evaporation-induced particle microseparations inside droplets floating...

Evaporation-Induced Particle Microseparations inside DropletsFloating on a Chip

Suk Tai Chang and Orlin D. Velev*

Department of Chemical and Biomolecular Engineering, North Carolina State UniVersity,Raleigh, North Carolina 27695

ReceiVed October 4, 2005. In Final Form: NoVember 14, 2005

We describe phenomena of colloidal particle transport and separation inside single microdroplets of water floatingon the surface of dense fluorinated oil. The experiments were performed on microfluidic chips, where single dropletswere manipulated with alternating electric fields applied to arrays of electrodes below the oil. The particles suspendedin the droplets were collected in their top region during the evaporation process. Experimental results and numericalsimulations show that this microsepration occurs as a result of a series of processes driven by mass and heat transfer.An interfacial tension gradient develops on the surface of the droplet as a result of the nonuniform temperaturedistribution during the evaporation. This gradient generates an internal convective Marangoni flow. The colloidalparticles transported by the flow are collected in the top of the droplets by the hydrodynamic flux, compensating forevaporation through the exposed top surface. The internal flow pattern and temperature distribution within evaporatingdroplets were simulated using finite element calculations. The results of the simulation were consistent with experimentsusing tracer particles. Such microseparation processes can be used for on-chip synthesis of advanced particles andinnovative microbioassays.

1. Introduction

Droplet-based microfluidic systems have emerged as apromising technology for solving some of the drawbacks ofmicrochannel-based devices, such as channel clogging withsuspended particles or biomolecules, poor mixing because of theintrinsically low Reynolds number of microfluidic flows, andthe difficulty of particle separation to analyze complex andheterogeneous samples.1-10 We developed a dielectrophoreticliquid-liquid chip system for capturing and manipulating micro-sized droplets freely suspended on the surface of a denseperfluorinated hydrocarbon oil (F-oil).11 The droplets weretransported using an alternating electric field applied by electrodearrays situated below the F-oil.

The droplets floating on these electronically controlleddielectrophoretic liquid-liquid chips can serve as “microreactors”for the assembly of novel supraparticles from nano- andmicroparticles during the process of droplet evaporation.12 Weobserved that during the assembly of supraparticles insideevaporating droplets the particles contained inside were rapidlyseparated in the top region of the droplet exposed to the ambientair, instead of collecting on the bottom because of sedimentation.This new phenomena could have importance in diverse processesfor on-chip materials and particle fabrication, chemical mi-crosynthesis, microbiassays, and sensing. Here, we investigate

the processes taking place in single floating droplets and themechanism of evaporation-driven vertical redistribution of themicrospheres suspended inside them.

Solvent evaporation in liquid films and droplets has been usedin convective assembly of micro- and nanoparticle coatings inthin evaporating film,13-15ring formation of suspended materialsby evaporation of sessile droplets on the substrate,16-19assemblyof colloidal particles on hydrophilic and hydrophobic surfaces,20,21

DNA stretching,22and others. Ball-like supraparticles have beenassembled inside evaporating spherical droplets containingmicrospheres.23-25 Transport and assembly of the suspendedparticles driven by solvent evaporation are related to the internalhydrodynamics in drying films and droplets.12-20,23,25Hydro-dynamic flows driven by solvent evaporation have beeninvestigated in much experimental and theoretical detail in sessiledroplets26-28 and in spherical droplets completely exposed toambient air.29-31 To our knowledge, however, detailed studies

* To whom correspondence should be addressed. E-mail: [email protected].

(1) Whitesides, G. M.; Stroock, A. D.Phys. Today2001, 42-47.(2) Blossey, R.Nature Mater.2003, 2, 301-306.(3) Paik, P.; Pamula, V. K.; Fair, R. B.Lab. Chip2003, 3, 253-259.(4) Stone, H. A.; Stroock, A. D.; Ajdari, A.Annu. ReV. Fluid Mech.2004, 36,

381-411.(5) Zeng, J.; Korsmeyer, T.Lab. Chip2004, 4, 265-277.(6) Song, H.; Tice, J. D.; Ismagilov, F.Angew. Chem. Int. Ed.2003, 42, 768-

772.(7) Roach, L. S.; Song, H.; Ismagilov, R. F.Anal. Chem.2005, 77, 785-796.(8) Weigl, B. H.; Yager, P.Nature1999, 283, 346-347.(9) Weigl, B. H.; Hedine, K.Am. Biotech. Lab.2002, January, 28-30.(10) Kutter, J. P.Trends Anal. Chem.2000, 19, 352-363.(11) Velev, O. D.; Prevo, B. G.; Bhatt, K. H.Nature2003, 426, 515-516.(12) Millman, J. R.; Bhatt, K. H.; Prevo, B. G.; Velev, O. D.Nature Mater.

2005, 4, 98-102.

(13) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura,H.; Nagayama, K.Langmuir1992, 8, 3183-3190.

(14) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura,H.; Nagayama, K.Nature1993, 361, 26-26.

(15) Prevo, B. G.; Velev, O. D.Langmuir2004, 20, 2099-2107.(16) Deegan, R. D.; Baksjin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.;

Witten, T. A. Nature1997, 389, 827-829.(17) Deegan, R. D.Phys. ReV. E 2000, 61, 475-485.(18) Shmuylovich, L.; Shen, A. Q.; Stone, H. A.Langmuir2002, 18, 3441-

3445.(19) Maillard, M.; Motte, L.; Ngo, A. T.; Pileni, M. P.J. Phys. Chem. B2000,

104, 11871-11877.(20) Uno, K.; Hayashi, K.; Hayashi, T.; Ito, K.; Kitano, H.Colloid Polym. Sci.

1998, 276, 810-815.(21) Fan, F.; Stebe, K. J.Langmuir2004, 20, 3062-3067.(22) Jing, J.; Reed, J.; Huang, J.; Hu, X.; Clarke, V.; Edington, J.; Housman,

D.; Anantharaman, T. S.; Huff, E. J.; Mishra, B.; Porter, B.; Shenker, A.; Wolfson,E.; Hiort, C.; Kantor, R.; Aston, C.; Schwartz, D. C.Proc. Natl. Acad. Sci. U.S.A.1998, 95, 8046-8051.

