, one or both of the cell channels 108 , 110 may have a curved region to decrease the focusing length required and to decrease the device foot-print.
  • the curved regions may be symmetrically curved. In some embodiments, the curved regions may be asymmetrically curved, such as S-shaped, sinusoidal, or sigmoidal shaped.
  • the bead channel 104 may have an expansion/contraction region which enables the adjustment of the spacing between beads inside the channel. In some embodiments, one or both of the cell channels 108 , 110 may have an expansion/contraction region which enables the adjustment of the spacing between cells inside the channel.
  • the cell inlet 106 is configured for introducing cells 130 suspended in a cell fluid 132 into the microfluidic system 100 through the cell channels 108 , 109 .
  • the oil inlet 112 is configured for introducing droplet generation oil 134 to the droplet generation junction 126 through the oil channels 114 , 116 .
  • the two lateral flows of droplet generation oil 134 pull droplets from the stream of aqueous bead fluid 124 with the same frequency, or multiple of, that beads reach the droplet generation junction 126 .
  • the two lateral flows of droplet generation oil 134 pull droplets from the stream of aqueous cell fluid 132 with the same frequency, or multiple of, that cells reach the droplet generation junction 126 .
  • droplets exit the microfluidic device 100 in an orderly fashion with every droplet generally encapsulating one bead and/or one cell in the particular design illustrated in FIG. 1 .
  • the chip 120 can also include a straight section of channel at an output region for analysis of focused particles, collection of focused particles, and/or for recombining stream lines.
  • the bead channels used in the microfluidic systems can have various geometries and cross-sections for focusing beads of a predetermined size suspended within a fluid.
  • FIG. 2A - FIG. 2D show dynamic bead self-assembly in a finite-Reynolds number flow. All views are from above bead channel 204 such that differences in position along the channel cross-sectional width can be visualized.
  • Inertial migration focuses beads to transverse equilibrium positions. Beads migrate to defined equilibrium positions, for example, four in a square channel ( FIG. 2A ) and two in a rectangular channel ( FIG. 2B ).
  • a straight channel is provided having a square cross-section with an aspect ratio of substantially 1 to 1.
  • Beads of a predetermined size flowing within such a channel geometry will be separated, ordered, and focused into four focusing positions shown in the cross sectional view of FIG. 2A . These four focusing positions correspond to four equilibrium points, or potential minimums, at a distance from each face of the four channel walls.
  • a channel with aspect ratio here defined as the ratio of the longer side to the shorter side of the cross-section
  • the number of focusing positions can be successfully decreased from four to two.
  • the aspect ratio may be greater than about 1.2, although other aspect ratios of about 1.1, 1.3, 1.4, 1.5 or more are also contemplated.
  • a straight bead channel is provided having a rectangular cross-section with an aspect ratio of substantially 2 to 1. Beads of a predetermined size flowing within such channel geometry can be separated, ordered, and focused into two focusing positions corresponding to two equilibrium points or potential minimums along the wider side walls across the width of the channel.
  • the wider side of the channel can be parallel to either y or z direction leading to bead focusing on either top-and-bottom or left-and-right of the channel respectively.
  • the beads interact with each other and order themselves longitudinally as well.
  • Bead may be both laterally focused (in an y-z plane) and/or longitudinally ordered (in an x direction). The inter-bead interactions create a repulsive force between bead pairs that spaces them out along the channel, leading to creation of bead lattices.
  • a dual-inlet co-flow system 200 with a rectangular inertial focusing bead channel 204 with a wider side in the z-direction (leading to left-and-right focusing in the cross-section view) as shown in FIG. 2D can be used.
  • the focusing position can be further decreased to 1. This leads to more efficient ordering of the beads along the channel.
  • Co-flowing with bead-free fluid was found to confine beads on one side of a microchannel resulting in a single line of beads with regular and repeatable spacing.
  • a similar concept can be used for focusing of cells and other types of particles as well.
  • FIG. 2D is a schematic view of a dynamic self-assembling bead system including a two-inlet bead channel. Randomly distributed beads are self-assembled through inertial lift forces and hydrodynamic bead-bead interactions.
  • the dual-inlet co-flow system 200 reduces the degrees of freedom by focusing beads 222 into a single substantially axially aligned stream at one focusing position 228 ( FIG. 2D ). Unprocessed, the beads 222 in a bead fluid 224 are flowed through the “lower” bead inlet 202 . A bead-free fluid 225 is flowed through the “upper” bead inlet 203 .
  • the bead-free fluid 225 flows through in the “upper” half of bead channel 204 and the beads 222 are confined to the “lower” half of the bead channel 204 so that the beads 222 align at the one focusing position 228 .
  • This equilibrium state becomes a one-dimensional system where inter-bead spacing is a dependent variable dependent on, for example, flow, fluid and geometric parameters.
  • focusing refers to a reduction in the area of a cross-section of a channel through which a flux of beads passes.
  • beads can be localized within an area having a width of, at most, 1.01, 1.05, 2, 3, 4, or 5 times the width of the beads. Localization can occur at any location within the channel, including within an unobstructed portion of the channel. For example, localization can occur in a portion of the channel having less than 50%, 40%, 30%, 20%, 10%, 5%, 2%, 1%, or 0.1% reduction in cross-sectional area. In certain embodiments, localization can occur in a channel having a substantially constant cross-sectional area.
  • This mechanism of dynamic self-assembly of microscale beads in a finite-Reynolds-number channel flow provides parameters for controlling bead stream self-assembling and allow expanded bead control in microchannel systems. Such control is useful for applications such as low-pass spatial filtering on bead spacing.
  • Microfluidic devices can be designed and operated to control bead-bead and bead-wall interactions in order to manipulate inter-bead spacing and reduce defocusing.
  • ⁇ is the density of the fluid
  • U m is the maximum flow speed
  • H is the hydraulic diameter
  • ⁇ is the dynamic viscosity of the fluid.
  • Many inertial effects have been observed in microfluidic devices at such Reynolds numbers.
  • One example is inertial migration of beads in square and rectangular channels. Randomly distributed beads migrate across streamlines due to inertial lift forces, which is a combination of shear gradient lift that pushes beads towards walls and wall effect lift that pushes beads towards the center of a channel.
  • These inertial lift forces focus beads to four ( FIG. 2A ) or two ( FIG. 2B ) dynamic “transverse equilibrium points” that are determined by channel symmetry.
  • the system is a non-equilibrium system that constantly dissipates energy and the transverse equilibrium point is where the inertial lift forces become zero in the cross-section of the channel.
  • focusing position refers to these transverse equilibrium points.
  • the beads While traveling down the channel, the beads are laterally (y direction and z direction) focused by inertial lift forces and simultaneously longitudinally (x direction) self-assembled by bead-bead interactions. Focusing occurs along the width and height of a microchannel, and assembling occurs along the longitudinal axis of the microchannel.
  • the system of beads In the final organized state, the system of beads has two degrees of freedom: inter-bead spacing and focusing position. Inter-bead spacing is determined by fluid and flow parameters (U m , ⁇ , ⁇ ) and geometric parameters (bead diameter (a), channel width (w), and height (h)). These parameters make up a bead Reynolds number
  • inter-bead spacing When beads are aligned at one focusing position, there is a default inter-bead spacing for any given set of flow and geometric parameters. However, with more than one focusing position, different cross-channel spacing and single-stream spacing appear. Inter-bead spacing does not show a strong dependence on channel aspect ratio. The selection of a focusing position for beads is intrinsically a random event, which makes diverse patterns in the organized structure. However, additional degrees of freedom in the form of additional focusing positions make the resulting bead stream more complicated.
  • FIG. 3 illustrates another embodiment of a microfluidic system 300 with a curved bead channel 304 .
  • the microfluidic system 300 generally includes three inlets: a bead inlet 302 that connects to the bead channel 304 , a cell inlet 306 that connects to two cell channels 308 , 310 on the two sides of the bead channel 304 , and an oil inlet 312 that connects to two oil channels 314 , 316 which are the outermost channels of the system 300 and are next to the cell channels 308 , 310 away from the bead channel 304 .
  • the microfluidic system 300 generally has one system outlet 318 .
  • the microfluidic system 300 can be provided on a microfabricated chip 320 with the various channels formed in the chip 320 .
  • the bead inlet 304 is configured for introducing beads 322 suspended in a bead fluid 324 into the microfluidic system 300 .
  • the beads 322 can be of any density made up of various materials.
  • the bead channel 304 formed in the chip 320 can have numerous configurations which will be described in detail below.
  • the bead channel 304 can have a specified geometry designed to separate, order, and focus the beads 322 to pre-determined lateral positions in the channel when entering the droplet generation junction 326 . These lateral locations correspond to similar flow velocities in the velocity profile of the bead fluid 324 such that, once focused, the beads 322 move at similar speeds and maintain their spacing and generally do not cross each other.
  • the bead channel 304 may be curved as shown. Curving channels can be used to decrease the focusing length required and to decrease the device foot-print.
  • the cell channels 308 , 310 have serpentine regions 309 , 311 respectively.
