Vorurrm 86, Nutvtnnn l8
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`PHYSICAL REVIEW LETTERS
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`30 Apnn 2001
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`Dynamic Pattern Formation in a Vesicle-Generating Microfluidic Device
`
`TMd Thorsen,l Richard W. Roberts,l Frances H. Arnold,l and Stephen R. Quake2
`rDivision of Chemistry and Chemical Engincering, Califomia hrstitwe of Technology, Pasadena, Califomia 91125
`zDepartment of Applied Physics, California Institure of Technology, Pasadena, Cakfomia 91125
`(Received 9 January 2001)
`Spatiotemporal pattem forrnation occurs in a varieg of nonequilibrium physical and chemical systems.
`Here we show that a microfluidic device designed to produce leverse micelles can gen€rate cornplex, or-
`dered patterns as it is continuously operated far from thermodynamic equilibriurn Flow in a microfluidic
`system is uzually simple-viscous effects dominate and the low Reynolds nurnber leads to laminar flow.
`Self-assembly of the vesicles into patterns depends on channel geometry and rclative fluid pressures,
`enabling tbe production of motifs ranging from monodisperse droplcts to helices and ribbons.
`
`DOI: 10. I 103/PhysRevlett.86.4163
`
`PACS numbers: 82.40.Ck, 47.54.+r, 61.30.Pc1, 82.70.Uv
`
`Complex pattern fonnation is ubiquitous in nature. Ef-
`forts to understand these effects have led to irnportant in-
`sights into nonlinear dynamical systems and fundarnental
`nonequilibrium physics UJ. Fluid systerns have been fer-
`tile ground for pattern formation, with classic examples
`such as Rayleigh-Benard convection, Taylor-Couette flow
`in rotary systeffis, nonlinear suface waves, liquid crystals,
`and falling droplets [2]. Key ideas that have emerged from
`the study of pattern formation are the central roles of insta-
`bility and nonlinearity, as well as the influence of pertu-
`bations and boundary conditions on the morphology of the
`patterns. The elements of instability and nonlinearity are
`generally not present in microfluidic devices because the
`lengft scales are small enough that inertial effects in the
`fluid can be neglected. As most microfluidic devices oper-
`ate at low Reynolds number [3J, the Navier-Stokes equa-
`tion for fluid flow becomes linear and the flow is laminar.
`This result has many practical consequences for effonts to
`miniaturize biological a,ssays and produce lab on a chip
`system [4,5J. In this Letter, we show how the interaction
`between two imrniscible fluids can be used to introduce
`nonlinearity and instability in a microfluidic device. The
`resulting complex pattern formation is an unexpected and
`fascinating example of self-organization in a dynamic sys-
`tem far from equilibrium.
`Emulsions are formed by shearing one liquid into a sec-
`ond immiscible one, often in the presence of a surfactant,
`to create small droplets. The droplets can be remarkably
`stable, maintaining their shape and distribution for years
`[6J. Significant advances have been made in the past few
`years to produce ernulsions that are monodisperse, with
`standard deviations in droplet size less than 5% 17 -10J.
`Unlike the standard crossflow techniques for generating
`water-in-oil ernulsions, in which the discontinuous phase
`is forced through narrow pores [8,10] or capillaries [7,11]
`into an open continuous phase, we accornplish droplet for-
`mation at the junction of two microfluidic channels con-
`taining water and an oil surfactant mixture, respectively.
`The water partially obstructs flow at the junction, but is not
`broken off at the channel interface as in traditional cross-
`flow devices. Droplet forrnation is achieved by high shear
`
`forces generated at the leading edge of the water perpen-
`dicular to the oil flow generating picoliter-scale droplets.
`Although the system remains at low Reynolds number, the
`flow is nonlinear because of interactions on the boundary
`between the two fluids. The two irnportant effects are that
`the boundary is not static and that the motion of one fluid
`can entrain the other U2l. The resulting instability that
`drives droplet formation is a well-kno\ryn competition be-
`tween surface tension and shear forces [13J.
