Dynamics of Electrically Modulated Colloidal Droplet Transport

Sep 30, 2015 - Electrically actuated transport dynamics of colloidal droplets, on a hydrophobic dielectric film covering an array of electrodes, is st...
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Dynamics of Electrically Modulated Colloidal Droplet Transport Ranabir Dey,† Udita Uday Ghosh,‡ Suman Chakraborty,† and Sunando DasGupta*,‡ †

Department of Mechanical Engineering and ‡Department of Chemical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India S Supporting Information *

ABSTRACT: Electrically actuated transport dynamics of colloidal droplets, on a hydrophobic dielectric film covering an array of electrodes, is studied here. Specifically, the effects of the size and electrical properties (zeta-potential) of the colloidal particles on such transport characteristics are investigated. For the colloidal droplets, the application of an electrical voltage leads to additional attenuation of the local dielectric-droplet interfacial tension. This is due to the electrically triggered enhanced colloidal particle adsorption at the dielectric-droplet interface, in the immediate vicinity of the droplet three-phase contact line (TPCL). The extent of such interfacial particle adsorption, and hence, the extent of the consequential reduction in the interfacial tension, is dictated by the combined effects of the three-phase contact line spreading, particle size, the interfacial electrostatic interaction between the colloidal particles (if charged) and the charged dielectric surface above the activated electrode, and the interparticle electrostatic repulsion. The electrical driving force of varying magnitude, stemming from this altered solid−liquid interfacial tension gradient in the presence of the colloidal particles, culminates in different droplet transport velocity and droplet transfer frequency for different colloidal droplets. We substantiate the inferences from our experimental results by a quasi-steady state force balance model for colloidal droplet transport. We believe that the present work will provide an accurate framework for determining the optimal design and operational parameters for digital microfluidic chips handling colloidal droplets, as encountered in a plethora of applications.

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INTRODUCTION Application of an electrical voltage to a conductive sessile droplet, resting on a dielectric film, culminates in electrostatic reduction of the droplet-dielectric interfacial energy, which manifests in spontaneous spreading of the droplet.1 Presently, the wettability gradient, emanating from such interplay of capillary and electrostatic phenomena, can be judiciously controlled by optimally designed array of planar electrodes to achieve efficient droplet transport.1−3 Electrocapillary-based actuation and transport of droplets constitute one of the major branches of digital microfluidics,1,4,5 and have triggered a technological paradigm shift in microscale thermal management,6 microscale mixing,7 and microscale chemical reactors,8 as well as in biomedical applications, especially rapid diagnostic tests.4,5,8,9 The majority of these applications, like immunoassays, point-of-care diagnostics, DNA-based applications, and microparticle collection and sampling, involve handling of droplets containing suspended micro/nanoparticles (e.g., synthetic particles - polystyrene latex beads; biological particles - proteins, spores, viral stimulants; metallic beads - antibody coated gold particles and paramagnetic beads).4,10−13 However, the electrocapillarity-induced transport dynamics of such colloidal droplets remains far from being well understood. Electrically actuated droplet motion is achieved on hydrophobic dielectric films by sequential activation of underlying, adjacent pairs of planar electrodes on a single open platform (open configuration), or in a microfluidic confinement where a © XXXX American Chemical Society

covering plate contains the ground electrode (closed configuration).4 The motion of a droplet resting on a dielectric film, with its footprint spanning at least over portions of two adjacent electrode pads, is triggered by the electrically induced reduction in the dielectric-droplet interfacial energy, on top of the activated electrode.1 Such electrically induced asymmetric change in the dielectric−droplet interfacial tension, and the consequential difference between the macroscopic droplet contact angle on top of the activated electrode (static advancing contact angle) and that on top of the nonactuated preceding electrode (static receding contact angle), results in a capillary force that imparts an initial momentum to the droplet.14−16 It is instructive to note here that the random pinning of the threephase contact line, by the surface microdefects, culminates in the existence of a minimum actuation voltage for initiating droplet motion by superseding the pinning-induced surface hysteresis.16,17 After the motion of the droplet is initiated, the viscous bending of the advancing droplet meniscus results in the increment of the advancing droplet contact angle.15,18 The difference between the variations of the velocity-dependent dynamic advancing contact angle and the dynamic receding contact angle generates a capillary force in the direction of the activated electrode.15,18 Such dynamic variations of the contact Received: May 27, 2015 Revised: September 24, 2015

