imperial.ac.ukbDepartment of Chemistry, Durham UniverscCentral Laser Facility, STFC, Harwell Oxfo
† Electronic supplementary informatimicrometer-sized oil droplet in water neshowing thermal capillary waves at10.1039/c4ra14967j
Cite this: RSC Adv., 2015, 5, 8114
Received 21st November 2014Accepted 22nd December 2014
DOI: 10.1039/c4ra14967j
www.rsc.org/advances
8114 | RSC Adv., 2015, 5, 8114–8121
ration of monodisperse ultra-lowinterfacial tension oil droplets in water†
Guido Bolognesi,a Alex Hargreaves,b Andrew D. Ward,c Andrew K. Kirby,b
Colin D. Bainb and Oscar Ces*a
We present a novel microfluidic approach for the generation of monodisperse oil droplets in water with
interfacial tensions of the order of 1 mN m�1. Using an oil-in-water emulsion containing the surfactant
aerosol OT, heptane, water and sodium chloride under conditions close to the microemulsion phase
transition, we actively controlled the surface tension at the liquid–liquid interface within the microfluidic
device in order to produce monodisperse droplets. These droplets exhibited high levels of stability with
respect to rupture and coalescence rates. Confirmation that the resultant emulsions were in the ultra-
low tension regime was determined using real space detection of thermally-induced capillary waves at
the droplet interface.
1 Introduction
Droplet-based microuidics underpins the generation, transportandmanipulation of femto- to picoliter sized droplets dispersed ina continuous phase.1 High precision, reproducibility, the potentialfor ultra-high throughput and the capability to compartmentalizebiological and chemical reactions within individual droplets aresome of the advantages that droplet-based microuidics offerswith respect to macroscopic emulsication approaches.
The formation of droplets within microuidic devices isgenerally the result of a spontaneous process where the owviscous stresses are balanced by the interfacial tension at theliquid–liquid interface.2 However, at low and ultra-low surfacetensions (namely, below 0.1 mN m�1), microuidic dropletgeneration is more challenging as the growth rate of interfacialinstabilities induced by the capillary forces, which drive break-up processes, are extremely low. When the capillary breakuptime becomesmuch larger than the characteristic ow time, theeffects of capillary instabilities become negligible on the timescale of thread formation and a stable jet is formed.3 Despitethese technical difficulties, oil droplets in water having ultra-low interfacial tensions (ULIFT) within a microuidic environ-ment support an ever growing number of exciting applications.As the surface tension reaches values as low as 1 mNm�1, opticalelds4 can be used to sculpt oil droplets intomore complex shapes,
e London, London, UK. E-mail: o.ces@
ity, Durham, UK
rd, UK
on (ESI) available: Video of aar the microemulsion phase transition
the droplet interface. See DOI:
possibly leading to new approaches for the synthesis of asym-metric solid particles with user-dened shapes.5 Additionally, inthe ULIFT regime when a single droplet is separated into twodroplets by two optical traps, the two droplets remain connected bya stable thread of oil with a typical diameter of less than a hundrednanometers.6 This phenomenon opens the way to the generationof complex nanouidic networks created and controlled by light.7
In recent years, microuidic approaches have been intro-duced for manufacturing ULIFT droplets by using aqueous twophase systems (ATPS).3 In such systems, droplets of one poly-mer solution are dispersed in another immiscible polymersolution. The water is the continuous component in both pha-ses and the resulting interfacial tension is ultra-low. In order toperturb an otherwise stable jet and to promote droplet forma-tion via the Rayleigh–Plateau instability, the aqueous two-phaseinterface can be destabilised by mechanically vibrating eitherthe chip8 or the so tubing carrying the dispersed phase.9 Forspecic systems, electrostatic forces can also be effectively usedto generate a monodisperse population.10 Interfaces with ultra-low interfacial tension can also be generated with oil–watersystems by adding surfactants in both phases. Similarly, longand stable jets can form11 and mechanical vibration sourceshave been used to promote droplet breakup.12 However, thereare a number of differences between the oil–water systems andATPS. More specically, the growth rates of capillary instabil-ities for jets formed with Newtonian oil–water phases werefound to agree with the theoretical prediction for connedthreads in microchannels.12,13 Conversely, the jets formed withATPS exhibited instability growths more than an order ofmagnitude slower than the Newtonian counterpart undersimilar conditions of ows, uid properties and degree ofconnement.12 That makes the generation of ULIFT dropletsmore difficult in ATPS than oil–water systems.