`The emergence of static crystalline sh:ucture in emul-
`sions has been documented previously [7,9]. In our experi-
`rnents, the droplets self-assemble into a variety of coherent,
`moving patterns as they are formed. We examine the con-
`trol parameters that lead to vesicle formation and organi-
`zation in an emulsion in a microfluidic device, illustrating
`the relationship between droplet pattern formation, pres-
`sure, and the geometric boundary conditions of the systern.
`The droplet size and frequency can be precisely conftolled
`by rnodifying the relative pressure of water and oil, en-
`abling the production of a wide range of vesicle shapes
`and patterns. Under conditions where the water pressure
`is lower than the oil pressurie, rnonodisperse separated re-
`verse micelles are forrned. As the relative water pressure
`is increased at fixed oil pressure, the droplets become or-
`dered into a single continuous stream. At water pressures
`that exceed the oil pressure, complex, organized patterns
`begin to emerge in the strearn, ranging from helical-like
`strrrctures to coherent ribbon motifs.
`The microfluidic devices utilized in our experiments are
`fabricated by pouring acrylated urethane (Ebeclyl 270,
`UCB Chemicals) on a, silicon wafer rnold containing
`positive -relief channels patterned in photonesist (S JRs 7 40,
`Shipley), which is then cured by exposure to UV light. The
`channels are fully encapsulated by curing the patterned
`urethane on a coverslip coated with a thin layer of urethane
`and bonding the two layers together through an additional
`UV light exposue. The rneasured channel dimensions
`are approximately 60 p,m wide x 9 pm high, tapering
`to 35 /lm X 6.5 pm in the region where the water and
`oil/surfactant mixture rneet at the crossflow intersection
`(Fig. 1). Input and post-crcssflow junction channel lengths
`
`0031-9007/01 /86(18)/4163(4)$15.00 @ 2001 The American Physical Society
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`4163
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`Volutvm 86, Nurvtsnn 18
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`PHYSICAL REVIEW LETTERS
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`30 Apnn 2001
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`produce only monodisperse reverse micelles with regular
`periodicity that associate with the walls of the wide chan-
`nel as they flow through the device (Fig. 2). The relative
`water/oil-surfactant pressures determine the size and spac-
`ing between the reverse micelles. The patterns in a rounded
`channel are more cornplex, ranging from periodic droplets
`to "ribbons," "pearl necklac€sr" and helical intermediate
`stnrctures. The self-organization of the reverse micelles
`depends on the differential presswe between the water and
`oil-surfactant phases, with higher relative water pressures
`driving the formation of increasingly cornplex droplet ar-
`rays (Fig. 3).
`The diverse pattem formation found in the rounded
`channels can be classified as follows. When the oil pres-
`sure greatly exceeds the water pressure, the water strearn is
`held in check by surface tension and only the oil flows. As
`the water pressure is increased past a critical point, single
`monodisperse separated droplets are formed at a frequency
`of 20-80 Hz. Srnall adjustments in the water pressure in
`this range change the radii of the formed droplets, with
`higher water pressures generating larger droplets, When
`the relative oil and water pressures are approxirnately
`balanced (P* - Po), droplets are formed in a pearl-
`necklacelike configuration [Figs. 3(D) and 3(E)J. They
`stack up against each other during the ransition frorn the
`30 1um channel to the wider 60 pmchannel due in part to
`the incteased drag of the necklace (which is larger than the
`separated rnonodisperse droplets). At water pressures that
`slightly exceed the oil pressure (Pn > P), the packing
`density of the droplets in the 60 p,m channel increases.
`The fust cornplex structure that emerges with increas-
`ing oil pressure is L transition from the pearl-necklace
`shape into a ngzag pattern of droplets [Fig. 3(G)1. At
`moderately higher water pressures (- ll%o higher than the
`relative oil pressure), shear occurs at both the crossflow
`junction and the transition from the narro\ry to wide
`microchannel. Polydisperse and bidisperse rnotifs appear
`as helices and patterned multilayer ribbon stnrctures. The
`patterns remain coherent as the arrayed droplets flow
`down the entire length of the channel from the breakpoint
`
`13.1112.4
`
`12"1 112.4
`
`11 ,1 112,4
`
`60pm I
`EIG. 2. Reverse micelles in square channels. Photomicro-
`graphs show the transition from the 30 pm wide channel to the
`60 pm wide channel. Respective pressurts for the water and
`oil/snrfactant (hexadecane/2% Span 80) are noted in the figure.