  • the oil channels 314 , 316 also have serpentine regions 315 , 317 respectively.
  • symmetrically, asymmetrically, or continuously curved channels can be provided such as S-shaped, sinusoidal, or sigmoidal shaped bead channels having a rectangular cross-section. Beads of a predetermined size flowing within such channel geometry will be generally focused into two focusing positions corresponding to one or two equilibrium points or potential minimums at a distance from left and right side faces of the channel.
  • An aspect ratio of a sigmoidal channel can be substantially 1 to 1 and/or can vary along a length thereof. For example, the aspect ratio of a sigmoidal channel can vary over the length of the channel between 1 to 1 and 2 to 1 depending on the configuration chosen.
  • the bead channel 404 has a curving region 438 .
  • asymmetrically curved channels can have various shapes and configurations as needed for a particular application, in one embodiment an asymmetric bead channel can generally have the shape of a wave having large and small turns, where a radius of curvature can change after each inflection point of the wave. Each large and small turn can have a specified width of the channel associated with the turn.
  • Asymmetrically curved channels enable both longitudinal ordering and lateral focusing.
  • one-half of a wavelength of the channel wave can have a large curve while one-half of a wavelength of the channel wave can have a small curve. These curves can then be repeated as many times as needed, varying after each inflection point, to provide a specified length of channel with an asymmetric curve.
  • the asymmetrically curved bead channel 404 can also have a rectangular cross-section with an aspect ratio that can vary as needed over the channel length depending on the nature of the asymmetry in the curves. In one embodiment, the aspect ratio can vary between 1 to 1 and 2 to 1. In this case, a single focused stream of beads is created corresponding to a single equilibrium point or potential minimum within the channel 404 .
  • asymmetric curving bead channels for example an expanding spiral shaped channel can be provided, having a rectangular cross-section with an aspect ratio of substantially 2 to 1. This aspect ratio may vary.
  • beads are focused into a single stream line a distance away from an inner wall of the channel corresponding to a single equilibrium point or potential minimum within the channel. Examples of systems that include spiral channels are shown in FIGS. 14A and 14B .
  • the spiral portion of the channel has an outer diameter of 2 to 10 mm, or about 3 to 7 mm, or about 5 mm, or about 10 mm.
  • a single chip may have bead channels with different channel geometries.
  • FIG. 4B shows another embodiment with the bead channel 405 having varying diameter.
  • An expansion/contraction region 440 after a bead focusing region (upstream, not shown) enables the adjustment of the spacing between beads inside the channel.
  • the expansion/contraction region 440 after the bead focusing region may be used to increase the spacing between beads 422 A-D inside the channel ( FIG. 4B ).
  • an expansion/contraction region after the bead focusing region may be used to decrease the spacing between beads inside the channel.
  • channel dimensions can decrease over the length of the chip to facilitate filtering of the sample, or for other reasons specific to an application, such as creating fluidic resistance.
  • Channel dimensions can be larger at the input area or at the output area to enable forks or valve systems to be positioned within the channels, or to enable multiple stream lines to be separated and directed to different locations for analysis or collection.
  • cross-sections of various channels can also be changed as needed within a single chip to manipulate stream lines of focused beads for particular applications.
  • any combination of channel geometries, channel cross-sections, and channel dimensions can be included on a single chip as needed to sort, separate, order, and focus beads of a predetermined size or beads of multiple predetermined sizes. For instance, different channel geometries and flow rates can be used for the streams of bead fluid and cell fluid to ensure desired focusing and ordering in each stream prior to droplet generation.
  • a straight section of bead channel is formed in the chip near the inlet for transporting and dividing flow lines as the bead is introduced into the microfluidic system.
  • the straight section of each channel can transition to any number of symmetric and/or asymmetric curving channels for focusing beads of a predetermined size as needed.
  • the bead channel 304 has a curved region 305 to decrease the focusing length required and to decrease the device foot-print.
  • one or both of the cell channels 308 , 310 may have a curved region to decrease the focusing length required and to decrease the device foot-print as shown in FIG. 4A .
  • the curved regions may be symmetrically curved. In some embodiments, the curved regions may be asymmetrically curved, such as S-shaped, sinusoidal, or sigmoidal shaped.
  • symmetrically, asymmetrically, or continuously curved channels can be provided such as S-shaped, sinusoidal, or sigmoidal shaped cell channel having a rectangular cross-section. Cells of a predetermined size flowing within such channel geometry will be generally focused into two focusing positions corresponding to one or two equilibrium points or potential minimums at a distance from left and right side faces of the channel.
  • An aspect ratio of a sigmoidal channel can be substantially 1 to 1 and/or can vary along a length thereof. For example, the aspect ratio of a sigmoidal channel can vary over the length of the channel between 1 to 1 and 2 to 1 depending on the configuration chosen.
  • cell channels 310 , 308 each may have a curving region. While asymmetrically curved channels can have various shapes and configurations as needed for a particular application, in one embodiment an asymmetric cell channel can generally have the shape of a wave having large and small turns, where a radius of curvature can change after each inflection point of the wave. Each large and small turn can have a specified width of the channel associated with the turn. Asymmetrically curved channels enable both longitudinal ordering and lateral focusing.
  • one-half of a wavelength of the channel wave can have a large curve while one-half of a wavelength of the channel wave can have a small curve. These curves can then be repeated as many times as needed, varying after each inflection point, to provide a specified length of channel with an asymmetric curve.
  • the asymmetrically curved cell channel can also have a rectangular cross-section with an aspect ratio that can vary as needed over the channel length depending on the nature of the asymmetry in the curves. In one embodiment, the aspect ratio can vary between 1 to 1 and 2 to 1. In this case, a single focused stream of cells is created corresponding to a single equilibrium point or potential minimum within the channel.
  • asymmetric curving cell channels in particular an expanding spiral shaped channel can be provided, having a rectangular cross-section with an aspect ratio of substantially 2 to 1. This aspect ratio may vary.
  • cells are focused into a single stream line a distance away from an inner wall of the channel corresponding to a single equilibrium point or potential minimum within the channel. Examples of systems that include spiral channels are shown in FIGS. 14A and 14B .
  • the spiral portion of the channel has an outer diameter of 2 to 10 mm, or about 3 to 7 mm, or about 5 mm, or about 10 mm.
  • Microfluidic devices as described herein may be manufactured using any suitable technology known to one of ordinary skill in the art.
  • such devices and systems may be manufactured using master molds combined with soft lithography techniques.
  • microfluidic devices or certain components of the microfluidic devices can be manufactured using three-dimensional printing technologies.
  • the channels are rectangular in shape.
  • the rectangular-shaped channels may be formed into a variety of geometries described herein, such as straight and curved channels.
  • the channel height to width aspect ratio may be selected to optimize particle ordering.
  • the rectangular channel aspect ratio is 7:1, or 5:1, or 4:1, or 3:1, or 2:1.
  • channel height can be in the range of about 0.5 ⁇ m to about 200 ⁇ m.
  • a single chip may have cell channels with different channel geometries. Similar to the bead channel 405 in FIG. 4B having varying diameter, one or both of the cell channels 308 , 310 can have varying diameter.
  • An expansion/contraction region after a cell focusing region enables the adjustment of the spacing between cells inside the channel. For example, the expansion/contraction region after the cell focusing region may be used to increase the spacing between cells inside the channel ( FIG. 4B ). Alternatively, an expansion/contraction region after the cell focusing region may be used to decrease the spacing between cells inside the channel.
  • channel dimensions can decrease over the length of the chip to facilitate filtering of the sample, or for other reasons specific to an application, such as creating fluidic resistance.
  • Channel dimensions can be larger at the input area or at the output area to enable forks or valve systems to be positioned within the channels, or to enable multiple stream lines to be separated and directed to different locations for analysis or collection.
  • cross-sections of various channels can also be changed as needed within a single chip to manipulate stream lines of focused cells for particular applications.
  • any combination of channel geometries, channel cross-sections, and channel dimensions can be included on a single chip as needed to sort, separate, order, and focus cells of a predetermined size or cells of multiple predetermined sizes. For instance, different channel geometries and flow rates can be used for the streams of cell flow and cell fluid to ensure desired focusing and ordering in each stream prior to droplet generation.
  • a straight section of cell channel is formed in the chip near the inlet for transporting and dividing flow lines as the cell is introduced into the microfluidic system.
  • the straight section of each channel can transition to any number of symmetric and/or asymmetric curving channels for focusing cells of a predetermined size as needed.
  • the bead channel 304 may have an expansion/contraction region as shown in FIG. 4B which enables the adjustment of the spacing between beads inside the channel.
  • one or both of the cell channels 308 , 310 may have an expansion/contraction region which enables the adjustment of the spacing between beads inside the channel.
  • the cell inlet 306 is configured for introducing cells suspended in a cell fluid into the microfluidic system 300 .
  • the oil inlet 312 is configured for introducing droplet generation oil to the droplet generation junction 326 through oil channels 314 , 316 .