Additionally, for an oil–water interface the interfacial tensioncan enter the ultra-low regime only if enough surfactant mole-cules have been adsorbed at the interface. If the droplet produc-tion rate is fast enough that surfactant cannot equilibrate at theinterface, common microuidic techniques can be used fordroplet generation. Indeed the dynamic surface tension is notultra-low and the jet can spontaneously break up under the Ray-leigh–Plateau instability with no need of external perturbationsources such as vibrating piezoelectric actuators or electric eldgenerators. That has important advantages such as easier designand simpler fabrication methods for the microuidic system.Such a strategy has been successfully used for the microuidicgeneration of ULIFT water droplets in oil14 with a ow focusingjunction. However, Hashimoto et al.14 showed that once thedynamic surface tension reached its equilibrium value, spatialconnement and variation of the channel width (such as expan-sions and contractions) induced extreme deformation and shear-driven instabilities on droplets, thereby resulting in highly poly-disperse emulsions. More specically, the onset of Rayleigh–Plateau instabilities in the stretched droplets promoted theformation of smaller droplets, whose nal size depended on theow conditions,15 the degree of connement16 as well as theviscosity ratio.17 Shear-driven instabilities were instead respon-sible for the break up of the droplets trailing edge into daughterdroplets, whose typical size was at least one order of magnitudesmaller than the channel depth. In order to overcome theseinstabilities, emulsion could be produced at low and moderatesurfactant concentrations in the continuous phase, so that theequilibrium interfacial tension would not be ultra-low and drop-lets would remain stable against shear-induced rupture and coa-lescence. A surfactant-rich continuous phase could be added tothe emulsion in a separate step aer formation, thereby reducingthe interfacial tension to ultra-low values. However, the resultingmonodisperse ULIFT droplets would be very difficult to handlesince even low viscous stresses, as those induced by nearby walls,would trigger shear-driven instabilities at the droplet interface.18
In this paper, we present a microuidic platform for thegeneration of stable monodisperse oil droplets in water whosenal interfacial tension is of the order of 0.1–1 mN m�1. Ouralternative method relies on a tuneable oil–water formulationwhose surface tension can be actively controlled within themicrouidic environment. Our device is capable of producingULIFT monodisperse droplets with diameters in the range of10–20 mm and high stability against coalescence as well as ruptureinduced by hydrodynamic stresses. A microuidic tool for theaccurate and repeatable delivery of ULIFT droplets with precisecontrol over composition and size offers the opportunity toimprove and extend the eld of applications of optical manipula-tion of ULIFT droplets6 as well as to investigate the fundamentalchemistry and physics behind it.
2 Methods and materials2.1 The oil–water–surfactant system
In our experiments heptane (VWR, 99%) was used as thedispersed phase and an aqueous solution containing NaCl anddiethylhexyl sodium sulphosuccinate (AOT) (Sigma-Aldrich,
98%) as the continuous phase. Aerosol OT has closelymatched hydrophilic and lipophilic properties19 that permitphase transitions in emulsion formation by increasing thehydrophobic character, e.g. by addition of salt. Increasing saltconcentration reverses the direction of the natural curvature ofthe surfactant lm from oil-in-water to water-in-oil and henceproduces an inversion in phase continuity.19 The transitionbetween low and higher salt concentrations thus corresponds toa sharp decrease of the interfacial tension, which can reachvalues down to 0.1 mN m�1, provided the surfactant concen-tration exceeds the critical micelle concentration (cmc).A similar transition occurs if the salinity of the aqueous solutionis kept constant and the emulsion temperature changes. Forinstance, at a salt concentration of 50 mM and temperatureshigher than 26 �C, AOT is hydrophilic and the surfactant onlypartitions into the oil phase at lower temperatures. Again, whenthe transition occurs, the surface tension goes into the ULIFTregime (i.e. �1 mN m�1). The temperature corresponding to theminimum attainable interfacial tension for a given salinity isdenoted as the phase inversion temperature (PIT). For AOTsolutions, the PIT varies from 15 �C to 40 �C when saltconcentration increases from 33 mM to 84 mM. The relation-ship between PIT and salinity as well as the dependency ofinterfacial tension on salt concentration and temperature forthe heptane–NaCl–water–AOT system have been characterizedby Aveyard et al.20–22 through spinning droplet tensiometry.