(23) Velev, O. D.; Lenhoff, A. M.; Kaler, E. W.Science2000, 287, 2240-2243.

(24) Yi, G. R.; Moon, J. H.; Yang, S. M.Chem. Mater.2001, 13, 2613-2618.(25) Iskandar, F.; Gradon, L.; Okuyama, K.J. Colloid Interface Sci.2003,

265, 296-303.(26) Kang, K. H.; Lee, S. J.; Lee, C. M.; Kang, I. S.Meas. Sci. Technol.2004,

15, 1104-1112.(27) Hu, H.; Larson, R. G.Langmuir2005, 21, 3972-3980.(28) Ruiz, O. E.; Black, W. Z.J. Heat Transfer2002, 124, 854-863.

1459Langmuir2006,22, 1459-1468

10.1021/la052695t CCC: $33.50 © 2006 American Chemical SocietyPublished on Web 12/23/2005

of particle transport and separations inside evaporating smalldroplets floating partially submerged in a denser liquid phasehave not been reported. This largely results from the experimentaldifficulty of carrying observations inside freely floating smalldroplets. These investigations have now been made easier by ourdielectrophoretic microfluidic chips, which allow droplet entrap-ment and precise positioning.

In general, as a droplet evaporates, a nonuniform temperaturedistribution is established by heat loss because of the phase changefrom liquid to vapor at the evaporating surface.28,31,32These localthermal imbalances create a surface tension gradient at the dropletsurface. The dependence of the surface tension (σ) on thetemperature imbalance is commonly represented by

whereσr is the reference surface tension,Tr is the referencetemperature, and|dσ/dT| is the surface tension derivative withtemperature. For common fluids, the value of dσ/dT is negative,so that the surface tension increases with a decreasing temperature.As a result of the surface tension gradient, the liquid interfaceis “pulled” toward the colder regions with a higher surface tension.Viscous drag moves the fluid adjacent to the surface, andconsequently, surface-tension-driven Marangoni flow isinitiated.31,33-37A convective Marangoni flow will be establishedwhen the surface tension force resulting from the externallyimposed temperature gradient overcomes the viscous resistiveforce in the liquid. The strength of the thermal instability,characterized by the ratio of the surface tension force to theviscous resistive force, is estimated by the dimensionlessMarangoni number, Ma,

The parameters in this expression are temperature difference∆T, characteristic length (droplet radius)R, dynamic viscosityη, and thermal diffusivityR. An interfacial tension gradientresulting from a temperature gradient in a droplet will causeconvective liquid flow inside a droplet if Ma is higher than acritical Marangoni number, Mac. The critical Marangoni numbersfor the emergence of fluid convection in a thin liquid film at afixed temperature of the rigid substrate below the thin film havebeen reported to be Mac ∼ 80.34,35 The transition from linearflow to Marangoni convection in horizontally heated liquid layersoccurs at Mac ∼ 20.35,36

The pattern of Marangoni flows driven by thermal instabilitiesdepends upon the aspect ratio (AR) of the fluid container, somewalls of which may be rigid or slippery.38,39The convective flowpatterns in a cylindrical container with a small aspect ratio havebeen reported.40-42 At AR ∼ 1, these flows are typically in the

form of one transverse cell (AR in this system is the ratio of thediameter to the height of the horizontal cylinder). Variousconcentric cell patterns with different azimuthal and wave modesform at other small ARs because of lateral wall effects. TheMarangoni flow patterns in systems where AR. 1 are organizedin a large number of hexagonal cells.

An alternative driving force for the convective flow insidedroplets, besides the Marangoni effect arising from surfacetension, is the buoyancy effect correlated with the liquid densitydependence on temperature.33,38,43-45 The dominant source ofconvection within the droplet can be estimated by the ratio ofthe Marangoni number (Ma) to the Rayleigh number (Ra)19,38

where the parameters include the liquid densityF, the liquidthermal expansion coefficientâ, the gravitational accelerationg, and the droplet radiusR. When Ma/Ra. 1, the convectiveflow inside a droplet is dominantly driven by the surface tensiongradient. In small evaporating droplets, the interfacial tensiongradient is reported as dominant and the buoyancy convectionhas usually been neglected.33,43

In this paper, we first describe the technique and theexperimental data obtained for microseparation of particles inthe top region of evaporating microdroplets floating on a liquid-liquid chip. The convective flows inside the droplets related tothe particle microseparations are visualized with the use ofsuspended particles. Results from two-dimensional (2D) nu-merical simulations of the temperature evolution and internalflow profiles are correlated with the experimental results. Weillustrate one potential use of the phenomena studied bydeveloping a new microbioassay technique based on dropletmicroseparations.

2. Experimental Procedures

Materials. Aqueous surfactant-free sulfate-stabilized 4.9µmpolystyrene latex microspheres were purchased from InterfacialDynamics Corp. (Portland, OR). Fluorescent sulfate 1µm micro-spheres in water and 2 mM azide solution were purchased fromMolecular Probes (Eugene, OR). The microspheres were centrifugedat 1700g for 3 min with a Marathon micro A centrifuge (FisherScientific, Hampton, NH) and washed with deionized (DI) waterobtained from Millipore RiOs 16 reverse osmosis water purificationsystems (Bedford, MA). The collected microspheres were resus-pended in DI water and sonicated (Branson Ultrasonics Corp.,Danbury, CT). Polymer microrods (∼23.5µm average length and0.60µm average diameter) were prepared in our laboratory.46,47Aninert, high-density perfluorinated oil, FC-70, was purchased from3M Corp. (St. Paul, MN).