  • the two lateral flows of oil pull droplets from the stream of aqueous bead fluid 324 with the same frequency, or multiple of, that beads reach the droplet generation junction 326 .
  • the two lateral flows of oil pull droplets from the stream of aqueous cell fluid with the same frequency that cells reach the droplet generation junction 326 .
  • every droplet generally encapsulates a predetermined number of beads greater or equal to zero and a predetermined number of cells greater or equal to zero.
  • each droplet may have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, about 15, 20, 30, 40, 50, 60, 70, 80, 90, or 100 beads, and each droplet may have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, about 15, 20, 30, 40, 50, 60, 70, 80, 90, or 100 cells.
  • the statistical distribution of beads is less than optimal, e.g., less than 1 bead per droplet.
  • the statistical distribution of cells is less than optimal, e.g., less than 1 cell per droplet.
  • the chip 320 can also include a straight section of channel at an output region for analysis of focused particles, collection of focused particles, and/or for recombining stream lines.
  • any number of curves or straight sections can be included as needed within the chip for one or more of the bead channel 304 , cell channels 308 , 310 . Additional curved sections of channels can serve as “off-ramps” for focused bead streams to facilitate additional separation based on labels or tags associated with the beads. Channel forks or splits can be included at any positions within the channels to further facilitate manipulation of focused beads as needed for various applications.
  • aspects ratios of all channels described above and herein, including straight, symmetric, and asymmetric, can vary as needed from one application to another and/or as many times as needed over the course of a channel.
  • aspect ratios are shown as 1 to 1 and 1 to 2; however, a person of ordinary skill will recognize that a variety of aspect ratios could be employed.
  • the choice of width to height as the standard for determining the aspect ratio is somewhat arbitrary in that the aspect ratio can be taken to be the ratio of a first cross-sectional channel dimension to a second cross-sectional channel dimension, and for rectangular channels this would be either width to height or height to width.
  • the aspect ratio of the channel of FIG. 2B could be expressed as either 2 to 1 or 1 to 2.
  • Channel cross-sections can include, but are not limited to, circular, triangular, diamond, and hemispherical. Beads of a predetermined size can be focused in each of these exemplary cross-sections, and the focusing positions will be dependent on the geometry of the channel. For example, in a straight channel having a circular or hemispherical cross-section, an annulus or arc of focused beads can be formed within the channel. In a straight channel having a triangular or diamond cross-section, beads can be focused into streams corresponding to focusing positions at a distance from the flat faces of each wall in the geometry. As symmetric and asymmetric curving channels are included having each of the exemplary cross-sections noted above, focusing streams and focusing positions can generally correspond to that described above with respect to the channels having a rectangular cross-section.
  • inertial forces can include, but are not limited to, inertial lift down shear gradients and away from channel walls, Dean drag (viscous drag), pressure drag from Dean flow, and centrifugal forces acting on individual beads.
  • microfluidic bead channels can be formed in the chip in any number of ways.
  • a single bead channel is formed on the chip for focusing beads therein.
  • a plurality of bead channels can be formed in the chip in various configurations of networks for focusing beads. For example, 2, 4, 6, 8, 10, 12, and more channels can be formed in the chip.
  • Any number of layers can also be included within a microfabricated chip of the system, each layer having multiple bead channels formed therein.
  • microfluidic cell channels can be formed in the chip in any number of ways.
  • a single cell channel is formed on the chip for focusing beads therein.
  • a plurality of cell channels can be formed in the chip in various configurations of networks for focusing cells. For example, 2, 4, 6, 8, 10, 12, and more channels can be formed in the chip.
  • Any number of layers can also be included within a microfabricated chip of the system, each layer having multiple cell channels formed therein.
  • L f is the length required for bead focusing; ⁇ is the dynamic viscosity of the fluid; h is the size of the bead channel (or the hydraulic dimeter, or another critical dimension of the channel); ⁇ is the density of the fluid; U m is the maximum flow speed; ⁇ is the bead diameter; and f L is a factor, which is in the range of 0.02-0.05 for most cases.
  • Other factors that affect bead channel length include wall features, wall geometries, wall coatings, fluid types, types and concentrations of components in fluids other than beads, bead shapes, bead coating, and bead weight.
  • Table 1 shows examples of the lengths for bead separation, focusing, and ordering for 30-50 ⁇ m beads that are relevant to high throughput single cell experiments in an aqueous liquid with properties close to that of water.
  • the number of focusing positions depends on the inlet configuration (single inlet vs. dual inlet) and their relative flow rates.
  • the first number in that column corresponds to the standard case of having a single inlet.
  • a microfluidic system 500 A has one straight bead channel that is 125 ⁇ 125 ⁇ m in dimension.
  • the microfluidic system 500 A includes three inlets: a bead inlet 502 A that connects to a single bead channel 504 A, a cell inlet 506 A that connects to two cell channels 508 A, 510 A on the two sides of the bead channel 504 A, and an oil inlet 512 A that connects to two oil channels 514 A, 516 A which are the outermost channels of the system 500 A and are next to the cell channels 508 A, 510 A away from the bead channel 504 A.
  • the microfluidic system 500 A generally has one system outlet 518 A.
  • the bead inlet 502 A is configured for introducing beads suspended in a bead fluid into the microfluidic system 500 A.
  • the beads can be of any density made up of various materials.
  • the bead inlet 502 A may have bead filters 542 A that prevent undesired particles such as dust from entering and clogging the bead channel 504 A.
  • the spacing between the bead filters 542 A should be at least 2-3 times the size of the beads so all beads can flow through the bead filters 542 A without the risk of clogging the bead channel 504 A.
  • the spacing between the bead filters 542 A may be 300 ⁇ m, e.g., ⁇ 5-10 times the bead size.
  • the cell inlet 506 A is configured for introducing cells suspended in a cell fluid into the microfluidic system 500 A.
  • the cell inlet 506 A may have cell filters 544 A that prevent undesired particles such as dust from entering and clogging the cell channels 508 A, 510 A.
  • the spacing between the cell filters 544 A should be at least 2-3 times the size of the cells so all beads can flow through the cell filters 544 A without the risk of clogging the cell channels 508 A, 510 A.
  • the spacing between the cell filters 544 A may be 300 ⁇ m, e.g., ⁇ 5-10 times the cell size.
  • the oil inlet 512 A is configured for introducing droplet generation oil to the droplet generation junction 526 A through oil channels 514 A, 516 A.
  • the oil inlet 512 A may have cell filters 546 A that prevent undesired particles such as dust from entering and clogging the oil channels 514 A, 516 A.
  • the spacing between the oil filters 546 A depends on the characteristics of the oil used, such as viscosity, so the oil can flow through the oil filters 546 A without the risk of clogging the oil channels 514 A, 516 A.
  • the spacing between the oil filters 546 A may be 300 ⁇ m.
  • the design and input concentrations can be adjusted such that not all droplets have a single bead or cell if needed.
  • each droplet may have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, about 15, 20, 30, 40, 50, 60, 70, 80, 90, or 100 beads, and each droplet may have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, about 15, 20, 30, 40, 50, 60, 70, 80, 90, or 100 cells.
  • the statistical distribution of beads is less than optimal, e.g., less than 1 bead per droplet.
  • the statistical distribution of cells is less than optimal, i.e. less than 1 cell per droplet.
  • a microfluidic system 500 B has one straight bead channel that is 125 ⁇ 125 ⁇ m in dimension.
  • the microfluidic system 500 B includes four inlets: two bead inlets 502 B, 503 B that connect to a bead channel 504 B (both inlets have bead solution, but only one of them contains beads while the other one is bead-free), a cell inlet 506 B that connects to two cell channels 508 B, 510 B on the two sides of the bead channel 504 B, and an oil inlet 512 B that connects to two oil channels 514 B, 516 B which are the outermost channels of the system 500 B and are next to the cell channels 508 B, 510 B away from the bead channel 504 B.
  • the dual-inlet co-flow design results in efficient bead ordering.
  • the two cell channels 508 B, 510 B in this dual-inlet co-flow system are longer in length when compared to the two cell channels 508 A, 510 A shown in FIG. 5 A even though both microfluidic systems have the same bead channel dimension of 125 ⁇ 125 ⁇ m.
  • the two oil channels 514 B, 516 B in this dual-inlet co-flow system are longer in length when compared to the two oil channels 514 A, 516 A shown in FIG. 5A even though both microfluidic systems have the same bead channel dimension of 125 ⁇ 125 ⁇ m.
  • the microfluidic system 500 B generally has one system outlet 518 B.
  • the bead inlet 502 B is configured for introducing beads suspended in a bead fluid into the microfluidic system 500 B.
  • the beads can be of any density made up of various materials.
  • the bead inlet 503 B is configured for introducing fluid not containing any beads.
  • the bead inlets 502 B, 503 B may have bead filters 542 B, 543 B respectively that prevent undesired particles such as dust from entering and clogging the bead channels 504 B.
  • the spacing between the bead filters 542 B, 543 B should be at least 2-3 times the size of the beads so all beads can flow through the bead filters 542 B, 543 B without the risk of clogging the bead channel 504 B.