2.2 Microuidic chips and image system
Droplets were generated in a 14 mm depth glass ow-focusingdevice with a cross-junction,23 fabricated by Dolomite Micro-uidics via standard photo-lithography and glass etchingtechniques. The cross-junction consisted of four channels17 mm in width and 135 mm in length which joined at rightangles. The cross-junction was connected to 500 mm width inletand outlet channels via expansion and contractions(see Fig. 1b). Hereaer this chip is referred to as the owfocusing junction (FFJ) chip. Syringe pumps (WPI-Aladdin2-220) were used to supply the dispersed phase in the centralchannel and the continuous phase in the side channels.Measurements were performed at least ve minutes aerchanging the ow rates of the two phases to ensure the systemstability. The FFJ chip was also tted with on-chip temperaturecontrol (see Fig. 1c), consisting of a resistance thermometer(PT100 Class A) and a Peltier cell (Ferrotec) attached to thebottom and top external walls of the chip, respectively. ThePeltier cell had a central 5 mm diameter hole to allow opticalaccess to the cross-junction. The cell was driven by aproportional-integral-derivative (PID) control unit (ElectronDynamics Ltd.), which allowed for temperature control with aprecision of 0.1 �C. In order to allow the system to reach thermalequilibrium, measurements began at least three minutes aerthe chip temperature had been set to a new value. In someexperiments, the temperature control unit was de-activated sothat droplet generation could be performed under laboratoryambient conditions.
Fig. 1 (a) Schematic view of the microfluidic platform. Two syringe pumps were used to mix two aqueous solutions with concentrations c1 andc2 NaCl. The mixed solution with final salinity c NaCl supplied the side channels of the flow focusing junction (FFJ) chip. The central channel ofthe chip was fed with heptane by a third syringe pump. (b) Scheme of the cross-junction where heptane droplets were formed. The dimensionsof the channels are the following: wo ¼ 500 mm, L ¼ 135 mm, w ¼ 17 mm. (c) Three dimensional schematic view of the on-chip temperaturecontrol system. The channels were located in the middle plane (dashed lines) of the FFJ glass slab, whose total thickness was t ¼ 4 mm.
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Aer formation, droplets were transferred into a separatedevice designed and fabricated for droplet storage and charac-terization purposes. The device was made of two microscopeslides separated by a PDMS layer, the fabrication protocol beingreported elsewhere.24 We refer to that device as the observationchamber (ObC) chip.
Images of droplets within both the FFJ and ObC chips werecaptured with an Olympus IX81 inverted microscope tted witha CCD camera (Q-Imaging Retiga EXi fast). Image post-processing for droplet sizing and characterization was per-formed with custom Java macros implemented in ImageJ andPython code.
3 The microfluidic platform
The heptane–water emulsion containing AOT and NaCl reachesthe ULIFT regime when the system is very close to the micro-emulsion phase transition. Such a condition can be obtained bynely tuning the salinity level and the temperature of theemulsion. We thus devised a microuidic system where boththose parameters could be controlled. The nal salinity of thecontinuous phase was obtained by mixing two aqueous solu-tions with different salt concentrations. Two syringes(see Fig. 1a) were charged with c1 and c2 mM NaCl aqueoussolutions plus 2 mM AOT. The liquids from the two syringesjoined together in a Y junction (Y1) and fully mixed by owingin a 250 mm diameter FEP tubing. Denoting the ow rates in thetwo syringes as Qc1 and Qc2, the nal salt concentration of themixed phase can be expressed as
c ¼ c1Qc1 þ c2Qc2
Qc1 þQc2
(1)
Aer mixing, the ow split at the junction Y2 and entered theside channels of the FFJ chip. Assuming a relative error of dci/ci¼ 0.2% (for i¼ 1, 2) for the salinity of the aqueous solutions anddQci/Qci ¼ 1% (for i ¼ 1, 2) for the ow rates of the syringe
8116 | RSC Adv., 2015, 5, 8114–8121
pumps, we can estimate that the accuracy on the salt concen-tration of the mixed phase is about dc/c ¼ 0.3%. For a 50 mMNaCl aqueous solution, that means an approximate error of0.2 mM in the nal salt concentration.