Experimental Setup. The dielectophoretic liquid-liquid chipwas based on a two-sided printed circuit board with electrode patcheson one side and connecting leads on the other. The electrode arrayswere connected by individual electronic switches either to the ACvoltage source or to the ground.12 A FG-7002C Sweep/Functiongenerator (EZ Digital Co. Ltd., Korea) was used as a source ofsquare waves of frequency 800 Hz. The generated signal wasamplified to the working voltage of 700 V using Piezo Driver/Amplifier (Model PZD 700, Trek, Inc.). The fabricated chip board

(29) Savino, R.; Paterna, D.; Lappa, M.J. Fluid Mech.2003, 479, 307-326.(30) Ha, V.; Lai C.Int. J. Mass Heat Transfer2002, 45, 5143-5158.(31) Hegseth, J. J.; Rashidnia, N.; Chai, A.Phys. ReV. E1996,54, 1640-1644.(32) Hu, H.; Larson, R. G.J. Phys. Chem. B2002, 106, 1334-1344.(33) Block, M. J.Nature1956, 178, 650-651.(34) Pearson, J. R. A.J. Fluid Mech.1958, 4, 489-500.(35) Davis, S. H.Annu. ReV. Fluid Mech.1987, 19, 403-435.(36) Smith, M. K.; Davis, S. H.J. Fluid Mech.1983, 132, 119-144.(37) Chaudhury, M. K.; Whitesides, G. M.Science1992, 256, 1539-1541.(38) Schatz, M. F.; Neitzel, P. G.Annu. ReV. Fluid Mech.2001, 33, 93-127.(39) Rosenblat, S.; Davis, S. H.; Homsy, G. M.J. Fluid Mech.1982, 120,

91-122.(40) Wagner, C.; Friedrich, R.Phys. Fluids1994, 6, 1425-1433.(41) Dauby, P. C.; Lebon, G.; Bouhy, E.Phys. ReV. E 1997, 56, 520-530.(42) Ramo´n, M. L.; Maza, D.; Mancini, H. L.Phys. ReV. E 1999, 60, 4193-

4198.

(43) Czechowski, L.; Floryan, J. M.J. Heat Transfer2001, 123, 96-104.(44) Nield, D. A.J. Fluid Mech.1964, 19, 341-352.(45) Krishnan, M.; Ugaz, V. M.; Burns, M. A.Science2002, 298, 793.(46) Alargova, R. G.; Bhatt, K. H.; Paunov, V. N.; Velev, O. D.AdV. Mater.

2004, 16, 1653-1657.(47) Alargova, R. G.; Warhadpande, D. S.; Paunov, V. N.; Velev, O. D.

Langmuir2004, 20, 10371-10374.

MaRa

)|dσdT|

FâgR2(3)σ ) σr - |dσdT|(T - Tr) (1)

Ma )|dσdT|∆TR

ηR(2)

1460 Langmuir, Vol. 22, No. 4, 2006 Chang and VeleV

was immersed inside a small Petri dish (Millipore Co., Bedford,MA) containing 4.5 mL of FC-70 oil.

All experiments were performed with single floating dropletsentrapped by the electric fields from the energized electrodes below.Water droplets of 750 nL containing the microspheres were injectedonto the F-oil with a ultramicropipette (Eppendorf North AmericaInc., Westbury, NY). The setup allowed for both top-down and sideobservation of the captured droplets (Figure 1). To investigate thedroplet from the side view, the chip was placed in a rectangularchamber made from optical quality glass slides to avoid imagedistortion. A SZ61 0.7-4.5× zoom stereomicroscope (OlympusAmerica Inc., Melville, NY) was set for top-down or side observationof the floating droplets by changing the configuration of themicroscope. Images of droplets were taken with DSC-V1 Cyber-Shot digital camera (Sony, Japan) attached to the microscope. AnOlympus BX-61 optical microscope (Olympus America Inc.,Melville, NY) and high-resolution DP70 digital CCD camera(Olympus America Inc., Melville, NY) were used for characterizingthe droplet geometry and measuring the flow velocity inside thesuspended droplet with a top-down view. The three-dimensionaldistribution of the particles in evaporating droplets containing 0.2wt % of 1 µm fluorescent latex was characterized by confocalmicroscopy using the FV 300 scanner of the Olympus BX-61 system.

Measurement of Droplet Size and Volume.The water dropletis of intermediate density between F-oil and air and assumes anequilibrium position at the oil-air interface. Most of it was immersedin the oil, while a small portion at the top was exposed to ambientair. The boundary of the droplet at the three-phase contact line hada smooth profile because of the equal balance between the surfacetension at the water-air interface and the sum of the tensions at theother two interfaces (σwater-air ) 72 mN/m,σwater-oil ) 53 mN/m,σoil-air ) 19 mN/m).23 The distortion of the droplet shape by gravitycan be estimated from the Bond number, Bo, which is the ratio ofthe gravitational force to the surface tension force

where∆F is the density difference between the droplet and thesurrounding liquid.23,32,33,48For values of Bo, 1, the effect of gravitycan be neglected and the droplet is strictly spherical. Drops (750 nL)were micropipetted onto the chip, and the droplet has initially a∼1.1 mm diameter. Using that value, we estimate a Bond number,Bo∼ 0.05. Thus, the droplet maintains a spherical shape unperturbedby gravity during drying; the curvature of the water-air interfaceis larger than the one of the water-oil interface, but its effect onthe distortion of the total droplet shape was also estimated to be

small.49 The droplet diameter (Dd) and water/oil/air contact linediameter (Dc) were continuously measured by monitoring the dropletfrom the top with the BX-61 microscope (Figure 2).

Measurement of Internal-Flow Velocity. We used a micro-particle tracer method to measure the internal-flow velocity in anevaporating droplet. The velocity of 1µm tracer particles (0.002 wt% in the water droplet) was measured at the depth of 50 and 100µm from the droplet apex and at the bottom of the droplet. Thevertical position of the focal plane was adjusted using the scale ofthe motorized microscope stage. The particle velocity was calculatedby measuring the time during which the particles crossed the opposingboundaries of the 112× 112µm square spot imaged by the DP70-BSW software. To prevent the floating droplet from swaying becauseof air currents in the laboratory, the chip was shielded with atransparent enclosure.