  • the spacing between the bead filters 542 B, 543 B may be 300 ⁇ m, e.g., ⁇ 5-10 times the bead size.
  • the cell inlet 506 B is configured for introducing cells suspended in a cell fluid into the microfluidic system 500 B.
  • the cell inlet 506 B may have cell filters 544 B that prevent undesired particles such as dust from entering and clogging the cell channels 508 B, 510 B.
  • the spacing between the cell filters 544 B should be at least 2-3 times the size of the cells so all beads can flow through the cell filters 544 B without the risk of clogging the cell channels 508 B, 510 B.
  • the spacing between the cell filters 544 B may be 300 ⁇ m e.g., ⁇ 5-10 times the cell size.
  • the oil inlet 512 B is configured for introducing droplet generation oil to the droplet generation junction 526 B through oil channels 514 B, 516 B.
  • the oil inlet 512 B may have cell filters 546 B that prevent undesired particles such as dust from entering and clogging the oil channels 514 B, 516 B.
  • the spacing between the oil filters 546 B depends on the characteristics of the oil used, such as viscosity, so the oil can flow through the oil filters 546 B without the risk of clogging the oil channels 514 B, 516 B.
  • the spacing between the oil filters 546 B may be 300 ⁇ m.
  • droplets were found to exit the microfluidic device 500 in an orderly fashion with every droplet generally encapsulating one bead and/or one cell in general.
  • the separation of 30 and 50 ⁇ m beads required 1.4-3.6 cm and 0.5-1.3 cm respectively.
  • the separation of 30 and 50 ⁇ m beads required 1.2-3 cm and 0.4-1.1 cm respectively.
  • the length of the channel can be adjusted for any different bead solution to accommodate the change in focusing length due to changes in fluid density or viscosity.
  • a microfluidic system 500 C has one straight bead channel that is 125 ⁇ 100 ⁇ m in dimension.
  • the microfluidic system 500 C includes three inlets: a bead inlet 502 C that connects to a bead channel 504 C, a cell inlet 506 C that connects to two cell channels 508 C, 510 C on the two sides of the bead channel 504 C, and an oil inlet 512 C that connects to two oil channels 514 C, 516 C which are the outermost channels of the system 500 C and are next to the cell channels 508 C, 510 C away from the bead channel 504 C.
  • the microfluidic system 500 C generally has one system outlet 518 C.
  • the bead inlet 504 C is configured for introducing beads suspended in a bead fluid into the microfluidic system 500 C.
  • the beads can be of any density made up of various materials.
  • the bead inlet 502 C may have bead filters 542 C that prevent undesired particles such as dust from entering and clogging the bead channel 504 C.
  • the spacing between the bead filters 542 C should be at least 2-3 times the size of the beads so all beads can flow through the bead filters 542 C without the risk of clogging the bead channel 504 C.
  • the spacing between the bead filters 542 C may be 300 ⁇ m, e.g., ⁇ 5-10 times the bead size.
  • the cell inlet 506 C is configured for introducing cells suspended in a cell fluid into the microfluidic system 500 C.
  • the cell inlet 506 C may have cell filters 544 C that prevent undesired particles such as dust from entering and clogging the cell channels 508 C, 510 C.
  • the spacing between the cell filters 544 C should be at least 2-3 times the size of the cells so all beads can flow through the cell filters 544 C without the risk of clogging the cell channels 508 C, 510 C.
  • the spacing between the cell filters 544 C may be 300 ⁇ m e.g., ⁇ 5-10 times the cell size.
  • the oil inlet 512 C is configured for introducing droplet generation oil to the droplet generation junction 526 C through oil channels 514 C, 516 C.
  • the oil inlet 512 C may have cell filters 546 C that prevent undesired particles such as dust from entering and clogging the oil channels 514 C, 516 C.
  • the spacing between the oil filters 546 C depends on the characteristics of the oil used, such as viscosity, so the oil can flow through the oil filters 546 C without the risk of clogging the oil channels 514 C, 516 C.
  • the spacing between the oil filters 546 C may be 300 ⁇ m.
  • a microfluidic system 500 D has one straight bead channel that is 125 ⁇ 100 ⁇ m in dimension.
  • the microfluidic system 500 D includes four inlets: two bead inlets 502 D, 503 D that connect to a bead channel 504 D, a cell inlet 506 D that connects to two cell channels 508 D, 510 D on the two sides of the bead channel 504 D, and an oil inlet 512 D that connects to two oil channels 514 D, 516 D which are the outermost channels of the system 500 D and are next to the cell channels 508 D, 510 D away from the bead channel 504 D.
  • the dual-inlet co-flow design results in efficient bead ordering.
  • the two cell channels 508 D, 510 D in this dual-inlet co-flow system are longer in length when compared to the two cell channels 508 C, 510 C shown in FIG. 5A even though both microfluidic systems have the same bead channel dimension of 125 ⁇ 100
  • the two oil channels 514 D, 516 D in this dual-inlet co-flow system are longer in length when compared to the two oil channels 514 C, 516 C shown in FIG. 5C even though both microfluidic systems have the same bead channel dimension of 125 ⁇ 100 ⁇ m.
  • the microfluidic system 500 D generally has one system outlet 518 D.
  • the bead inlet 502 D is configured for introducing beads suspended in a bead fluid into the microfluidic system 500 D.
  • the beads can be of any density made up of various materials.
  • the bead inlet 503 D is configured for introducing fluid not containing any beads.
  • the bead inlets 502 D, 503 D may have bead filters 542 D, 543 D respectively that prevent undesired particles such as dust from entering and clogging the bead channels 504 D.
  • the spacing between the bead filters 542 D, 543 D should be at least 2-3 times the size of the beads so all beads can flow through the bead filters 542 D, 543 D without the risk of clogging the bead channel 504 D.
  • the spacing between the bead filters 542 D, 543 D may be 300 ⁇ m, e.g., ⁇ 5-10 times the bead size.
  • the cell inlet 506 D is configured for introducing cells suspended in a cell fluid into the microfluidic system 500 D.
  • the cell inlet 506 D may have cell filters 544 D that prevent undesired particles such as dust from entering and clogging the cell channels 508 D, 510 D.
  • the spacing between the cell filters 544 D should be at least 2-3 times the size of the cells so all beads can flow through the cell filters 544 D without the risk of clogging the cell channels 508 D, 510 D.
  • the spacing between the cell filters 544 D may be 300 ⁇ m, e.g., ⁇ 5-10 times the cell size.
  • the oil inlet 512 D is configured for introducing droplet generation oil to the droplet generation junction 526 D through oil channels 514 D, 516 D.
  • the oil inlet 512 D may have cell filters 546 D that prevent undesired particles such as dust from entering and clogging the oil channels 514 D, 516 D.
  • the spacing between the oil filters 546 D depends on the characteristics of the oil used, such as viscosity, so the oil can flow through the oil filters 546 D without the risk of clogging the oil channels 514 D, 516 D.
  • the spacing between the oil filters 546 A may be 300 ⁇ m.
  • a microfluidic system 500 E has one straight bead channel that is 125 ⁇ 100 ⁇ m in dimension.
  • the microfluidic system 500 E includes three inlets: a bead inlet 502 E that connects to a bead channel 504 E, a cell inlet 506 E that connects to two cell channels 508 E, 510 E on the two sides of the bead channel 504 E, and an oil inlet 512 E that connects to two oil channels 514 E, 516 E which are the outermost channels of the system 500 E and are next to the cell channels 508 E, 510 E away from the bead channel 504 E.
  • the microfluidic system 500 E generally has one system outlet 518 E.
  • the bead inlet 504 E is configured for introducing beads suspended in a bead fluid into the microfluidic system 500 E.
  • the beads can be of any density made up of various materials.
  • the bead inlet 502 E may have bead filters 542 E that prevent undesired particles such as dust from entering and clogging the bead channel 504 E.
  • the spacing between the bead filters 542 E should be at least 2-3 times the size of the beads so all beads can flow through the bead filters 542 E without the risk of clogging the bead channel 504 E.
  • the spacing between the bead filters 542 E may be 300 ⁇ m, e.g., ⁇ 5-10 times the bead size.
  • the cell inlet 506 E is configured for introducing cells suspended in a cell fluid into the microfluidic system 500 E.
  • the cell inlet 506 E may have cell filters 544 E that prevent undesired particles such as dust from entering and clogging the cell channels 508 E, 510 E.
  • the spacing between the cell filters 544 E should be at least 2-3 times the size of the cells so all beads can flow through the cell filters 544 E without the risk of clogging the cell channels 508 E, 510 E.
  • the spacing between the cell filters 544 E may be 300 ⁇ m, e.g., ⁇ 5-10 times the cell size.
  • the oil inlet 512 E is configured for introducing droplet generation oil to the droplet generation junction 526 E through oil channels 514 E, 516 E.
  • the oil inlet 512 E may have cell filters 546 E that prevent undesired particles such as dust from entering and clogging the oil channels 514 E, 516 E.