The chip temperature was set through a thermal controlunit. Denoting the thermal diffusivity of any liquid phase as aT,the liquid reaches thermal equilibrium with the surroundingwalls aer owing for a distance lT x Q/2aT, where Q is theliquid ow rate. Considering the thermal diffusivity of water(aT ¼ 14.3 � 10�8 m2 s�1) and heptane (aT ¼ 8.5 � 10�8 m2 s�1)at 25 �C and a maximum ow rate Q ¼ 20 mL min�1, we obtainlT x 1 � 2 mm. Since the area covered by the Peltier cell is 13mm� 13 mm, it can be assumed that at the cross-junction bothphases are at thermal equilibrium with the channel walls. Byperforming stationary nite element analysis in Comsol Mul-tiphysics (COMSOL Ltd.), the temperature eld in the FFJ glassslab was determined assuming that heat enters the system fromthe Peltier module and leaves it through the external walls bynatural convection. With a typical room temperature of 23 �C,for an average chip temperature of 30 �C the standard deviationof the temperature eld in the volume of the FFJ glass slabunder by the Peltier unit is about 0.2 �C. That value can beconsidered as a good estimate for the precision of the emulsiontemperature measurements.
4 Results and discussion
Droplets cannot readily be generated in the ULIFT regimebecause the effects of capillary forces, which drive the interfa-cial instability leading to the breakup of the dispersed phasestream, are dramatically slowed down. Consequently, forsurface tension lower than a critical value gc (see Appendix)droplets do not form at the cross-junction and parallel ows ofthe two phases are obtained instead. If, however, the time scalefor interface generation is less than the characteristic diffusiontime for the surfactant to the interface, the equilibrium surfacecoverage is not reached on the time scale of droplet formation.25
Under these conditions, the dynamic surface tension gd
assumes values between the surface tension at equilibrium ge
and the surface tension of a clean surfactant-free interface g0,depending on the device geometry, the ow rates and the typeand concentration of surfactant.25 For gd typically higher thangc, it is hence possible to produce monodisperse dropletsimmediately at the junction whereas the droplet equilibriumsurface tension still lies in the ULIFT regime. For typicalsurfactant concentrations in the millimolar range, the diffusiontimescale is of the order of milliseconds. Aer formation, thedroplets go through the junction and enter the wider outputchannel, where the diffusive and convective transport ofsurfactant molecules to the interface25 causes the surfacetension gd to drop to ultra-low values on a time scale of tens ofmilliseconds aer generation. For that reason, ULIFT dropletsare unstable and they can easily tear apart due to the highviscous stresses downstream of the junction, yielding a highlypolydisperse emulsion.14
The most effective method to produce and manipulatemonodisperse ULIFT droplets is to control the equilibriumsurface tension according to the operation required. For dropletgeneration and transport, ge has to be higher than gc and thecapillary number Ca lower than a critical value Cac whereas fordroplet storage, manipulation and optical deformation ge canbe lowered down to the ULIFT regime. Such control is quitedifficult to implement when ge mainly depends on theconcentration of surfactant in either phases, as it occurs for theoil–water–surfactant systems typically used in droplet micro-uidics. Moreover, in those systems where surfactant concen-tration exceeds the cmc, ge reaches its minimum value and it nolonger depends on the amount of surfactant.
On the contrary, for the heptane–brine–AOT system at asurfactant concentration higher than the cmc, ge stronglydepends on salinity and temperature. By controlling these twoparameters, the equilibrium surface tension can be indepen-dently tuned in the FFJ chip for droplet generation and in theObC chip for droplet storage and characterization. In thefollowing sections, we separately assess the effects of salinityand temperature on droplet formation and we show how thismicrouidic platform can be used to generate and storemonodisperse ULIFT droplets.
Fig. 2 Outside of the junction, the droplets were stretched by thesurrounding flow and assumed very elongated shapes. At the top ofeach panel, the salt concentration and the estimated correspondingequilibrium surface tension are reported. The typical production rate isabout 200 Hz. The surface tension were interpolated from data inref. 20.
4.1 Effect of salinity on droplet formation
According to the literature,20 the equilibrium surface tension ofthe heptane–water–AOT–NaCl system at 25 �C reaches valuesbelow 10 mN m�1 for salt concentrations in the range of38 mM–58 mM. To assess the effects of salinity on dropletformation, the FFJ chip temperature was xed and the emulsionsalinity was varied in the range corresponding to the lowestsurface tensions. The continuous phase syringes were lledwith aqueous solution at salt concentrations c1 ¼ 0 mM andc2 ¼ 100 mM. The corresponding ow rates Qc1 and Qc2 werevaried between 0.06 mL min�1 and 0.14 mL min�1 in order totune the nal salinity of the emulsion. The total water ow rateQc ¼ Qc1 + Qc2 and oil ow rate Qd were xed to 0.2 mL min�1 and0.05 mL min�1, respectively. The droplet generation was
performed under laboratory ambient conditions. The labtemperature was monitored through the on-chip resistancethermometer and it was constant at 23.6 �C for all experiments.