Numerical Simulation. The temperature distribution and con-vective flow profile inside evaporating droplets were simulated with2D heat and momentum transfer calculations using the FEMLABMultiphysics finite element method modeling package (COMSOL,Inc., Burlington, MA). Experimentally measured time-dependentvalues for the diameter (Dd) and vertical position (z) of the floatingdroplet were used in the specification of the geometry of the system.The solution space was divided into two subdomains: the evaporatingdroplet and surrounding F-oil. The values of the physical propertiesof water and F-oil used are listed in the Supporting Information. Aconformal triangular mesh was generated by the software for eachof the two subdomains. The stationary nonlinear solver package wasthen used to solve for the temperature distributions and flow profilesfor all elements.

3. Experimental Results

Effect of Water Evaporation on the Vertical Separationof Microspheres.The dielectrophoretic liquid-liquid chip wasopen to the ambient air in these experiments to allow theevaporation of water from the droplets. The evaporation takesplace at the top water-air interface as the droplet floats at theF-oil surface. Sequential images from the microscope focusedon the top surface of an evaporating water droplet on F-oil areshown in Figure 3. Two concurrent effects were seen. First, thedrop radius decreased with time because of evaporation.Simultaneously, the particles dispersed in the liquid becameaccumulated in the top region as seen by the white-colored capof concentrated particles growing at the top section of the droplet.The continued flotation of the droplet containing microspheres

(48) Princen, H. M. InSurface and Colloid Science; Matijevic, E., Ed.; Wiley:New York, 1969; Vol. 2, pp 1-84.

(49) de Gennes, P.; Brochard-Wyart, F.; Que´ré, D. Capillarity and WettingPhenomena: Drops, Bubbles, Pearls, WaVes; Springer: New York, 2004; pp33-67.

Figure 1. Schematic of the experimental setup. A single floatingdroplet is entrapped by the electric field from the energized electrodebelow. The particle position within the drying droplet can bemonitored with a top-down or side microscope equipped with adigital camera. The droplet and components are not to scale.

Bo ) ∆FgR2

σ(4)

Figure 2. Geometry of aqueous droplet floating on F-oil.Dc )diameter of contact line.Dd ) diameter of droplet.H ) distancefrom the apex to the three-phase contact line of the droplet.

EVaporation-Induced Particle Microseparations Langmuir, Vol. 22, No. 4, 20061461

resulted in the latex particles organizing in a colloidal crystal,much like in the supraparticles studied previously.12

The particle collection process in the top section of theevaporating droplet was remarkably rapid. Naturally, as the waterevaporates leaving behind the suspended particles, some mi-crospheres should be accumulated in the droplet top. However,experimental evidence pointed out that the particles collected inthe apex have been drawn out from within the whole droplet vol-ume. The 3D reconstruction of the confocal images in an evap-orating droplet containing 0.2 wt % fluorescent latex proves thatthe majority of the particles in this diluted system have beenaccumulated in the apex of the droplet, while almost no micro-spheres remain dispersed in the bulk. These results demon-strating the 3D particle distribution within a droplet are avail-able as Supplementary Movie 1 provided in the SupportingInformation.

To investigate the particle dynamics inside droplets in theabsence of evaporation, the liquid-liquid chip was kept in atightly sealed chamber saturated with water vapor. During thisexperiment, the droplet volume did not change (data not shown),and no noticeable evaporation occurred. Sedimentation of thelatex particles in the bottom region of the droplet was observed,while no particles were collected on the top section (Figure 4).Thus, water evaporation from the droplet surface is the majorfactor that overcomes sedimentation and makes the microspheresmigrate and recollect in the top part of the droplets.

Finally, we proved that evaporation is able to draw to the topeven particles sedimented to the bottom of the droplet. In these

experiments, after all suspended latex particles had sedimentedto the bottom, the sealing cap was removed to allow waterevaporation on the top surface of the droplet. The movement ofthe particles was continuously observed while changing the focalplane of the microscope (Figure 5). The latex microspheres thathad accumulated near the bottom of the droplet in the absenceof evaporation began directionally moving toward the top regionof the droplet along one side of the interface between the waterand F-oil. After some time, latex particles began to be concentratedbelow the top surface of the droplet, where the water evaporationwas taking place. These observations suggest that the strongparticle collection process within the evaporating droplet wasrelated to internal liquid flows, which were also caused by thewater evaporation. The fluid fluxes inside the droplets wereinvestigated in the next cycle of experiments to better characterizethe process.

Figure 3. Typical micrographs of an evaporating droplet from a top-down perspective. (a) 10 min after floating on the F-oil surface, (b)20 min, and (c) 40 min. The original droplet contains 4.1 wt % of 4.9µm polystyrene microspheres in DI water. As the water evaporates,the particles are collected in the droplet top. The scale in the images is superimposed by the microscope optics (10 div.) 210 µm).

Figure 4. Typical image of the contents of nonevaporating waterdroplet from a side perspective. The droplet contains 0.41 wt % of4.9µm polystyrene microspheres in DI water, which have sedimentedto the bottom after 45 min of the experiment. Scale bar) 200µm.

Figure 5. Experimental images of particle collection on the top ofthe droplet when the cap was opened to allow water evaporation.(a) Before the evaporation begins, the particles have sedimented onthe bottom (microscope focused on the bottom of the droplet); (b)15 min after evaporation, the particle slug begins moving up alongthe droplet surface (microscope focused on the bottom of the droplet);(c) 15 min after evaporation (microscope focused on the top of thedroplet); (d) 60 min after evaporation, some particles are collectedin the top section (microscope focused on the top of the droplet).The original droplet contains 0.41 wt % of 4.9µm polystyrenemicrospheres in DI water. The scale in the images is superimposedby the microscope optics (10 div.) 210 µm).


Internal Flow within an Evaporating Droplet. In the ex-periments described above, we recognized that the water evap-oration from the floating droplet played a key role in microsepa-ration of colloid particles into the top section of the droplet. Theevaporation is coupled with internal flows in the droplets. Thegoal of the next series of experiments was to identify the flowpattern, recognize the mechanism responsible for the emergenceof the flow, and correlate the microseparation of particles to thehydrodynamic flows within the evaporating droplet.