  • the spacing between the oil filters 546 E depends on the characteristics of the oil used, such as viscosity, so the oil can flow through the oil filters 546 E without the risk of clogging the oil channels 514 F, 516 F.
  • the spacing between the oil filters 546 E may be 300 ⁇ m.
  • a microfluidic system 500 F has one straight bead channel that is 125 ⁇ 100 ⁇ m in dimension.
  • the microfluidic system 500 F includes four inlets: two bead inlets 502 F, 503 F that connect to a bead channel 504 F, a cell inlet 506 F that connects to two cell channels 508 F, 510 F on the two sides of the bead channel 504 F, and an oil inlet 512 F that connects to two oil channels 514 F, 516 F which are the outermost channels of the system 500 F and are next to the cell channels 508 F, 510 F away from the bead channel 504 F.
  • the dual-inlet co-flow design results in efficient bead ordering.
  • the two cell channels 508 F, 510 F in this dual-inlet co-flow system are longer in length when compared to the two cell channels 508 E, 510 E shown in FIG. 5E even though both microfluidic systems have the same bead channel dimension of 125 ⁇ 80
  • the two oil channels 514 F, 516 F in this dual-inlet co-flow system are longer in length when compared to the two oil channels 514 E, 516 E shown in FIG. 5E even though both microfluidic systems have the same bead channel dimension of 125 ⁇ 80
  • the microfluidic system 500 F generally has one system outlet 518 F.
  • the bead inlet 502 F is configured for introducing beads suspended in a bead fluid into the microfluidic system 500 F.
  • the beads can be of any density made up of various materials.
  • the bead inlet 503 F is configured for introducing fluid not containing any beads.
  • the bead inlets 502 F, 503 F may have bead filters 542 F, 543 F respectively that prevent undesired particles such as dust from entering and clogging the bead channels 504 F.
  • the spacing between the bead filters 542 F, 543 F should be at least 2-3 times the size of the beads so all beads can flow through the bead filters 542 F, 543 F without the risk of clogging the bead channel 504 F.
  • the spacing between the bead filters 542 F, 543 F may be 300 ⁇ m, e.g., ⁇ 5-10 times the bead size.
  • the cell inlet 506 F is configured for introducing cells suspended in a cell fluid into the microfluidic system 500 F.
  • the cell inlet 506 F may have cell filters 544 F that prevent undesired particles such as dust from entering and clogging the cell channels 508 F, 510 F.
  • the spacing between the cell filters 544 F should be at least 2-3 times the size of the cells so all beads can flow through the cell filters 544 F without the risk of clogging the cell channels 508 F, 510 F.
  • the spacing between the cell filters 544 F may be 300 ⁇ m, e.g., ⁇ 5-10 times the cell size.
  • the oil inlet 512 F is configured for introducing droplet generation oil to the droplet generation junction 526 F through oil channels 514 F, 516 F.
  • the oil inlet 512 F may have cell filters 546 F that prevent undesired particles such as dust from entering and clogging the oil channels 514 F, 516 F.
  • the spacing between the oil filters 546 F depends on the characteristics of the oil used, such as viscosity, so the oil can flow through the oil filters 546 F without the risk of clogging the oil channels 514 F, 516 F.
  • the spacing between the oil filters 546 F may be 300 ⁇ m.
  • L f is the length required for cell focusing; ⁇ is the dynamic viscosity of the fluid; h is the size of the cell channel (or the hydraulic dimeter, or another critical dimension of the channel); ⁇ is the density of the fluid; U m is the maximum flow speed; a is the cell diameter; and f L is a factor in the range of 0.02-0.05 for most cases.
  • Other factors that affect cell channel length include wall features, wall geometries, wall coatings, fluid types, types and concentrations of components in fluids other than cells, cell shape, cell surface coating, and cell state.
  • a bead to volume ratio can optionally be manipulated or adjusted for conservation of mass within the channels.
  • separating, ordering, and focusing of beads is, in part, dependent on inter-bead spacing within channels as well as the ratio of bead size to hydrodynamic size of the channel.
  • Various channel geometries described herein may require a predetermined bead to volume ratio of the bead to be focused in order to achieve a required inter-bead spacing and thereby maintain ordering and focusing of that bead.
  • the bead to volume ratio of a bead suspended within a fluid can be calculated and adjusted as needed to achieve focusing within certain channel geometries.
  • a maximum bead to volume ratio for a specific bead size and channel geometry can be determined using the formula, assuming a rectangular channel and non-overlapping focusing positions:
  • beads can be diluted or concentrated to attain a predetermined ratio before and/or during introduction of the bead into the system. Additionally, certain exemplary systems may require the ratio to be adjusted after the bead is introduced into the channels.
  • Bead to volume ratios of a bead within the channels described herein can have any value sufficient to enable ordering and focusing of beads.
  • the bead to volume ratio can be less than about 50%.
  • bead to volume ratios can be less than about 40%, 30%, 20%, 10%, 8%, or 6%. More particularly, in some embodiments, bead to volume ratios can be in a range of about 0.001% to about 5%, and can be in a range of about 0.01% to about 4%. Alternatively, the ratio can be in the range of about 0.1% to about 3%. Alternatively, the ratio can be in the range of about 0.5% to about 2%.
  • the bead to volume ratio of additional or extraneous beads within the bead, apart from the bead to be focused need not necessarily be considered or adjusted.
  • any number of beads may not require any adjustment to the bead to volume ratio of the bead to be focused before, during, and/or after introduction into the system.
  • a bead can be diluted or concentrated in batches before introduction into the system such that the bead ultimately introduced into the system has the required ratio before being introduced through the inlet.
  • the system can include two or more inlets for introducing the bead simultaneously with a diluent or concentrate to effect dilution or concentration. In this way, the bead to volume ratio can be adjusted within the system, whether adjustment occurs within a chamber before the bead and diluent or concentrate enter the channels or whether adjustment occurs through mixing of the bead and the diluent or concentrate within the channels.
  • the diluent or concentrate can be introduced into a center portion, fork, or branch of a channel as may be required by various applications after the unadjusted bead has traveled within the channel for some distance.
  • a person skilled in the art will appreciate the variations possible for adjusting the bead to volume ratio of a bead within the embodiments described herein.
  • a cell to volume ratio can optionally be manipulated or adjusted for conservation of mass within the channels.
  • separating, ordering, and focusing of cells is, in part, dependent on inter-cell spacing within channels as well as the ratio of cell size to hydrodynamic size of the channel.
  • Various channel geometries described herein may require a predetermined cell to volume ratio of the cell to be focused in order to achieve a required inter-cell spacing and thereby maintain ordering and focusing of that cell.
  • the cell to volume ratio of a cell suspended within a fluid can be calculated and adjusted as needed to achieve focusing within certain channel geometries.
  • a maximum cell to volume ratio for a specific cell size and channel geometry can be determined using the formula, assuming a rectangular channel and non-overlapping focusing positions:
  • N is the number of focusing positions in a channel
  • a is the focused cell diameter
  • h is the channel height
  • w is the channel width.
  • Cell to volume ratios of a cell within the channels described herein can have any value sufficient to enable ordering and focusing of cells.
  • the cell to volume ratio can be less than about 50%.
  • cell to volume ratios can be less than about 40%, 30%, 20%, 10%, 8%, or 6%.
  • cell to volume ratios can be in a range of about 0.001% to about 5%, and can be in a range of about 0.01% to about 4%.
  • the ratio can be in the range of about 0.1% to about 3%.
  • the ratio can be in the range of about 0.5% to about 2%.
  • the cell to volume ratio of additional or extraneous cells within the cell, apart from the cell to be focused need not necessarily be considered or adjusted.
  • any number of cells may not require any adjustment to the cell to volume ratio of the cell to be focused before, during, and/or after introduction into the system.
  • a cell can be diluted or concentrated in batches before introduction into the system such that the cell ultimately introduced into the system has the required ratio before being introduced through the inlet.
  • the system can include two or more inlets for introducing the cell simultaneously with a diluent or concentrate to effect dilution or concentration. In this way, the cell to volume ratio can be adjusted within the system, whether adjustment occurs within a chamber before the cell and diluent or concentrate enter the channels or whether adjustment occurs through mixing of the cell and the diluent or concentrate within the channels.
  • the diluent or concentrate can be introduced into a center portion, fork, or branch of a channel as may be required by various applications after the unadjusted cell has traveled within the channel for some distance.
  • a person skilled in the art will appreciate the variations possible for adjusting the cell to volume ratio of a cell within the embodiments described herein.
  • inertial focusing of beads may be combined with droplet generation to produce extremely high concentrations of droplets and a bead ⁇ approaching 1, but avoid having droplets with multiple bead occupancy.
  • ⁇ is the average of Poisson distribution, the probability of an event occurring, such as a droplet with one single bead.
  • the effect of Poisson distribution on single-cell analysis and sorting using droplet-based microfluidics has been described in Mazutis et al., Nature Protocols 8:870-91 (2013), which is hereby incorporated by reference.