Under these conditions, ge depends strongly on theconcentration of NaCl and its value can be qualitativelyassessed through the deformations droplets underwent in theexpanding output channel. Fig. 2 shows the generated dropletsowing outside of the junction for salinity levels between35 mM and 60 mM. By interpolating the experimental dataavailable in the literature,20 we could estimate that the equi-librium surface tensions ge varied in the range of 1–22 mN m�1
(see labels in Fig. 2). As droplets le the junction, the viscousstresses exerted by the continuous phase ow in the expandingoutput channel deformed the droplets.
The continuous phase ow was quite complex for theexamined channel geometry. It had an irrotational componentinduced by the increasing width of the channel as well as arotational component induced by the over-connement of thedroplets, whose undeformed diameter d0 was typically largerthan the channel depth h. Moreover, the simultaneous presenceof several droplets in the output channel affected the ow itself.
As drops slowed down, the separation distance between themwas reduced and the uid was squeezed out from the regionbetween the drops, thereby increasing the total strain rateapplied to the drops.14 Finally, the viscous stresses exerted onindividual droplets was not constant in time since as the dropletabandoned the expanding section of the output channel thecorresponding extensional component of the ow ceased.
Generally, if the capillary number exceeds a critical valueCac, no equilibrium droplet shape exists in order to balance theviscous and capillary forces and the ow keeps deforming thedroplets until Rayleigh–Plateau instabilities prevail and dropletbreakup occurs. Droplet breakup of conned droplets forspecic ows, such as simple shear and extensional, have beeninvestigated in the literature.18,26 For instance, for viscosity ratiol < 1 and simple shear ow,26,27 spatial connement is expectedto stabilize the droplets by increasing the value of Cac withrespect to the case of unbounded ow. For viscosity ratio l ¼ 1and over-connement (d0 > h), extreme droplet deformationshave also been reported,28 the nal droplet length beforerupture being up to 10 times the undeformed droplet radius.Even though the geometry of our droplet generation device doesnot allow to easily estimate the character and the intensity ofthe viscous stresses, and, hence, of the Cac, our experimentaldata showed that for the examined ow rates droplets did notbreak up in the output channel when the equilibrium surfacetension was higher than 0.1 mN m�1. Moreover, at constanttemperature (hence, constant liquid viscosity) and constantliquid ow rates, the viscous stresses are expected to be thesame for all experiments. Consequently, the Ca number was afunction of the surface tension only and the deformed shape ofthe droplets exclusively depended on the surface tension of theoil–water interface with higher deformations corresponding tolower values of ge.
In agreement with our physical description of the process,Fig. 2 shows that for most salt concentration, the degree ofdroplet deformation kept increasing as droplets owed down-stream up to the point that the capillary instability prevailedand the droplet broke up into two or more smaller droplets.That behaviour is very similar to the “rain” regime reported for aHele-Shaw cell.14 Despite the fact that droplets had very lowinterfacial tension, they showed high stability against coales-cence, on the timescale of a few hundred milliseconds. Thatstability is essential for subsequent transport and storage of thedroplets. The droplet deformability can be assessed through thehighest ratio Dmax ¼ l/d0 reached by the droplet before rupture,l being the droplet length. At 35 mM NaCl (ge x 22 mN m�1),Dmax was about 4 whereas at 45 mM NaCl (ge x 1 mN m�1) itwent up to 9. In the latter case, the salt concentration was veryclose to the value corresponding to the phase inversion (namely,46.5 mM at 23.6 �C) and the droplets remained stable to breakup within the eld of view of the microscope (Fig. 2c). A similarcondition occurs in the “shbone” regime for a Hele-Shawcell.14 Such result can be explained by comparing the breakuptime and the drop residence time in the eld of view. We canassume that in supercritical conditions (Ca > Cac), the time of
capillary breakup scales with the visco-capillary time tvc ¼ hcd0ge
.
8118 | RSC Adv., 2015, 5, 8114–8121
Under the same condition of temperature and ow rates, lowerinterfacial tensions would hence result in longer breakup time.For extremely low interfacial tensions (�1 mNm�1), the breakuptime exceeded the residence time and droplets no longer brokeup within the eld of view of the microscope.
To conclude, our experiments show that droplet deform-ability depends on water salinity and it increases withdecreasing ge. Such behaviour demonstrates the capability ofthe microuidic platform to tune the equilibrium surfacetension of the oil–water interface by controlling the saltconcentration in the continuous phase.