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Figure 1. (a) Designs of the electrode-array and the individual electrode units. (b) The aluminum electrode-arrays fabricated on a glass slide by photolithography. (c) The experimental setup used for investigating the electrically modulated transport dynamics of colloidal droplets. The electrocapillary-based droplet actuator chip is shown in inset (i). Inset (ii) shows a sample (top-view) image captured by the high speed camera during a colloidal droplet transport, under an applied electrical voltage.

does not address the alterations in the transport dynamics caused by the modifications to the electrostatic and capillary interactions, over the solid−liquid interfacial scales, due to the presence of the colloidal particles. In the present work, we delineate the characteristic features of the transport dynamics of droplets of colloidal suspensions of micro/nanoparticles, under electrical actuation. We experimentally demonstrate that the presence of suspended particles significantly alters the displacement, instantaneous velocity, and acceleration characteristics of electrically actuated colloidal droplet motion over a hydrophobic dielectric film, from those perceived for droplets of only the base liquid. Interestingly, we show that the electrocapillarity-induced transport characteristics of colloidal droplets are intrinsically dependent on the size and the electrical properties of the suspended particles; specifically, such transport dynamics is dependent on the magnitude of the particle (negative) surface charge, as reflected by the magnitude of the associated particle ζ-potential. Furthermore, we attempt to substantiate our experimental inferences by an average velocity based quasi steady-state force balance model. This model, unlike the existing theoretical framework, coherently addresses the variations in droplet transport velocity, due to colloidal particle induced alterations in the solid−liquid interfacial electrocapillarity. We believe that the present endeavor will provide new physical insights into the electrically mediated transport mechanism for colloidal droplets, containing suspended micro/nanoparticles of varied sizes and electrical properties. Additionally, this work provides a methodology for accurate estimation of the important parameters, like average droplet transport velocity and maximum droplet transfer frequency, associated with the electrocapillarity-actuated colloidal droplet motion. Hence, the present research work will also provide an efficient design and operational paradigm for numerous digital microfluidic applications, which involve handling of colloidal droplets, like biomedical applications and material handling.

angles are associated with a continuous deformation of the droplet, in order to accommodate the consequential change in the drop contact area. During such droplet motion, the internal hydrodynamics of the droplet also generates a net viscous shear force on the droplet, at the dielectric−droplet interface.15,17,19 The other forces, resisting the droplet motion, include a viscous drag force due to the surrounding filler liquid (applicable only for the closed configuration), a friction force at the contact line, and a secondary viscous force due to the excitation of capillary waves along the droplet surface.14,15,17,19 The temporal evolution of the electrocapillarity-induced droplet transport dynamics is governed by the interplay of the aiding capillary force, and all the resisting friction forces, as discussed here.14,15,17−20 It must be also noted here that the average droplet transport velocity can be determined from a quasisteady state balance of these forces.14,20 However, the aforementioned description of the droplet transport dynamics is restricted to single-phase (liquid) droplets only, and does not apply to droplets of colloidal suspensions containing micro/ nanoparticles, as actually encountered in the vast majority of microfluidic applications. In general, the inclusion of micro/nanoparticles unilaterally alters the electrically modulated wetting characteristics of sessile drops, in comparison to that observed for the droplets of only the base liquid under identical conditions.21−23 It was shown that the presence of nanoparticles resulted in enhanced electrowetting of sessile droplets, under an applied DC electrical voltage.22,23 The particle induced enhanced electrowetting of sessile droplets was attributed to the additional reduction in the dielectric-droplet interfacial energy, due to nanoparticle adsorption at the solid−liquid interface.22 It must be further noted that the inclusion of micro/nanoparticles generally augments the advancing/receding contact line motion of a sessile droplet.24 Hence, on the basis of these recent findings, it can be conjectured that the electrocapillarityinduced transport dynamics of droplets of colloidal suspensions, containing micro/nanoparticles, will be different from that of the pure base liquid droplet, under identical conditions. Moreover, the essential features of such electrically induced colloidal droplet transport cannot be addressed within the existing physical framework (as discussed in the preceding paragraph). This is because the existing theoretical paradigm