  • This high concentration of droplets with single bead occupancy allows systems that require such droplets (such as high throughput single cell systems) to improve throughput, for example by 2-25 times, or 5-25 times, or 5-10 times, or 10-20 times, as compared to other encapsulation methods, with decreased error rate (e.g., decreased proportion of droplets with more than one bead).
  • inertial focusing of cells may be combined with droplet generation to produce extremely high concentrations of droplets and a cell ⁇ approaching 1, but avoid having droplets with multiple cell occupancy ⁇ for cells is the probability of a droplet to have only one single cell.
  • This high concentration of droplets with single cell occupancy allows systems that require such droplets (such as high throughput single cell systems) to improve throughput, for example by 2-25 times, or 5-25 times, or 5-10 times, by 10-20 times, as compared to other encapsulation methods, with decreased error rate (e.g., decreased proportion of droplets with more than one cell).
  • focusing such as inertial focusing
  • a and B particles such as beads and cells
  • This method creates a system with double-underdispersed-Poisson statistics and a further enhanced improvement in throughput (e.g., at least 5, 10, 25, 50, or 100X) over non-ordered systems.
  • Embodiments of the invention may be operated continuously and at high volumetric flow rates with cascading outputs. The invention also requires no interactions with mechanical filters or obstacles and requires very low maintenance.
  • particles such as beads, nucleic acid fragments, and cells may have statistical distribution other than Poisson, such as normal distribution, log-normal distribution, Pareto distribution, discrete uniform distribution, continuous uniform distribution, Bernoulli distribution, binomial distribution, negative binomial distribution, geometric distribution, hypergeometric distribution, beta-binomial distribution, categorical distribution, multinomial distribution, multivariate hypergeometric distribution, log-Poisson distribution, exponential distribution, Gamma distribution, Rayleigh distribution, Rice distribution, Chi-squared distribution, student's t distribution, F-distribution, Beta distribution, Dirichlet distribution, and Wishart distribution.
  • Poisson such as normal distribution, log-normal distribution, Pareto distribution, discrete uniform distribution, continuous uniform distribution, Bernoulli distribution, binomial distribution, negative binomial distribution, geometric distribution, hypergeometric distribution, beta-binomial distribution, categorical distribution, multinomial distribution, multivariate hypergeometric distribution, log-Poisson distribution, exponential distribution, Gamma distribution, Rayleigh distribution
  • the bead concentration can be adjusted to obtain a large ⁇ (still smaller than 1).
  • bead fluid is injected into the bead inlet connected to the bead channel at the pre-designated flow rate (for example, 60 ⁇ L/min).
  • cells are injected into the cell inlet connection to cell channels at the pre-designated flow rate (for example, 60 ⁇ L/min).
  • the droplet generation oil is injected into the oil inlet connected to the oil channels at the appropriate flow rate (for example, 150-250 ⁇ L/min).
  • the third stream (e.g., oil) flow rate may be the same or greater than the flow rates of the bead and cell fluids.
  • FIG. 6 illustrates another embodiment of a microfluidic system 600 .
  • a bead channel 604 may be curved or straight.
  • the microfluidic system 600 generally includes three inlets: a bead inlet that connects to a bead channel 604 , a cell inlet that connects to two cell channels 608 , 610 on the two sides of the bead channel 604 , and an oil inlet that connects to two oil channels 614 , 616 which are the outermost channels of the system 600 and are next to the cell channels 608 , 610 away from the bead channel 604 .
  • the microfluidic system 600 generally has one system outlet 618 .
  • the microfluidic system 600 can be provided on a microfabricated chip with the various channels formed in the chip.
  • a bead inlet is configured for introducing beads 622 suspended in a bead fluid 624 into the microfluidic system 600 .
  • the beads 622 can be of any density made up of various materials.
  • the bead channel 604 can have a specified geometry designed to separate, order, and focus the beads 622 to pre-determined lateral positions in the channel when entering the droplet generation junction 626 . These lateral locations correspond to similar flow velocities in the velocity profile of the bead fluid 624 such that, once focused, the beads 622 move at similar speeds and maintain their spacing and do not cross each other.
  • the bead channels used in the microfluidic systems can have various geometries and cross-sections for focusing beads of a predetermined size suspended within a fluid.
  • bead channel 604 may have a square cross-section.
  • the cell inlet is configured for introducing cells 630 suspended in a cell fluid into the microfluidic system 600 .
  • the oil inlet is configured for introducing droplet generation oil 632 to the droplet generation junction 626 through oil channels 614 , 616 .
  • the two lateral flows of oil pull droplets from the stream of aqueous bead fluid 624 with the same frequency, or multiple of, that beads reach the droplet generation junction 626 .
  • the two lateral flows of oil pull droplets from the stream of aqueous cell fluid 634 with the same frequency, or multiple of, that cells reach the droplet generation junction 626 .
  • the beads 622 are ordered prior to entering the droplet generation junction 626 .
  • the cells 630 are ordered prior to entering the droplet generation junction 626 .
  • droplets 634 are formed with one bead and one cell each.
  • This embodiment generates more single-particle droplets (e.g., one cell and one bead) and fewer empty or multiple-particle droplets (e.g., two beads and one cell) than would have been possible from stochastic (Poisson) loading.
  • FIG. 7 illustrates another embodiment of a microfluidic system 700 .
  • a bead channel 704 may be curved or straight.
  • the microfluidic system 700 generally includes three inlets: a bead inlet that connects to a bead channel 704 , two cell inlets that connect to two cell channels 708 , 710 on the two sides of the bead channel 704 , and an oil inlet that connects to two oil channels 714 , 716 which are the outermost channels of the system 700 and are next to the cell channels 708 , 710 away from the bead channel 704 .
  • the microfluidic system 700 generally has one system outlet 718 .
  • the microfluidic system 700 can be provided on a microfabricated chip with the various channels formed in the chip.
  • a bead inlet is configured for introducing beads 722 suspended in a bead fluid 724 into the microfluidic system 700 .
  • the beads 722 can be of any density made up of various materials.
  • the bead channel 704 can have a specified geometry designed to separate, order, and focus the beads 722 to pre-determined lateral positions in the channel when entering the droplet generation junction 726 . These lateral locations correspond to similar flow velocities in the velocity profile of the bead fluid 724 such that, once focused, the beads 722 move at similar speeds and maintain their spacing and do not cross each other.
  • the bead channels used in the microfluidic systems can have various geometries and cross-sections for focusing beads of a predetermined size suspended within a fluid.
  • bead channel 704 may have a square cross-section.
  • One cell inlet is configured for introducing cells 730 suspended in a cell fluid into the microfluidic system 700 through cell channel 708 .
  • Another cell inlet is configured for introducing a cell-free fluid into the microfluidic system 700 .
  • the oil inlet is configured for introducing droplet generation oil 732 to the droplet generation junction 726 through oil channels 714 , 716 .
  • the two lateral flows of oil pull droplets from the stream of aqueous bead fluid 724 with the same frequency, or multiple of, that beads reach the droplet generation junction 726 .
  • the two lateral flows of oil pull droplets from the stream of aqueous cell fluid 734 with the same frequency, or multiple of, that cells reach the droplet generation junction 726 .
  • the beads 722 are ordered prior to entering the droplet generation junction 726 .
  • the cells 730 are ordered prior to entering the droplet generation junction 726 .
  • droplets 734 are formed with one bead and one cell each. This embodiment generates more single-particle droplets (e.g., one bead and one cell) and fewer empty or multiple-particle (e.g., two beads and one cell) droplets than would have been possible from stochastic (Poisson) loading.
  • a design parameter to consider is the width of the fluidic channel after the bead channel and the cell channel meet, and before the droplet formation junction, e.g., width m in FIG. 15A .
  • the bead fluid in this region gets squeezed and diluted by the cell fluid, which increases the distance between the beads and lowers the occupancy rate of beads in droplets. Therefore, the width m can be adjusted to compensate for this phenomenon, and in turn increase the bead's encapsulation efficiency in the droplets.
  • the width of the channel m was increased proportionally to the ratio of the flow rate of bead and cell fluids.
  • the flow rate for the bead fluid was 30 ⁇ L/min and the flow rate for cell fluid was 30 ⁇ L/min.
  • the width of the fluidic channel post droplet generation junction e.g., width d, was also wider by ⁇ 200% as shown in FIG. 15B .
  • the ratio of the channel width m/b can vary from 1 to as high as 3 depending on the flow rates of the bead and cell fluids.
  • non-clumped beads are fed into the bead fluidic channel. Feeding non-clumped beads can be achieved by introducing structures or constrictions at the bead inlet or at the beginning of the bead channel to disrupt the clumps of beads. For example, in FIG. 16 , intra-channel constrictions are shown as wavy structures. In this example, the channel width at the constriction is greater than the bead diameter, but less the twice the bead diameter.
  • inertial forcing and droplet generation to beads, cells, and nucleic acids is suitable for applications in any type of DNA sequence analysis, including long-read DNA sequencing and single cell sequencing.
  • the generation of droplets each with one bead and one cell enable the continuous high throughput analysis and sequencing of single cells.
  • a microchannel device is designed to generate droplets each containing a single cell and a single bead.