The internal flow profiles were visualized with rodlikemicroparticles as a tracer suspended within the evaporatingdroplet. The advantage of using microrods is that they immediatelybecome aligned so that their long axis point in the direction ofthe flow.46 A circular one-directional hydrodynamic flow wasobserved inside evaporating droplets floating on the F-oil surface(Figure 6, see also Supporting Movies 2 and 3 in the SupportingInformation). The internal fluid circulation continued for periodsof tens of minutes to a few hours; however, as the size of thedroplet decreased because of the water evaporation, the circularflow eventually stopped.

A cycle of experiments were performed to characterize indepth the evolution of the internal flow during the dropletevaporation process. Water droplets (750 nL) containing 1µmpolystyrene latex particles as tracers (0.002 wt %) were floated

on the F-oil. The droplet volume change and the velocity of theinternal flow were measured over time for two experimentalconditions (1) relative humidity (RH) of 55% and temperatureof 23°C and (2) RH of 51% and temperature of 28°C. The datafor the normalized volumes of the droplets, defined as the ratioof the droplet volume at the specific time (Vt) to the initial dropletvolume (V0), are plotted in Figure 7. As expected, the dropletvolume decreased more rapidly in the second experimental cycle,because of the higher evaporation rate at a lower RH and higherambient temperature.

The flow velocities inside the same droplets were measuredwith the help of tracer particles. Data for three vertical positionsof the measurement plane were collected by adjusting themicroscope focus along the center axis of the floating dropletat a distance of 50µm (Vtop-50) and 100µm (Vtop-100) from theapex of the droplet and near the droplet bottom surface (Vbottom).The flow directions at the bottom and at the top sections wereopposite because of the circular flow within the droplet. In bothexperimental conditions, the flow velocity was faster at the bottomof the droplet than at the top region. Within the top region, thevelocity near the air-water interface is much slower (Vtop-50 <Vtop-100). As the water evaporation progressed, the liquid velocitygradually decreased and abruptly stopped at a smaller dropletsize.

The data for all velocity measurements are summarized inFigure 8. In the same figure, we also plot the time dependenceof the evaporation rate (m̆) of the droplet

wheremis the mass of the droplet,V is the volume of the droplet,Fwateris the density of water, andt is the time. The data demonstratea good correlation between the evaporation rate and fluid velocityin the droplet, because the tracer particle velocity was also fasterat the high evaporation rate. The fluid flow, however, stoppedafter the evaporation rate decreased to a certain point.

The combined results of the particle collection, dropletevaporation, and particle velocity measurements allow forextending a model for the processes that take place inside thedroplets. The experiments point out that the evaporation processis critical both for the collection of particles and for mixing thecontents of the droplets. The evaporation of the water at the capopen to the air decreases the local temperature because of thelatent heat of vaporization. A temperature gradient is generated

Figure 6. Typical experimental images of the internal flow in theevaporating water droplet viewed from aside. The image in b istaken after a 90° change in perspective from a. The tracers are polymermicrorods synthesized by a technique reported by us earlier.46,47Thecamera exposure time was 2 s. Scale bar) 200 µm. Moviesdemonstrating particle circulation within similar droplets are availablein the Supporting Information.

Figure 7. Change in the volume of 750 nL droplets with timebecause of evaporation.V0 ) initial droplet volume.Vt ) dropletvolume at the specific time.

m̆ ) - dmdt

) -Fwater(dVdt ) (5)


within the evaporating droplet because of the heat loss at the top.Two possible effects leading to fluid circulation as a result ofthe vertical temperature gradient can be suggested. The first oneoriginates from the resulting gradient of the interfacial tension.The interfacial tension gradient is engendered as a result of thesurface tensiondependenceon temperature.The interfacial tensionwould be higher at the colder top surface of the droplet. Thesurface tension gradient “pulls” the droplet surface toward regionsof higher surface tension. Consequently, convective Marangoniflow inside the droplet is created by momentum transfer into theinterior of the droplet by the viscous friction.

The second possible reason for the emergence of convectiveflow within an evaporating droplet, described in section 1, is thedependence of liquid density on the temperature. The relativeimportance of these two effects, Marangoni flow and density-driven (Rayleigh) flow can be estimated from the ratio of theMarangoni number/Rayleigh number (eq 3). For our dryingaqueous droplet, we estimate Ma/Ra∼ 150 (the numerical valuesof the parameters used and their sources are listed in the SupportingInformation). As Ma/Ra. 1, we assume that the Marangonieffect is the dominant origin of the convective flow inside ourdroplets.

The schematic of the mechanism by which the evaporationleads to the vertical microseparation of the suspended particlesin our droplet is shown in Figure 9. The particles in the vicinityof the top air-water interface are entrained and transported to

the surface by the normal flux of water compensating for theevaporation. As mentioned in the Introduction, evaporation-drivenparticle transport and assembly have been found to be the basisof other types of colloidal assembly processes.13-21 In addition,as a result of the evaporation process, the circular Marangoni-driven flow inside the evaporating droplet makes possible thecontinuous mixing and transport of the particles into the topportion of the droplet. Once the particles from the bulk aretransported near the region of the water evaporation on the topsurface, the internal hydrodynamic replacement flux of waterbecause of the evaporation sucks them into the growing particlecrystal in the top. The smaller velocity of the tracer particles atthe top of the droplet (Figure 8) can be explained by thecompensating evaporation outflux as well as the no-slip conditionat the slug of closely packed particles collected at the surface.The convection inside the evaporating droplet plays a key rolein the transport of the suspended particles, and thus, their collectionin the top portion can occur without complete evaporation of allof the solvent. In the next section, we demonstrate that numericalsimulations of the heat and momentum transfer processes insideevaporating droplets based on this model are in good agreementwith the experimental evidence.

4. Simulation of Temperature Distribution and FlowProfile

The mechanism by which the thermal gradient inside our dryingdroplet leads to the emergence of convective flow was studiedin detail by numerical simulations. We developed a procedurefor calculating the temperature distribution and the flow profilewithin an evaporating droplet floating on F-oil. The flow profilesand temperature distributions were calculated in the vertical cross-section (2D geometry) of the water droplet and F-oil layer in asmall dish (Figure 10a) by numerical solutions of the continuity,Navier-Stokes, and energy-balance equations using FEMLABsoftware

whereV is the velocity vector,P is the pressure,ν is the kinematicviscosity, andR is the thermal diffusivity.