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EXPERIMENTAL SECTION

Design and Fabrication of the Electrode Pads. The electrodearray, used for actuating the droplet, is designed using the AutoCAD software (v. 2007), as shown in Figure 1a. Each electrode unit consists of two interconnected pads - the bigger pad (a square having the dimensions of 1.4 mm × 1.4 mm) acts as the control electrode pad, B

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Langmuir while the smaller one (a square having the dimensions of 1 mm × 1 mm) acts as the connection pad for the external electrical connections. The distance between two adjacent control electrode pads is 80 μm. After completion of the design, the corresponding mask is fabricated on a 3-in. square glass blank by a laser pattern generator. For fabricating the electrodes, a cleaned glass slide is coated with aluminum by the thermal vapor deposition technique. The electrodearray is then fabricated on the aluminum-coated glass slide by photolithography, using a positive photoresist (S-1813) and the photomask. The glass chip containing the fabricated electrode-array is shown in Figure 1b. Fabrication of the Hydrophobic Dielectric Layer. Sylgard 184 (PDMS; Dow Corning, USA; dielectric constant, εr,S = 2.65) is used as the dielectric material due to its ease of availability and convenience in rapid prototyping. The prepolymer is prepared by mixing the base and the cross-linker in the weight ratio of 10:1. The degassed prepolymer is then poured over the electrode chip. During the pouring process, the connection-pads of the electrodes are covered with a strip of parafilm tape (Pachiney Plastic Packaging, USA), in order to keep these uncoated for completing subsequent electrical connections. Thereafter, the Sylgard 184 is spin-coated (spin coater: Süss MicroTec, Germany) on the electrode chip by following a two-step procedure: In the first step, the spin speed is maintained at 500 rpm for 30 s, while in the second step it is maintained at 5000 rpm for 70 s (intermediate acceleration: 4000 rpm/sec2). After spin -coating, the parafilm strip is removed, and the Sylgard 184 film is subsequently cured overnight at 95 °C. The Sylgard 184 film is further coated with an ultrathin layer of Teflon (3% w/w of amorphous fluoropolymer (Teflon AF 1600, DuPont) in FC-40 (Acros Organics, USA); dielectric constant, εr,T = 2.2). The Teflon solution is spin coated, on top of the cured Sylgard 184 film, at 3000 rpm for 30 s. Thereafter, the Teflon film is cured in two steps: first, at 110 °C for 10 min, and then at 175 °C for 25 min. The root-mean-square surface roughness (rrms) of the fabricated hydrophobic, insulating film is estimated to be 3.16 nm, by atomic force microscopy. For further characteristics of the hydrophobic dielectric film, see Table S1 in the Supporting Information. Experimental Setup. The schematic of the entire experimental setup is shown in Figure 1c, with a blow-up of the droplet actuator chip at the inset (Figure 1c(i)). The electrodes on the chip are connected to a PCB board by thin copper wires, which are attached to the connection-pads of the electrodes by conductive silver paste (Alfa Aesar: sheet resistance ts, thereby failing to exhibit continuous transport with sequential switching of the electrodes. For describing the electrically actuated droplet transport dynamics, we choose here only those values of V (beyond Vmin) at which the droplets undergo repeatable, continuous transfers, as demonstrated by the displacement (d) versus time (t) characteristics over three consecutive transfers, at 250 and 275 V (see Figure 3a), for the 100 mM KCl drop. The temporal variations of the instantaneous velocity (u), over a single transfer, and the resulting maximum droplet transfer frequencies (f tr), at varying magnitude of V beyond Vmin, are shown in Figure 3b. Here, for the sake of generality, the instantaneous velocity is presented in a nondimensional form as u̅ = u/uref, where uref = L/ts = 0.636 mm/s; while the nondimensional time is defined as t ̅ = t/ts(ts = (1/fs) = 2.325 s).