  • the microchannel device is configured to separate, order, and focus streams of barcoded beads to one or more focusing positions within a channel flow field.
  • the microchannel device is configured to separate, order, and focus streams of cells to one or more focusing positions within a channel flow field.
  • the microchannel device receives an oil as another input.
  • Step 4 by combining the ordered barcoded bead, the ordered cells, and an oil, the microchannel device generates droplets with a-double-underdispersed-Poisson statistics, where each droplet contains one bead and one cell.
  • the design of the microfluidic device, concentrations of beads, cells, other components of the bead fluid and cell fluid, the type of oil, and the flow rates of the bead fluid, cell fluid, and oil are designed so the microfluidic device generates droplets with any desired numbers of beads and cells per droplet.
  • the statistical distribution of beads is less than optimal, e.g., less than 1 bead per droplet.
  • the statistical distribution of cells is less than optimal, e.g., less than 1 cell per droplet.
  • This ratio is beneficial for single cell sequencing applications, as a high proportion of populated droplets contain one cell and one bead, and low proportions of droplets contain one cell and no bead, one bead and no cell, or are empty. Thus, a high proportion of cells will be sequenced.
  • Each barcoded bead shown in FIG. 8 includes numerous nucleotide fragments, and each nucleotide fragment includes a unique DNA tag (e.g., a barcode, the same on all fragments on a single bead), an index (e.g., a unique molecular identifier, different for each fragment on a single bead), along with a capture region comprising a poly-T tail.
  • a unique DNA tag e.g., a barcode, the same on all fragments on a single bead
  • an index e.g., a unique molecular identifier, different for each fragment on a single bead
  • This construct makes each bead uniquely tagged in comparison to all other beads being used in the device.
  • each of the four droplets shown in FIG. 8 contains one barcoded bead and one cell.
  • Each of the four barcoded beads is uniquely tagged in comparison to the other three barcoded beads.
  • the poly-T region may be at an
  • the bead fluid contains a lysis buffer.
  • Step 5 when a cell and a bead become encapsulated into a droplet and the droplet contains lysis buffer, the cell is lysed.
  • each polyadenylated mRNA in each cell becomes bound to the poly-T tail of a nucleotide fragment on the bead, e.g., hybridization between the nucleotide fragment on the bead and the mRNA. Because of the index region, each mRNA from a cell is uniquely tagged in comparison to other mRNA sequences from the cell. And because of the unique DNA tag, each mRNA from a cell is uniquely tagged in comparison to other mRNAs from other cells.
  • the emulsion of droplets is broken, releasing beads with hybridized nucleotide fragments and mRNA into solution.
  • Resolution of an emulsion may be accomplished by any suitable means, such as by chemical, physical, or electrolytic means.
  • the means may be chosen to be compatible with the particles in the system, or may be chosen to degrade one or both particle types to allow for subsequent analysis, such as sequencing.
  • the hybridized nucleotide fragments and mRNAs are subject to reverse transcription using a reverse transcriptase to generate cDNAs.
  • each cDNA strand formed has an original mRNA sequence along with the unique DNA tag of the bead that was encapsulated with the cell and the unique index from the nucleotide fragment on the bead.
  • the amplified cDNAs are subject to library preparation, such as Nextera library preparation.
  • the nucleotides in the library are subject to sequencing, such as paired-end sequencing. Because each mRNA from a cell is uniquely tagged in comparison to other mRNAs from the same cell and mRNAs from other cells, sequencing reactions of the library can be performed in bulk, with cDNA samples from many cells being sequenced, but each uniquely tagged so that they can be sorted from one another. Each library sequence has a unique DNA tag or barcode, an index, and a capture region comprising a poly-T region. The index can be used to correct for amplification errors and avoid multiple-counting of a single molecule. After sequencing, the mRNA population and expression level of individual cells can be determined.
  • the beads include nucleotide fragments.
  • the nucleotide fragments include a barcode region, an index region, and a capture region comprising a poly-T tail.
  • the barcode region of each nucleotide fragment is at least about six nucleotides in length, or is about six to eight nucleotides in length, or is about six nucleotides in length.
  • the index region of each nucleotide fragment is at least about four nucleotides in length, or is about four to ten nucleotides in length, or is about four nucleotides in length.
  • the capture region includes poly-T nucleotides and is at least about ten nucleotides in length, or is about ten to twenty nucleotides in length, or is about ten nucleotides in length.
  • an analysis region is provided in proximity to the output channel to monitor, sort, count, image, or otherwise analyze the localized and focused streams of particles.
  • a chip can be, or be part of, a particle enumerating system.
  • an analysis region, in which the particles have been focused and ordered could be subject to interrogation by a detector for the purpose of counting the particles.
  • detectors are discussed below, as are systems for tagging particles for detection, and these elements can also be used for enumeration.
  • Particles can be made of or derived from various materials, and can have different properties such as a density higher equal or lower than water.
  • Particles suspended within a sample can have any size which allows them to be ordered and focused within the microfluidic channels described herein.
  • particles can have a hydrodynamic size that is in the range of about 100 microns to about 0.01 microns.
  • particles can have a hydrodynamic size that is in the range of about 20 microns to about 0.1 microns.
  • particles can have a hydrodynamic size that is in the range of about 10 microns to about 1 micron. It will be appreciated that particle size is only limited by channel geometry, and particles both larger and smaller than the above-described ranges can be ordered and focused within predetermined channel geometries having laminar flow conditions.
  • Particles can be cells or nucleic acids.
  • Cells and nucleic acids can be derived from any biological system, such as animal, bacteria, virus, fungus, or plant, and any source such as water, food, soil, or air.
  • a solid sample serves as a source of particles of interest. If a solid sample is obtained, such as a tissue sample or soil sample, the solid sample can be liquefied or solubilized prior to subsequent introduction into the system. If a gas sample is obtained, it may be liquefied or solubilized as well.
  • the sample may consist of bubbles of oil or other kinds of liquids as the particles suspended in an aqueous solution.
  • a sample can be derived from an animal such as a mammal.
  • the mammal can be a human.
  • Exemplary fluid samples containing particles derived from an animal can include, but are not limited to, whole blood, partitioned blood, blood components, sweat, tears, ear flow, sputum, bone marrow suspension, lymph, urine, brain fluid, cerebrospinal fluid, saliva, mucous, vaginal fluid, semen, ascites, milk, secretions of the respiratory, intestinal and genitourinary tracts, and amniotic fluid.
  • exemplary samples can include fluids that are introduced into a human body and then removed again for analysis, including all forms of lavage such as antiseptic, bronchoalveolar, gastric, peritoneal, cervical, arthroscopic, ductal, nasal, and ear lavages.
  • exemplary particles can include any particles contained within the fluids noted herein and can be both rigid and deformable.
  • particles can include, but are not limited to, cells, alive or fixed, such as adult red blood cells, fetal red blood cells, trophoblasts, fetal fibroblasts, white blood cells, epithelial cells, tumor cells, cancer cells, hematopoeitic stem cells, bacterial cells, mammalian cells, protists, plant cells, neutrophils, T lymphocytes, CD 4+ cells, B lymphocytes, monocytes, eosinophils, natural killers, basophils, dendritic cells, circulating endothelial, antigen specific T-cells, and fungal cells.
  • particles may include or be derived from viruses, organelles, or liposomes.
  • Particles can be non-cellular or non-biological items, or synthetic items, including such as beads, droplets, nanoparticles, or molecular complexes.
  • Different particle forms include but are not limited to solid beads, porous solid beads, hydrogel beads, double- or multi-emulsions, deformable or non-deformable beads, spherical or complex-shaped beads.
  • particles are beads, such as beads suitable for oligonucleotide (DNA or RNA) sequencing applications.
  • Beads may be synthetic polymer beads, such as beads of polystyrene, sepharose, agarose, polyacrylamide, chitosan, gelatin, and the like. Beads may also include magnetic beads. Beads may be of any diameter, such as 10 to 100 ⁇ m, or 10 to 20 ⁇ m, or 25 to 50 ⁇ m, or 30 ⁇ m, or 40 ⁇ m.
  • Particles may be suspended generally in any suspensions, liquids, and/or fluids with at least one type of particle, cell, droplet, or otherwise, disposed therein. Further, focusing can produce a flux of particles enriched in a first particle based on size.
  • one or more particles may stick, group, or clump together within a sample.
  • a grouping or clumping of particles can be considered to be “a particle” for the purposes of systems of the invention. More particularly, a grouping or clumping of particles may act and be treated as a single particle within channels of the invention described herein and can thus be sorted, ordered, separated, and focused in the same way as a single particle.
  • Particles from non-biological samples can include, for example, any number of various industrial and commercial samples suitable for particle separating, ordering, and focusing.
  • Exemplary industrial samples that contain particles that can be introduced into the system can include, but are not limited to, emulsions, two-phase chemical solutions (for example, solid-liquid, liquid-liquid, and gas-liquid chemical process samples), waste water, bioprocess particulates, and food industry samples such as juices, pulps, seeds, etc.