4.2 Effect of temperature on droplet formation
The control over the salt concentration allowed us to bring thewater–oil system very close to the microemulsion phase tran-sition, thereby generating very low interfacial tensions. Asshown in Fig. 2, that condition is not ideal for droplet genera-tion because droplets were so deformable that viscous stressescould tear them apart, resulting in a highly polydisperse pop-ulation. However, for a given salinity the equilibrium interfacialtension can still be modied through temperature. Thereforewe used the on-chip temperature control unit to increase theequilibrium surface tension in the FFJ chip so that droplets nolonger broke.
According to the literature,20 at 50 mM NaCl the surfacetension drops below 10 mN m�1 in a temperature range of 18 �Cand 29 �C. In order to assess the effect of temperature ondroplet formation in the device, the system was rst broughtvery close to the microemulsion phase transition (namely, 47.3mM NaCl and 24.3 �C) and then the temperature was graduallyincreased while keeping the salt concentration constant. As forthe previous experiments, the total ow rate of the continuousphase was Qc ¼ 0.2 mL min�1 whereas the ow rate of thedispersed phase was Qd ¼ 0.05 mL min�1. Under those condi-tions, the droplet surface tension is expected to increase withthe temperature. We note that the increase in temperature doesnot only affect the interfacial property of the emulsion, but italso changes the bulk rheology of the liquid phases. Indeed theviscosity of heptane and water decrease by about 19% and 35%,respectively, for a temperature rise from 20 �C to 40 �C. Theviscosity affects the uid stresses as well as the droplet size so itis not possible to relate the droplet shape directly to the surfacetension as in the previous experiments.
Fig. 3a and b show droplets at the junction exit at tempera-tures of 29.9 �C and 43.4 �C, respectively. It is evident thatdroplet formation and shape were highly affected by tempera-ture. Interpolating the data available in the literature,20 theequilibrium surface tension at 29.9 �C was estimated to be16 mNm�1. On the other hand, 43.4 �C is outside of the range oftemperature for which surface tension measurements areavailable at the examined salinity. However, since thattemperature is about 20 �C higher than the PIT, we canreasonably assume ge > 0.1 mN m�1. As expected, the experi-mental results show that for a high value of ge, the capillaryforce successfully opposed the viscous stresses, thereby pre-venting droplet rupture in the outlet channel. The resulting
Fig. 3 Droplets at the junction exit with salt concentration of 47.3 mMat temperatures higher than the corresponding PIT, namely 24.3 �C.The equilibrium surface tension increased with increasing temperatureand for values higher than 0.1 mN m�1, the droplet population wasmonodisperse. In panel (b), the droplet diameter is 22.7 � 0.8 mm.
Fig. 4 Thermal capillary waves at the interface of a droplet near themicroemulsion phase transition (44.5 mM NaCl at 22.2 �C). (a–d): fourconsecutive frames extracted from a 10 fps frame rate video. The fullvideo is available in the (ESI†). The scale bar is 5 mm. The solid line inpanel (a) shows the actual interface position whereas the dashed linesis the corresponding best fit circle. (e) Histogram of the dropletinterface displacements, which are computed as the radial distancebetween the actual interface and the best fit circle. The dashed line isthe corresponding histogram for a rigid droplet, whose salinity andtemperature conditions are far from the microemulsion phasetransition.
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droplet population was monodisperse. To assess quantitativelythe monodispersity of the emulsion, 180 droplets from imagessimilar to Fig. 3b were analysed, resulting in an average dropletdiameter of 22.7 mm with a coefficient of variation (i.e. the ratioof the standard deviation and the mean value) less than 3.5%.In previous studies on droplet formation in a cross-junctiondevice,29 it has been demonstrated that the droplet diameterscales as (Qc/Qd)
�aCa�b, where a and b are positive constants. Ifwe thus increase the ow rate ratio Qc/Qd and the continuousphase ow rate Qc, we can generate even smaller droplets. As anexample, when we set Qc/Qd ¼ 100 and Qc ¼ 20 mL min�1, weobtained droplets with an average diameter of 11 mm and acoefficient of variation less than 5% (data not shown).