The evaporation of the droplet is a nonequilibrium process,because the volume and temperature of the droplet and theevaporation rate keep changing continuously. To simplify theanalysis, a quasi-steady approximation was used. The charac-teristic time of heat diffusion in our droplet (R2/R) is 2 ordersof magnitude smaller than the characteristic time of droplet surfacecompression because of evaporation (R/Ṙ, Ṙ is rate of decreaseof the radius of the droplet). Because the thermal instabilitiesarise at the initial stage of evaporation, the decrease of the dropletdiameter can be neglected during a short interval of interest.30

In addition, it was assumed that the physical properties of theliquid domains, except the surface tension, remain constant duringthis period.

The geometry of the system specified is plotted in Figure 10a.The boundary conditions used in the simulation are as follows:

Top Water/Air Interface of the Droplet. The particlessuspended in the droplets were collected in a close-packed crystalon the water side of this surface. We also observed in theexperiments that the top layer of particles was adsorbed at the

Figure 8. Flow velocity and evaporation rate measured with floatingdroplets. (a) Data at 55% relative humidity and 23°C, (b) Data at51% relative humidity and 28°C. Vtop-50 ) velocity at 50µm downfrom the apex of droplet.Vtop-100) velocity at 100µm from the apexof droplet.Vbottom ) velocity at the bottom of droplet. The tracerparticles are 0.002 wt % of 1µm polystyrene microspheres in DIwater. The data were fitted to decaying exponential functions.

∇‚V ) 0 (6)∂V∂t

+ V‚∇V + 1F∇P ) ν∇2V (7)

∂T∂t

+ V‚∇T ) R∇2T (8)


interface. Thus, because of the immobilization of the top surfaceby closely packed particles, the boundary condition can besimplified by assuming that there is no tangential fluid slip. Thethermal boundary condition at this surface was a balance betweenthe conduction and the sum of natural heat convection and heatoutflux because of the evaporative mass transport,

wherekwater denotes the thermal conductivity of water,h is thenatural heat transfer coefficient,hl is the latent heat of vaporizationfor water, JE is evaporation mass flux, andn is unit normal

vector of the surface. The evaporation mass flux was calculatedfrom the measured evaporation rate (eq 5) divided by the surfacearea of the top region of the droplet (2πRH, whereR is the radiusof the droplet andH is the distance from the apex to the three-phase contact line of the droplet, Figure 2). The natural heattransfer coefficient,h, is derived from the Nusselt number, Nu∼ 2, approximated for natural convection over a sphericaldroplet,28,50

wherekair is the thermal conductivity of the surrounding air,(0.026 J m-1 s-1 K-1 atT ) 23°C) andD0 is the initial diameterof the droplet.

Water/F-oil Interface of the Droplet. The viscous shearstresses balance the surface tension gradient in the tangentialdirection at the interface. The conductive heat balance acrossthe water-oil interface was used as the thermal boundarycondition,

whereτwateris the shear stress at the water surface,τoil is the shearstress at the oil surface,t is unit tangential vector of the surface,andkoil is the thermal conductivity of F-oil. The interfacial tensiongradient∇σ is coupled to the temperature gradient by eq 1.

F-oil/Air Interface. The boundary conditions were a balanceof viscous forces with surface shear forces because of the surfacetension gradient and the conductive heat balance along the planesurface contacting the ambient air,

Surface of Contact between F-oil and the Vessel.Theboundary conditions were a no-slip condition for the velocity,V ) 0, andT) T∞, whereT∞ is the uniform ambient temperature.

Simulation Results and Correlation with ExperimentalData. The computed temperature distribution and velocity fieldin the evaporating floating droplets after 15 min at RH of 51%and an ambient temperature of 23°C are shown in Figure 10b.A vertical temperature gradient is established inside the systembecause of water evaporation at the top droplet surface. The

(50) Yang, W.Lett. Heat Mass Transfer1978, 5, 151-166.

Figure 9. Schematics of the proposed mechanism of circulation and particle microseparations in evaporating droplets.

Figure 10. Simulation for the temperature distribution and velocityprofile in the drying droplet using FEMLAB. (a) Schematic of thegeometry specified (dimensions are not to scale). (b) Computedtemperature distribution and velocity profile inside the droplet after15 min of drying for the system with a relative humidity of 55% andan ambient temperature of 23°C. The velocity vector magnitudesare represented by the lengths of the arrows. Colors show thetemperature. The results confirm the emergence of circular flowinside the system.

V ) 0 (9)

-kwater∇T‚n ) h(T - T∞) + hlJE (10)

h )2kairD0

(11)

τoil - τwater) ∇σoil/water‚t (12)-kwater∇T‚n ) - koil∇T‚n (13)

τoil - τair ) ∇σoil/air‚t (14)-koil∇T‚n ) -kair∇T‚n (15)


resulting interfacial tension gradient along the droplet surfaceinitiates Marangoni flows in both the water and oil and a self-sustaining convective flow within the droplet. The velocity vectorsin the droplet show the presence of a convective flow with aone-directional vortex, which is in a good agreement with theexperimental flow profile observed in real droplets (Figure 6 andSupporting Movie 2). The flow is centrosymmetric; interestingly,the direction of the circular flow in the numerical solutions(clockwise or anticlockwise) varies with changes in the size ofthe triangulation grid parameters in the FEMLAB simulator.Changing the grid size introduces small differences in the initialconditions that make the computation converge on one solutionor the other. Both solutions, however, have a similar flow pattern;i.e., the change of the grid size changes the direction of flow butnot the flow pattern. The existence of two symmetric solutionsshould be expected because there is no experimental evidenceor other reason for the liquid in the simulation to circulate in apreferred direction. The magnitude of the flow velocity, asdetermined by the length of the vectors, is higher at the bottomthan at the top region of the evaporating droplet as also seen inthe experimental data in Figure 8.