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RESULTS AND DISCUSSION The first step is to establish a control study for easier comprehension of the effects of inclusion of suspended micro/ nanoparticles on the electrically actuated transport dynamics of microliter drops. To this end, the transport characteristics of a 100 mM KCl droplet, at varying magnitudes of V, are first shown in Figure 3. It must be first noted here that the displacement of the droplet, albeit culminating in an incomplete transfer, is first observed at a definite magnitude of the applied electrical voltage. This threshold voltage, at which the droplet just begins to move, is the hysteresis-induced minimum actuation voltage (Vmin).16,17,19,20 The approximate value of Vmin for each type of colloidal droplet, used in the present study, is independently evaluated by gradually increasing V in steps of 5 V until the droplet starts moving. D

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Figure 5. Variations in the maximum droplet transfer frequency, at different magnitudes of the nondimensional electrowetting number η, (a) for the 100 mM KCl droplet, droplets of colloidal suspensions (DCS) containing neutral polystyrene particles of different sizes and the colloidal droplet containing negatively charged particles, and (b) for colloidal droplets containing negatively charged particles of identical size, but having varying magnitude of the ζ-potential.

Moreover, due to the greater initial acceleration, the colloidal droplet attains this higher peak velocity (or equivalently, zero acceleration) within a shorter time interval, than that required by the 100 mM KCl droplet (see inset in Figure 4a; DCS attains the peak velocity, corresponding to a̅ = 0, within 57.28% less time at η = 0.82). After the attainment of the peak velocity, the colloidal droplet decelerates faster (see the inset), and hence, the transport velocity decreases at a faster rate, as compared to the 100 mM KCL droplet. However, beyond a threshold, the deceleration gets arrested. Eventually, the retardation becomes asymptotically zero (see inset in Figure 4a), and accordingly, the droplets attain a dynamic quasiequilibrium state with an asymptotically reducing velocity (see Figure 4a). However, the overall velocity and acceleration characteristics for DCS containing neutral particles of dp = 1.1 μm culminate in comparatively smaller droplet transfer time (ttr). This consequently results in higher average droplet transport velocity (uavg) and greater maximum droplet transfer frequency ( f tr) (see Figure 5a), as compared to the 100 mM KCl droplet. Figure 4a also shows the temporal variation of u̅ for drops of a colloidal suspension containing neutral polystyrene particles of a smaller size (dp = 0.055 μm), but with the same particle weight fraction ϕ = 0.01. At a definite magnitude of η, the presence of smaller neutral particles results in higher peak velocity during droplet transfer, and smaller ttr, as compared to those for the colloidal drop containing bigger neutral particles (dp = 1.1 μm) (see Figure 4a). Accordingly, DCS containing smaller sized particles exhibits greater values of uavg and f tr (see Figure 5a), than those for the colloidal drop containing bigger particles, for the same magnitude of η. Effects of Surface Charge on Colloidal Particles. Figure 4a further pinpoints the alterations in the electrically actuated droplet transport dynamics, induced by the presence of negative surface charge on the colloidal particles. At a definite value of η, the presence of negative surface charge on the particles (as reflected by the ζ-potential value, ζp ≈ −25.3 mV) results in even greater initial acceleration of the colloidal droplet, as compared to that attained by the colloidal droplet containing neutral particles (ζp ≈ 0) of comparable size (dp = 1.1 μm; see inset in Figure 4a). The greater acceleration over the initial transfer period manifests in steeper rate of increase of u̅ and higher value of u̅peak for DCS containing surface-charged particles, than those for DCS of uncharged particles of