`
`FIG. 1. Microfabricated channel dimensions at the point of
`crossflow and photomicrograph of the disconfinuous water phase
`introduced into the continuous oil phase. Dashed rectangle in-
`dicates uea in photornicrograph.
`
`(60 pm wide X 9 plrn) ar€ ^- 1 and ^.4 cill, respectively.
`The fluids are introduced into the urethane microfluidic
`devices through pressunzd reservoirs containing water
`ard oil. The reservoirs are connected to the device through
`approximately 30 crn of 500 pm i.d. Tygon tubing. Pres-
`flue was applied to the reseryoirs with cornpressed air,
`and the device output channel was allowed to vent to the
`atmosphere. All reported pressures are relative to atrno-
`spheric pressure (psig). Various oils were tested in the
`device, including decane, tetradecane, ord hexadecane,
`combined with the srufactant Span 80 concentrations
`(u /u) of 0.5Vo, L}Vo, nod 2Eo. The device is equilibrated
`prior to crossflow by prirning the outflow channel with
`oil/surfactant to eliminate water interaction with the
`hydrophilic urethane. The production of reverse micelles
`is then initiated by modifying relative oil/surfactant and
`water pressures such that the water enters the crossflow
`junction pe{pendicular to the oil stream, shearing off into
`discrete droplets (Fig. 1).
`The shape of the channels influences the size distribution
`and rnorphology of the droplet patterning and can be rnodi-
`fied by heating the photoresist mold on the silicon wafer
`(80-1 10'C) to round the normally rectangular channels.
`The photoresist flows duing the heating process, creating
`localized maxima and minima at the perpendicular inter-
`section in the rnold where the water is sheared into ttre
`oil/surfactant phase and the transitions from the restricted
`to the wide channels. Channels that have not been rounded
`
`4rffi
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`2
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`

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`Vorunnn 86, Ntuenn 18
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`PHYSICAL REVIEW LETTERS
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`30 Apnn 2001
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`flows through the restriction at velocities up to ^-6.4 cmf s.
`Equation (1) gives a good approximation of the droplet
`sizes generated in the microfluidic device when the shear
`rate is estimated as 6 - 2u /yo, where )o is the channel ra-
`dius at the center of flow estimated by triangular approxi-
`rnation, nrd u is the velocity of the fluid through the gap.
`Predicted droplet sizes are within a factor of 2 of actual
`droplet size rnea.sured by video rnicroscopy for monodis-
`perse droplets generated at water and oil pressures ranging
`from 8.0-22.4 psi (Fig. 4).
`Pattern formation in the microchannels appears to be
`driven by the drag force of the droplets and contain fric-
`tion with the floor and ceiling of the device. As the droplets
`transition frorn the narrow crossflow junction to the 60 pm
`channel, they slow down significantly relative to the oil
`phase. At higher droplet frequencies, they begin to col-
`lide, stacking up into organized patterns at the transition
`between the 30-60 pmchannel. Complex structures form
`in rounded channels at high relative water pressures as
`colliding droplets are pushed frorn the center of ttre flow
`stream. The pattern formation results as a trade off be-
`tween the interfacial tension of the drcplets and the shape
`of the channels-droplets prefer to stay in the middle of
`the rounded channels in order not to pay an energy penalty
`for deforrnation in the crevices at the edge of the channels.
`Secondary shearing at the slowing junction also affects pat-
`tern formation-if the initial droplet is not coiltmensurate
`with the size selected by the junction, then size dispenity
`is introduced to the stream and asynunetric motifs appear
`[Figs. 3(J) and 3(L)].