Numerical simulations matching the two experimental condi-tions studied were performed at increasing evaporation times tocheck to what extent the simulation could explain the decreasein the fluid velocity and the cessation of the flow at the lateststages of the process. These calculations were based onexperimental data for the decreasing droplet size and evaporationrate. The diameters (Dd) and vertical positions (z) of the dropletsubdomain in the FEMLAB geometry were set to the experi-mentally measured values at the specific drying times. The valuesof the evaporation mass flux,JE, in eq 10 were also provided byexperimental data. The temperature distributions inside the dryingdroplets computed with FEMLAB are shown in Figure 11.

The simulations show how, as the evaporation progresses, thesmaller droplet size and the decrease in the evaporation ratesuppress the temperature gradient at both experimental conditions.The initial temperature difference in the droplet is much largerat the higher evaporation rate. However, the diameter and thetemperature gradient in the droplet with the higher evaporationrate decrease much faster, in agreement with the experimentaldata.

We now interpret the experimentally measured flow velocitiesin the framework of the above simulation results. The fluid inside

each droplet will circulate as long as the Marangoni number,Ma, is above the critical Mac. The intensity of the circulationflow inside the droplets can be estimated by comparing their Ma.At RH of 55% and 23°C after 15 min of drying, the temperaturedifference,∆T, within the droplet is 0.61°C from the simulationand Ma (eq 2) is calculated as 223. At RH of 51% and 28°Cafter 10 min of drying, the numerical simulation showed∆T )1.63°C and Ma) 750. Both Marangoni numbers are larger thanthe critical Marangoni number, Mac. The evaporative mass andheat transport in the droplet lead to a convective Marangoni-driven flow. The magnitude of Marangoni flow velocity isdependent upon the magnitude of the thermal differential. Ahigher value of Ma indicates that the system has a tendency forfaster flow velocity. Indeed, in the experiments, we measuredhigher initial fluid velocity in the droplet at RH of 51% and28 °C.

The convective fluid motion inside evaporating droplets stopsabruptly at the moment when Ma< Mac. The moment when thecirculation stopped was reached faster at RH of 51% and 28°C,even though the flow velocity in these droplets at the early stageof the evaporation was much higher (Figure 8). This is expected,because the higher evaporation generates a higher initialtemperature gradient and faster circulation; however, the dropletsize also decreases faster, suppressing the temperature differentialbetween top and bottom (Figure 11). We estimated the criticalMarangoni numbers on the basis of the calculated temperaturegradient and the experimental data for size, evaporation flux,and liquid velocity at which the convective flows in the dropletsstopped. For both experimental conditions, the critical Marangoninumbers were Mac ∼ 20. These values are similar to the criticalMarangoni number at which the first flow cell emerges in aliquid film with a temperature gradient along the fluid surface.35,36

Although the geometry of our system is different, we believethat that the similarity of the critical Marangoni numbers isreasonable.

The results obtained from the FEMLAB simulation confirmour hypothesis that the convective fluid motion inside smalldrying droplets is driven by the temperature gradient createdfrom water evaporation at the top surface. The restriction of thissimulation to 2D systems is dictated by the limitations of thesoftware and processing power. In effect, the simulation is validfor a liquid cylinder rather than a 3D sphere, and the velocitiesand temperatures calculated will not be accurate for the real

Figure 11. Simulation results for the temperature distribution in droplets at increasing drying times. (a) Relative humidity of 55% and ambienttemperature of 23°C. (b) Relative humidity of 51% and ambient temperature of 28°C.


system. Nevertheless, we were able to establish a good semi-quantitative correlation between the numerical simulation resultsand the experimental data. We believe that the simulation captureswell the physics of the process and supports the model ofcirculation driven by a temperature gradient across the droplet.

The phenomenon of a convective flow generation is concep-tually related to the earlier research on the fluid flow in theevaporating sessile or spherical droplet.19,26-30 One differencebetween the flows that we have observed and simulated in thefloating droplets and the flows reported in sessile droplets is thatin our system the flow is in the form of one large flow cell,instead of a being axisymmetric with respect to the vertical axisof the droplet. The nonaxisymmetric flow pattern in our floatingdroplet can be explained with the dependence of interfacial-driven flow patterns on the aspect ratio (AR) of the fluidcontainer.38,39One-directional convective flow has been observedfor systems with AR∼ 1,40-42 which is also the case of ourdroplets.

We did not observe axisymmetric flows experimentally, butsuch flows are possible under certain conditions. For example,to understand the effect of the particle layer immobilizing thetop surface, we preformed numerical simulations for a dropletwith a particle-free surface with a Marangoni stress boundarycondition similar to eq 12. The results are shown in SupplementaryFigure 1 of the Supporting Information. The simulation pointsto the initial formation of two vortices, which are plane-symmetricin the 2D simulation. The plane of symmetry, however, is skewedto one side, because the coldest point is not on top of the dropletbut on the side opposite to where warm liquid is delivered bythe internal flow. It is difficult to observe the top vortexexperimentally, because that part of the droplet is obscured bythe meniscus, but observations from above showed that the liquidon top of freshly deposited droplets indeed moves in one direction,while the liquid below moves in another direction (SupplementaryMovie 4). The situation changes significantly when the top sur-face becomes immobilized by the layer of collected particle. Thelack of top-surface mobility seems to suppress the top vortex,leaving only one large vortex in the droplet. The result is thecentrosymmetric pattern observed experimentally and in thesimulations reported in Figure 10. The system “self-organizes”by misbalancing the stresses and coupling them to flows.