Moreover, the applied electrical voltage is presented in a nondimensional form by the electrowetting number1: η = (CeqV2)/2γref, where Ceq = εo/((hS/εr,S) + (hT/εr,T)) is the equivalent specific capacitance of the Sylgard 184 and the Teflon films, and γref (71.64 mN·m) is the reference liquid surface tension, which is taken here as that of 100 mM aqueous KCl solution. It must be noted here that as the droplet advances, a dynamic equilibrium is eventually reached between the aiding capillary force and the resisting frictional forces culminating in an asymptotically reducing droplet velocity (“droplet settling velocity”; see Figure 3b).15 Hence, in reality, the drop continues to move at this velocity, even after completing a transfer. However, to maintain a controlled transfer of the drop, subsequent switching of the electrode pads is imperative. In the present discussion, the transport characteristics are always delineated over the time period in which a drop almost completes traversing a distance L(i.e., a single transfer), and not over the time period in which it literally comes to rest after one switching of the electrode. Now, the strength of the electrical driving force increases with progressively increasing magnitude of η, which culminates in greater droplet velocity, and consequently, triggers rapid droplet transfer (see Figure 3b).15 The decreasing value of ttr manifests in increasing value of f tr with increasing magnitude of η (see inset of Figure 3b). Effects of Neutral Colloidal Particles. The nondimensional velocity (u)̅ and the nondimensional acceleration (a)̅ characteristics, for the electrically actuated transport of drops of a colloidal suspension (“DCS”) containing neutral (ζp ≈ 0) polystyrene particles of a definite size (dp = 1.1 μm), are shown in Figure 4a, for η = 0.82. The depicted characteristics highlight the fact that at a definite magnitude of η, the presence of suspended particles significantly alters the transport dynamics of drops, from that observed for the drops of the base liquid (i.e., 100 mM KCl solution). Specifically, at a definite magnitude of η, the electrically induced initial acceleration is greater for the colloidal droplet (DCS; dp = 1.1 μm, ζp ≈ 0) than that for the identical-sized 100 mM KCl drop (see inset in Figure 4a). Accordingly, the peak droplet velocity (u̅peak), during a transfer, increases with the inclusion of the neutral suspended particles (see Figure 4a; there is a 45.3% increase in u̅peak for DCS containing uncharged 1.1 μm particles, as compared to that for the 100 mM KCl drop at η = 0.82). E

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Figure 6. Fluorescence microscopy images showing an instance of the electrically triggered TPCL spreading on the dielectric film (Sylgard 184+Teflon), for a colloidal droplet (DCS; dp = 1.1 μm, ζp ≈ − 25.3 mV, taken as an example here) (a) before electrical actuation (η = 0), and (b) on electrical actuation (η = 0.6). These images, along with the corresponding fluorescence intensity color maps, demonstrate the significant increment in particle concentration (bright white spots in actual images; dark red spots in color maps) in the immediate vicinity of the TPCL, on electrical actuation. This increment in particle concentration implies enhanced particle adsorption at the dielectric−colloidal droplet interface in close proximity of the TPCL. The plane of focus for these microscopy images is approximately at the dielectric−droplet interface.

identical size) having a definite magnitude of negative ζp (see Table S2 in the Supporting Information). Accordingly, the transport characteristics of these colloidal droplets containing positively charged particles (as shown in Figure S4 of the Supporting Information) represent the combined effects of the significantly reduced surface tension and the presence of positive surface charge on the microparticles. Hence, the sole influence of the latter on the electrically actuated colloidal droplet transport cannot be conclusively inferred from the observed transport characteristics, by a method of comparison with that for the colloidal droplets containing negatively charged particles of identical size. This reduced surface tension of the positively charged microparticle suspension may be due to the physical nature of the commercially available aminemodified particle suspension, which is used to prepare the 1% w/w colloidal suspension in 100 mM KCl (in this regard, we have tried three different amine-modified particle suspensions, but with similar end results). Theory. A quasi-steady state force balance approach is used herein to probe the physical phenomena behind the observed transport characteristics of the colloidal droplets. In the case of the transport of the 100 mM KCl droplet, the applied electrical voltage (V) results in the reduction of the dielectric surface− droplet interfacial tension, above the activated electrode pad.1 Since the hydrophobic dielectric film takes a finite time to get charged15,26 after the activation of an electrode pad, a timeaveraged form of the corresponding transient electrical driving force for the droplet, due to such electrocapillarity-induced solid−liquid interfacial tension gradient between the activated and ground electrodes, is considered here. The transient electrical driving force is averaged over the time period (tc = 2.3RC)15 in which saturation in dielectric charging is effectively attained, on considering an equivalent RC circuit. This timeaveraged electrocapillarity-induced driving force can be written as14−16,20 F̅e = (eCeq/2tc) ∫ t=2.3RC [Veff(t)]2 dt, where e is the t=0 electrode pad length normal to the direction of motion, Veff(t) = V0eff(1 − e−t/RC), and V0eff = (V2 − V2min)1/2. Here, R is the series resistor (including the resistance offered by the droplet) and C is the total capacitance (offered by the droplet-dielectric system) of the equivalent RC circuit.15,27 Furthermore, the consideration of V0eff, instead of the applied electrical voltage (V), incorporates the inherent surface hysteresis effect into the present model.17,19 It must be noted here that the electrically triggered spreading of the contact line, and the consequential reduction (increment) of the three-phase contact line (TPCL)