  • exemplary commercial samples that contain particles can include, but are not limited to, bacteria/parasite contaminated water, water with particulates such as coffee grounds and tea particles, cosmetics, lubricants, and pigments.
  • particles from a fluid sample obtained from an animal is directly applied to the system described herein, while in other embodiments, the sample is pretreated or processed prior to being delivered to a system of the invention.
  • a fluid drawn from an animal can be treated with one or more reagents prior to delivery to the system or it can be collected into a container that is preloaded with such a reagent.
  • Exemplary reagents can include, but are not limited to, a stabilizing reagent, a preservative, a fixant, a lysing reagent, a diluent, an anti-apoptotic reagent, an anti-coagulation reagent, an anti-thrombotic reagent, magnetic or electric property regulating reagents, a size altering reagent, a buffering reagent, an osmolality regulating reagent, a pH regulating reagent, and/or a cross-linking agent.
  • Suitable carrier fluids for the particle channels include aqueous solutions, water, buffer solutions, salt-based solutions, and mixtures thereof.
  • the cell carrier fluid is compatible with cells, such as an aqueous buffer, for example, phosphate-buffered saline.
  • the carrier fluid may be water or an aqueous solution optionally further comprising a chemical agent that provides the desired amount of expansion of the polymer bead.
  • the bead fluid comprises a cell lysis buffer.
  • Suitable oils include organic oils, such as olive oil or vegetable oil, or mineral oils, or silicone oils (such as derivatives of octamethyltrisiloxane), or perfluorinated oils (such as Fluorinert FC-40) or long chain hydrocarbon acids, such as oleic acid or dioctyl phthalate. Oils used in the third stream may also comprise stabilizers or surfactants.
  • Flow rates for the first and second particle streams may be the same or different. Flow rates may be in the range of about 10 to 75 ⁇ L/min, or about 10 to 50 ⁇ L/min, or about 10 to 35 ⁇ L/min, or about 40 to 75 ⁇ L/min, or about 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, or 75 ⁇ L/min. In some embodiments, the bead stream flow rate is higher than the cell stream flow rate.
  • the particle fluids may be introduced to the system with a particular particle concentration.
  • particles may be present in the particle fluids at a concentration of 100 to 3500 per ⁇ L, or 100 to 750 per ⁇ L, or 100 to 600 per ⁇ L, or 100 to 300 per ⁇ L, or 500 to 3000 per ⁇ L, or 1000 to 3000 per ⁇ L.
  • the particles are cells, which are present in the cell fluid at a concentration of 100 to 750 per ⁇ L, or 100 to 300 per ⁇ L.
  • particles are beads, which are present in the bead fluid at a concentration of 500 to 3000 per ⁇ L or 1000 to 3000 per ⁇ L.
  • particle A or bead occupancy rates for droplets produced by the systems described herein are at least 60, 70, 75, 80, 85, or 90%.
  • particle B or cell occupancy rates for droplets produced by the systems described herein are at least 10, 20, 30, 40, 50, 60, 70, 80, or 90%.
  • This example demonstrates that the focusing of 30 ⁇ m-diameter beads to the four focusing positions in a square channel was achieved within a length of 1.2-3 cm from the bead fluid inlet.
  • a set of microfluidic devices were designed that allowed for beads of different sizes to focus and order prior to entering the droplet generation junction.
  • a microfluidic device 900 with a 125 ⁇ 125 ⁇ m straight bead channel 904 was made that focused 30 ⁇ m diameter beads to their four focusing positions within a length of 1.2-3 cm from the inlet at the flow rate of 60 ⁇ L/min.
  • the beads 922 were ordered prior to entering the droplet generation junction 926 .
  • droplets 934 exited the microfluidic device 900 in an orderly fashion with every droplet encapsulating one bead in general.
  • the combination of bead channel dimension, flow rate generated more single-particle droplets and fewer empty or multiple-particle droplets than would have been possible from stochastic (Poisson) loading.
  • a microfluidic device was designed that allowed for beads of 40 ⁇ m or less (for example, 20 to 40 ⁇ m, or 30 ⁇ m) to focus and order prior to entering a droplet generation junction of the microfluidic device.
  • the microfluidic device had a bead channel with a cross-sectional dimension of 100 ⁇ 125 ⁇ m that focused the beads to their two focusing positions within a length of approximately 1.2-3 cm from the inlet.
  • the flow rate of the bead solution and the cell solution were set at 50 ⁇ L/min.
  • the flow rate of the oil was set at 300 ⁇ L/min, which resulted in approximately 4000 droplets per second being created. At these flow rates, clear bead ordering was observed and an ordered stream of beads was observed entering the droplet generation junction. Only about 0.6% of the resulting droplets had more than one bead within a droplet and a 90% reduction compared to Poisson statistics.
  • This example demonstrates that focusing of 40 ⁇ m-diameter polystyrene beads to the two focusing positions in a rectangular microchannel was achieved within a length of 1.2-3 cm from the bead fluid inlet. As shown in FIG. 10 , this configuration of device resulted in the vast majority of droplets containing one bead per droplet.
  • a microfluidic device was designed that allowed for beads of 40 ⁇ m or less to focus and order prior to entering a droplet generation junction of the microfluidic device.
  • the microfluidic device had a bead channel with a cross-sectional dimension of 75 ⁇ 125 ⁇ m that focused the beads to their two focusing positions within a length of approximately 1.2-3 cm from the inlet.
  • the flow rate of the bead solution was set at 50 ⁇ L/min and the cell solution were set at 10 ⁇ L/min.
  • the input bead concentration was set at 2000 beads/ ⁇ L.
  • the flow rate of the oil was set at 250 ⁇ L/min, which resulted in approximately ⁇ 2000 droplets per second being created. At these flow rates, clear bead ordering was observed and an ordered stream of beads was observed entering the droplet generation junction ( FIG. 10 ). Only about 2.7% of the resulting droplets had more than one bead within a droplet and a 83.3% reduction compared to Poisson statistics. Results for the distribution of beads inside droplets for other flow rate conditions are shown in Table 2.
  • a microfluidic device was designed that allowed for PMMA beads of 40 ⁇ m or less to focus and order prior to entering a droplet generation junction of the microfluidic device.
  • the microfluidic device had a bead channel with a cross-sectional dimension of 75 ⁇ 125 ⁇ m that focused the beads to their two focusing positions within a length of approximately 1.2-3 cm from the inlet.
  • the flow rate of the bead solution was set at 60 ⁇ L/min and the cell solution were set at 10 ⁇ L/min.
  • the input bead concentration was set at 1500 beads/ ⁇ L.
  • the flow rate of the oil was set at 260 ⁇ L/min, which resulted in approximately ⁇ 2000 droplets per second being created. At these flow rates, as shown in FIG. 11 , clear bead ordering was observed and an ordered stream of beads was observed entering the droplet generation junction. As shown in Table 3, only about 5.3% of the resulting droplets had more than one bead within a droplet and a 67.3% reduction compared to Poisson statistics.
  • a microfluidic device was designed that allowed for beads of 40 ⁇ m or less to focus and order prior to entering a droplet generation junction of the microfluidic device.
  • the microfluidic device had a bead channel with a cross-sectional dimension of 75 ⁇ 125 ⁇ m that focused the beads to their two focusing positions within a length of approximately 1.2-3 cm from the inlet.
  • the flow rate of the bead solution was set at 60 ⁇ L/min and the cell solution were set at 10 ⁇ L/min.
  • the input bead concentration was set at 2100 beads/ ⁇ L.
  • the flow rate of the oil was set at 270 ⁇ L/min, which resulted in approximately ⁇ 2500 droplets per second being created. As shown in FIGS. 12A and 12B , at these flow rates, clear bead ordering was observed and an ordered stream of beads was observed entering the droplet generation junction. As shown in Table 4, only about 6.1% of the resulting droplets had more than one bead within a droplet and a 62.3% reduction compared to Poisson statistics.
  • a spiral microfluidic device was designed that allowed for gel beads of 40 ⁇ m or less to focus and order prior to entering a droplet generation junction of the microfluidic device.
  • the microfluidic device had a bead channel with a cross-sectional dimension of 75 ⁇ 100 ⁇ m that focused the beads to their two focusing positions within a length of approximately 1.2-3 cm from the inlet.
  • the flow rate of the bead solution was set at 50 ⁇ L/min and the cell solution were set at 10 ⁇ L/min.
  • the input bead concentration was set at 1800 beads/ ⁇ L.
  • the flow rate of the oil was set at 180 ⁇ L/min, which resulted in approximately ⁇ 2000 droplets per second being created. At these flow rates, as shown in FIGS. 13A and 13B , clear bead ordering was observed and an ordered stream of beads was observed entering the droplet generation junction. As shown in Table 5, about 5.2% of the resulting droplets had more than one bead within a droplet and a 67.9% reduction compared to Poisson statistics.
  • a range includes each individual member.
  • a group having 1-3 articles refers to groups having 1, 2, or 3 articles.
  • a group having 1-5 articles refers to groups having 1, 2, 3, 4, or 5 articles, and so forth.

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