4.3 Thermal capillary waves at the ULIFT droplet interface
In order to demonstrate the capability of the microuidicplatform to produce an emulsion with such a low surfacetension, we generated and stored droplets under temperatureand salinity conditions corresponding to the ULIFT regime andmonitored the thermally-driven perturbations at the dropletinterface. It is well known that thermal motion is able toproduce statistical uctuations of the position of a two-phaseinterface.30 The typical amplitude of those thermally-inducedcapillary waves scales as
ffiffiffiffiffiffiffiffiffiffiffiffiffikBT=g
p, where kB is the Boltzmann
constant and T the absolute temperature. For the most commonwater–oil–surfactant systems adopted in droplets microuidics,the surface tension is of the order of 1 to 10 mNm�1, which setsthe wave amplitude in the range of 1 nm. Such a small pertur-bation can only be detected via light and X-ray scattering tech-niques and, hence, the interface of a droplet appears to besmooth down to the molecular length scale. On the other hand,if the surface tension is lowered down to 0.1–1 mN m�1, theinterface roughness increases up to 50–200 nm, and the thermalcapillary waves can be observed in real space through standardoptical microscopy.31
Droplet were generated with a salt concentration whosecorresponding PIT was equal to the lab temperature. Undersuch conditions, the equilibrium surface tension is expected tobe very close to the minimum value, which is less than
1 mN m�1. Droplet production and transport to the ObC chipwas performed at temperatures higher than 40 �C, so thatviscous stresses did not break the droplets and the emulsionremained monodisperse. As the droplets reached the ObC chip,the ow was stopped and the droplets, at rest, were allowed toequilibrate at the lab temperature. Alternatively, droplets couldalso be produced at lab temperature but with high salinity levelsto satisfy the condition ge > gc and the ObC chip temperaturecould be adjusted with a heating device to let the emulsionenter the ULIFT regime. As the emulsion temperatureapproached the PIT, the droplet interfaces began to uctuateunder the effect of thermal motion. Fig. 4 shows the thermalcapillary waves at the interface of a 15 mm diameter droplet(Video available in the ESI†). Tracking the motion of the dropletinterface we measured a root mean squared displacement ofapproximately Ds ¼ 110 � 50 nm (see Fig. 4e), which accordingto the scale law Ds x (kBT/g)
tension lower than 1 mN m�1, as expected. The root meansquare displacement of the interface of a rigid droplet (namely,50 nm) is considered as a good estimate for the accuracy of thedroplet interface trackingmethod. The comparison between thehistograms of the interface displacements for a deformabledroplet and a rigid one (see Fig. 4e) shows that the adoptedbright-eld interface tracking method is accurate enough todiscriminate between ULIFT and non-ULIFT droplets. Higheraccuracy for the interface tracking can be obtained by usingalternative optical methods as, for instance, uorescencemicroscopy.31
5 Conclusions
In this paper we present a novel approach for the stablegeneration of monodisperse ULIFT oil droplets in water. Wehave devised and successfully tested a microuidic platform,which allowed us to tune the surface tension of the liquid–liquid interface by accurate control of the salinity and temper-ature. As a consequence of that, droplets could be generatedwith common microuidic techniques, such as the use of ow-focusing device, with no need of external perturbation sourcesas required when ATPS are used. Aer formation, droplets weretransferred in a separate chip for storage and characterizationpurposes. The aqueous phase was pumped from two syringeslled with solutions having different salt concentrations. Theow rate ratio of the syringes determined the nal salinity of theemulsion. On-chip temperature control units were adopted toadjust the emulsion temperature.
Droplet formation in microuidic devices is challengingwhen the interfacial tension is in the ULIFT regimes. Thegrowths of interfacial disturbances, which drive the capillarybreakup, are extremely delayed and the dispersed phase canform long and stable jets. Using the theory of absolute andconvective instabilities for conned jets, we determined a crit-ical value for the surface tension of about 0.1 mN m�1, abovewhich no jet is stable and droplets form immediately at thecross-junction. We showed that droplets can be generated evenfor equilibrium surface tensions in the ULIFT regimes, but onlyif the production rate is fast enough that surfactant cannotequilibrate at the interface. However, aer formation thedynamic surface tensions quickly drop to the equilibrium ultra-low value and the resulting capillary forces cannot competeagainst the viscous stresses; the droplets tear apart and theresulting emulsion is polydisperse.
For that reason, the droplet production and manipulationwere performed at temperatures higher than 40 �C for salt–surfactant–water–oil formulations with PIT close to 20 �C.Under those conditions, the hydrodynamic instabilities, whichcharacterize the dynamics of ULIFT drops,14 could be avoidedand the formed droplets were highly stable with respect torupture as well as coalescence. As droplets were collected in aseparate device and brought under conditions close to themicroemulsion phase transition, thermally-driven capillarywaves with a typical amplitude of 100 nm were observed at theliquid–liquid interface, thereby proving that the emulsion hadnally entered the ULIFT regime.