comparable size (see Figure 4a; specifically, there is 80.58% increase in the peak velocity at η = 0.82). Moreover, the former attains the peak velocity (i.e., zero acceleration) within a smaller time interval (59.04% less time) than the latter (see inset in Figure 4a). Thereafter, the droplet containing charged particles decelerates faster than the colloidal droplet containing uncharged particles of comparable size, until the rate of decrease of the velocity gets arrested (see inset in Figure 4a). Finally, all the droplets asymptotically attain zero acceleration, and hence, reach the transport regime characterized by asymptotically reducing velocity. However, the unique droplet transport characteristics triggered by the negatively charged particles result in smaller transfer time (see Figure 4a). This culminates in higher values of uavg and f tr, as compared to the droplet containing neutral particles of comparable size (see Figure 5a). Interestingly, at a definite magnitude of η, the initial acceleration, and consequently, the rate of increase of u̅ and the value of u̅peak, for the colloidal droplet containing charged microparticles, increase with decreasing magnitude of the negative surface charge on the colloidal particles (of identical size), as reflected by the decreasing magnitude of the corresponding negative ζ-potential (ζp) (see Figure 4b and its inset). As a consequence of such acceleration and velocity characteristics, as shown in Figure 4b, the value of ttr reduces, while the value of f tr increases (see Figure 5b) with decreasing magnitude of the negative ζp. It must be noted here that the transport characteristics of different colloidal droplets, as shown in Figure 4a and Figure 4b for η = 0.82, are also qualitatively valid for other practically feasible values of η (see Figure S3a and Figure S3b in the Supporting Information for the instantaneous transport characteristics, and Figure 5a and Figure 5b for values of f tr, corresponding to η = 0.98). The only effect of increasing (decreasing) η, for a definite type of droplet, lies in increasing (decreasing) the magnitude of the electrical driving force, and consequently, in increasing (decreasing) the initial rate of increase of u,̅ and the values of u̅peak (compare Figure 4 and Figure S3) and f tr (see Figure 5). It must be further noted here that experiments are also performed with colloidal droplets containing positively charged (amine-modified; ζp ≈ + 10.3 mV) polystyrene particles of dp = 1.1 μm. However, the surface tension (30.45 ± 0.4 mN·m) of the 1% w/w colloidal suspension of positively charged polystyrene particles is found to be less than half of that of each of the 1% w/w colloidal suspensions of negatively charged polystyrene particles (of F