`We have mapped a crude phase diagram that shows the
`pattern rnorphology is predominantly dependent on only
`the dimensionless differential input pressue. However,
`some of the most interesting patterns are found only at cer-
`tain absolute values of the input pressure (Fig. 3). Some-
`what surprisingly, these stuctures maintain a high degree
`
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`Water Pressure (psi)
`FIG. 4. Predicted vs actual drop size at different water and
`oil/surfactant pressur€s. The predicted sizes were calculated
`using Eq. (l). Open symbols, predicted size; solid symbols,
`experimental.
`
`4165
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`FlG. 3. Droplet patterns in rounded channels at different
`water and oil/surfactant pressures (noted in the flgure) and the
`conesponding phase diagrarn depicting the relationship between
`the oil and water pressure differences and droplet morphology.
`Solid lines are used to defrne approxirnate boundaries between
`the following droplet states (top to bottorn): solid water stream,
`ribbon layer, pearl necklace, single droplets, and solid oil stream.
`Symbol deflnition: solid water stream (solid circle); elongated
`droplets (open circle); triple droplet layer (solid triangle);
`double droplet layer (open triangle); jointed droplets (solid
`square); separated droplet (open square). Photomicrographs
`show 60 pm channel regions downstream of the point of
`ctossflow.
`
`to the outlet (*4 cm). At excessive water pressure, water
`coflows with the oil as separate streams, as one would
`expect for larninar flow of two conjoined strearns.
`The simplest rnodel for droplet formation is based on the
`shear forces generated between the water and oil surfactant
`at the crossflow junction. The predicted size of a droplet
`under external shear force is approxirnated by equating the
`Laplace pressure with the shear force [13J:
`rN+,
`(1)
`qe
`where r is the final droplet radius, c is the interfacial
`tension between the water/oil-stufactant, T is the viscosity
`of the continuous phase, and e is the shear rate.
`In the microfluidic device, a shear gradient is estab-
`lished as water tries to expand into the pressurized con-
`tinuous phase. The water strearn never completely blocks
`the flow of the continuous phase, and the oil surfactant
`
`3
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`

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`Voluun 86, Nuunnn 18
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`PHYSICAL REVIEW LETTERS
`
`30 Apnn 2001
`
`of coherence, despite the fact that they are formed dynami-
`cally when the system is far from therrnodynamic equilib-
`rium. Furtherrnore, this systern shows an unusual richness
`in the rariety of phases it can display, especially consid-
`ering that the boundary conditions (which also function as
`order parameters) are sirnply constant pressure applied to
`fluid inputs.
`Pattern formation also occurs in granular materials,
`which have some striking similarities with our system.
`In both cases, the fundamental particles are so large
`that therrnal fluctuations are negligible, Also, granular
`systems can display a,'lurtt*ing" phenomena, in which
`the particles get trapped in metastable configurations that
`are difficult to escape from. The pearl necklaces and
`zigzag patterns in our system shown an ability to get into
`jammed states of high stress. The joined droplets behave
`similar to a spring, continually trying to relieve the added
`strain within the system by trying to orient themselves
`in the center of the stream. This behavior is shown by
`rnultiparticle defects that propagate as waves through
`the pearl necklaces with a speed greater than the droplet
`stream [Fig. 3(A)J.
`In conclusion, we have shown how instability can de-
`velop as a competition between shear forces and surface
`tension in a microfluidic device. The system is technically
`at low Reynolds number, but the equations of rnotion are
`nonlinear because the boundary between the two fluids is
`not static. Although we have outlined sorne of the basic
`physics leading to the vesicle forrning instability and sub-
`sequent pattern formation, it is clear that rnore work needs
`to be done to achieve a complete understanding of the sys-
`tem. Since geometric effects play a significant role in the
`pattern fonmation, one should be able to take advantage
`of the powerful microfabrication technology both to ex-
`plore the consequences of this observation and to provide
`stringent tests of theoretical rnodels. This system rnay also
`
`find application as a compongnt in a rnicrofluidic screen-
`ing chip, since it has been shown that subnanoliter vesicles
`have significant potential as tools for screening of biologi-
`cal and synttretic compounds t14-161.
`We thank R. Goldstein for helpful discussions. This
`work was partially supported by Research Corporation and
`the NSF,
`
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