8120 | RSC Adv., 2015, 5, 8114–8121
Appendix
At low Reynolds and Weber numbers, the droplet formationprocess is controlled by the balance of viscous and capillaryforces. Viscous forces tend to stabilize the interfaces betweenthe two phases whereas the capillary forces promote the growthof interfacial disturbances which eventually lead to the breakupof the dispersed phase stream. The time of breakup scales as thevisco-capillary time tvc¼ hca/g, where hc is the dynamic viscosityof the continuous phase, a is the radius of the dispersed phasethread and g is the surface tension. At ultra-low values ofsurface tension, tvc becomes much larger than the characteristicow time and the onset and growth of the interfacial pertur-bations is extremely delayed. Under these conditions, the effectsof capillary forces are negligible on the time scale of threadformation and a long and stable jet can form. Considering thegeometry, the ow rates and the liquid properties of ourmicrouidic system, we now determine an estimate of theminimum value of surface tension for which jets are no longerstable and droplets break up promptly at the junction.
According to the theoretical predictions of Guillot et al.,32 thedisturbance growth rate for a jet of radius r0 and viscosity hd,conned in a cylindrical channel of radius Rc and focused by acontinuous phase stream of viscosity hc is given by
u ¼ g
16hcRc
Fðx; lÞ�~k2 � ~k
4�
x9�1� l�1
�� x5(2)
where ~k ¼ kr0 is the dimensionless wavenumber of the pertur-bation, x ¼ r0/Rc is the dimensionless jet radius, l ¼ hd/hc is theviscosity ratio and the function F(x, l) is equal to F(x, l)¼ x4(4�l�1 + 4 ln x) + x6(�8 + 4l�1) + x8(4 � 3l�1 � (4 � 4l�1)ln x). Theradius of the perturbed jet is equal to r ¼ r0 + 30 exp(ikz + ut),where r0 is the unperturbed jet radius and 30 is the initialperturbation amplitude. Numerical simulations have showedthat eqn (2) provides accurate results also for jets owing insquare channels at low and moderate degrees of connement(namely, x < 0.6).13 Since the junction cross-section of the chipused in our experiments is almost square, eqn (2) can be used toestimate the growth rate of the fastest disturbance by replacingthe channel radius R with the equivalent radius
ffiffiffiffiffiffiwh
p=2, where w
and h are the junction width and depth, respectively.In order to prove that droplets cannot be easily produced in
the ULIFT regime, we now determine the jet break up time forultra-low values of surface tension. If we assume the ow rate andviscosity of the continuous (dispersed) phase to be Qc ¼ 0.2mL min�1 (Qd ¼ 0.05 mL min�1) and hc ¼ 10�3 Pa s (hd ¼ 0.39 �10�3 Pa s), respectively, we can predict from the Stokes equa-tions32 a dimensionless jet size of x ¼ 0.3 and from eqn (2) amaximal growth rate of u* ¼ 20 Hz at the dimensionless wave-number ~k* ¼ 0.7. The jet breakup time tb can be dened as thetime at which the disturbance amplitude equals the unperturbedjet radius, namely 30 exp(u*tb) ¼ r0. If we assume an initialperturbation amplitude 30 of the order of 1 nm and a surfacetension in the ULIFT regime, such as 1 mN m�1, the fastestperturbation will take about tb ¼ 0.4 s to break up the dispersed
phase stream. If the cross-junction channel were long enough, wecould expect that in the ULIFT regime a stable jet with a totallength more than 300 times the junction width would form.Under such conditions, an accurate control over the size andmonodispersity of the droplet population would be extremelydifficult.
The extremal velocity of the envelope of the perturbation canbe written as32
convected away from the junction but it also travels backwards.The transition from a convectively unstable jet (v*� > 0) to anabsolutely unstable jet (v*� < 0) occurs when surface tensionequals the critical value
gc ¼�dzP
0Rc2x3Eðx; lÞ
C1Fðx; lÞ (4)
Considering the ow conditions, the uid properties and thedevice geometry parameters reported above, we can predict fromeqn (4) that for surface tensions higher than gc x 0.1 mN m�1,the jet is no longer stable and droplet breakup occurs imme-diately at the junction.
Acknowledgements
We are pleased to thank all the members of the Optonano-uidics research team for interesting discussions. This work wassupported by EPSRC grants EP/I013342/1 and EP/G00465X/1.
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