5. Potential Applications

A variety of potential technological applications of the effectsdescribed here can be foreseen. The vertical distribution andmicroseparations of small particles suspended in the evaporatingdroplets can be useful in diverse droplet-based microfluidicsystems. One possible application area is the on-chip synthesisof advanced particles from mixed particle suspensions. Our earlierwork demonstrated how various anisotropic “supraparticles” fromgold nanoparticles, silica spheres, latex particles, and polymerscan be synthesized in droplets on a chip.12 The one-directionalcircular flow in the evaporating droplet can be used in alternativestrategies for mixing in microfluidic systems. Mixing inconventional microfluidic systems is a challenge because of thelow Reynolds numbers of the liquid flow in microfluidicchannels.1,4,51 The circular flow inside our droplet, combinedwith the no-slip condition on the particle-blocked top surface,may prove helpful for mixing in various chemical reactions andmaterial synthesis processes.52

We demonstrate here a new microbioassay technique as anapplication directly based on the internal separation of particles

within droplets on a chip. As a proof of that concept, evaporatingdroplets were used for on-chip detection of antibody-antigenbinding (Figure 12). The method is based on a common particleagglutination assay.53 Two different types of 1µL droplets weredeposited on the F-oil, held by the electric field, and observed.Both droplets contained 0.01 M phosphate-buffered saline (PBS)solution with 0.2 mg/mL bovine serum albumin (BSA). Thecontrol droplet contained a dispersion of 3 wt % 1µm latexparticles coated with anti-rabbit immunoglobulin (IgG) and 0.02wt % 40 nm gold nanoparticles coated with anti-rabbit IgG. Thetest droplet contained the same suspension of both types of colloidsplus 10µg/mL rabbit IgG (the antigen for the IgG on the particles).The suspensions were incubated for 15 min before droplets weredeposited on the chip and observed during drying.

As the droplets began to dry, a dark gold nanoparticle “eyeball”spot appeared on the top surface of the negative control dropletwithout rabbit IgG (Figure 12a). The gold nanoparticles in thedroplet with rabbit IgG, however, were not visible on the surface(Figure 12b). The reason is that the gold nanoparticles in the testdroplet bind to the surface of the larger latex particles becauseof the antibody-antigen IgG interaction, forming as a result ofthe agglutination process large clusters seen by higher magni-fication microscopy (Figure 12d). The gold nanoparticles in thenegative control droplet on the other hand do not agglutinate andremain freely dispersed (Figure 12c). The agglutinated goldnanoparticles in the test droplet cannot pass through the interstices

(51) Purcell, E. M.Am. J. Phys.1977, 45, 3-11.

(52) Brody, J. P.; Yager, P.; Goldstein, R. E.; Austin, R. H.Biophys. J.1996,71, 3430-3441.

(53) Kasahara, Y. InImmunochemical Assays and Biosensor Technology forthe 1990s; Nakamura, R. M.; Kasahara, Y.; Rechnitz, G. A., Eds.; AmericanSociety for Microbiology: Washington, DC, 1992; pp 127-147.

(54) Holman, J. P.Heat Transfer, 7th ed.; McGraw-Hill, Inc.: U.K., 1992.(55) Savino, R.; Monti, R.; Alterio, G.Phys. Fluids2001, 13, 1513-1516.

Figure 12. Typical experimental images of a microbioassay wherethe results are detected on the basis of particle separations insideevaporating droplets on a chip. Both droplets contain a binarysuspension of 3 wt % 1µm anti-rabbit IgG-coated latex particlesand 0.02 wt % 40 nm anti-rabbit IgG-coated gold nanoparticles. (a)Negative control droplet after 30 min of drying. (b) Test dropletwhere 10µg/mL of antibody (rabbit-IgG) is added after 30 min ofdrying. (c) Optical micrograph of the same mixture as a, illustratingthat the particles remain dispersed. (d) Optical micrograph of samemixture as b, proving that the agglutination has bound them in gold-latex clusters. Scale bars: (a and b) 200µm and (c and d) 20µm.


between the latex particles collected on the top section of thedroplet, while the unbound free nanoparticles in the negativecontrol droplet are dragged to the surface and form the darkerring seen in Figure 12a. Thus, the process of microseparationinside the droplets allows direct and easy distinguishing of theaggregation state of the suspended particles affected by bio-molecular binding. The droplet microseparation phenomena maythus enable the development of novel microfluidic techniquesfor highly sensitive, high-throughput biological microassays. Amore detailed characterization of these miscrobioassays is underway and will be presented elsewhere.

6. Conclusions

We present a detailed investigation of vertical particlemicroseparations and a mechanism of flow generation withinevaporating small droplets floating in denser oil. The majorcontribution of this work is obtaining experimental data for thetransport of particles and liquid inside these freely suspendedmicrodroplets. The data were obtained by the use of ourdielectrophoretic liquid-liquid chip as an experimental tool forcontinuous monitoring of mass transfer in floating droplets. Thephenomena observed were explained as a result of a series ofprocesses driven by the mass and heat transfer in the evaporatingdroplet. The internal circulation is driven by Marangoniinstabilities. The FEMLAB simulation for hydrodynamic flowsinside the droplet was in a good correlation with the experimentalobservations. These results present a beautiful illustration of asystem with self-organizing dissipative structures. The circulationhelps transport the particles to the top surface, where they are

captured by the evaporation outflux and separated in a close-packed phase.

The mechanism of vertical redistribution of particles suspendedin the droplet allows controlling particle separations on themicroscale with a change of relative humidity, ambient tem-perature, and volatility of the liquid in the droplet. Thismicroseparation technique has potential in various “microdropletengineering” processes, as we demonstrated earlier by the directedsynthesis of novel structured particles12 and presently with thedevelopment of a new microbioassay technique using theevaporation as a means of detection. Such processes can findapplication in lab-on-a-chip devices for microsyntheis, micro-assays, manipulation and analysis of single cells, and others.

Acknowledgment. We are grateful to Ketan Bhatt and BrianPrevo for performing the confocal microscopy experiments andto Dr. Rossitza Alargova for preparing the polymer microrodsused as tracers. This study was supported by CAREER and NERgrants from the National Science Foundation.

Supporting Information Available: Movies (in AVI format)of the 3D reconstruction by confocal microscopy of particle collectionon the top of an evaporating droplet, the circular flow in a dropletviewed from the side and from above, and the flow in a droplet viewedfrom above before particles are collected to immobilize the surface.Numerical simulation of the flow patterns in a droplet with particle-freewater/air surface. Table with the values of the physical properties ofwater and F-oil used in the simulations. This material is available freeof charge via the Internet at http://pubs.acs.org.

LA052695T


evaporation-induced particle microseparations inside droplets floating...

Documents