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extent of adsorption of the neutral microparticles of comparable size. Such electrostatically mediated enhanced adsorption of the negatively charged microparticles compounds the reduction of the dielectric-droplet interfacial tension, which manifests in further increment of the additional electrical driving force. Now, with reducing magnitude of the negative surface charge of the microparticles, as represented by the reducing magnitude of the negative ζp, the existing interparticle electrostatic repulsion progressively reduces. This, in turn, progressively increases the propensity of the negatively charged microparticles to get adsorbed near the TPCL above the activated electrode, under an applied electrical voltage. Hence, the associated electrical driving force further increases with decreasing magnitude of the negative ζp. This further enhanced (time-averaged) electrical driving force due to increased particle adsorption, in the presence of the additional electrostatic interactions, can be addressed by rewriting F̅′e as F̅′e = (eαAnpc /tc) ∫ t=2.3RC Veff(t) dt. t=0 Here, α is a nondimensional factor which addresses the alteration in F̅e′, due to the combined interplay of the interfacial dielectric surface−microparticle electrostatic attraction and the interparticle electrostatic repulsion, under an applied electrical voltage. It must be noted here that for the electrical dropletactuation methodology, as being discussed here (see Figure 2), generally α > 1 for negatively charged particles, and its value increases with decreasing magnitude of the negative ζp; while α = 1 for neutral particles. So finally, for the electrical actuation of colloidal droplets, the total time-averaged electrical driving force, due to the colloidal particle adsorption mediated electrocapillary phenomenon, can be written as

curvature (radius), are accompanied by the reduction in the liquid pressure at the TPCL. Generally, such alterations of the TPCL curvature and the liquid pressure at the TPCL of a sessile droplet lead to liquid adsorption at the solid−liquid interface, in the vicinity of the TPCL;28 this enhancement in the interfacial liquid concentration leads to reduction of the solid−liquid interfacial tension.28 Accordingly, in the case of the colloidal droplets containing neutral particles (ζp ≈ 0), the electrically triggered contact line spreading (see Figure 6) and the reduction in the liquid pressure at the TPCL, on top of the activated electrode, lead to enhanced adsorption of the suspended particles at the solid−liquid interface, in the immediate vicinity of that TPCL (see Figure 6; to demonstrate the repeatability of the increased adsorption of the particles, on application of V, another instance of this phenomenon is shown in Figure S5 of the Supporting Information). Furthermore, this phenomenon is not specific to the Teflon surface, and can also be observed on the surface of only the Sylgard 184 film (see Figure S6 in the Supporting Information). Now, such interfacial adsorption of the particles culminates in enhanced reduction of the local dielectric-colloidal droplet interfacial tension (compared to the classical electrocapillary phenomenon for the 100 mM KCl drop), above the activated electrode, which in turn manifests in an additional electrical driving force. The timeaveraged (to address the finite charging time of the dielectric film) driving force, due to electrically triggered enhanced neutral particle adsorption, can be written as F̅e′ = (eAnpc /tc) Veff(t) dt (see the Supporting Information for a detailed ∫ t=2.3RC t=0 discussion on the total electrical driving force for the colloidal droplets). Here, A (C·m/mol) is a dimensional constant dependent on the physical characteristics of the homogeneous colloidal suspension of neutral particles and the dielectric film, and npc = 6ϕρcs/ρpπd3pNA (mol/m3) is the concentration of the polystyrene particles in the colloidal suspension, where ρcs is the average density of the colloidal suspension, ρp is the density of bulk polystyrene (1.05 g/mL; as supplied by the manufacturer), and NA is the Avogadro number. For the 100 mM KCl drop, the particle weight fraction ϕ = 0 ⇒ npc = 0 ⇒ F̅′e = 0, and the droplet is driven only by F̅e. Now for a colloidal droplet with a definite value of ϕ, the value of npc increases with decreasing value of dp. This implies that the concentration of the adsorbed particles, and the consequential reduction in the dielectric−colloidal droplet interfacial tension, increase with the decreasing value of dp. Consequently, the magnitude of F̅e′ is more for the colloidal droplet containing smaller neutral polystyrene particles of dp = 0.055 μm, as compared to that for the colloidal droplet containing bigger neutral polystyrene particles of dp = 1.1 μm, at a definite magnitude of V. In case of the colloidal droplets containing negatively charged microparticles (of dp = 1.1 μm), the adsorption of the microparticles, at the solid−liquid interface near the TPCL, is further enhanced due to the involved electrostatic interactions. Under the applied electrical voltage, as shown in Figure 2, there are two underlying electrostatic interactions: the electrostatic attraction between the negatively charged microparticles, in the interfacial region, and the positively charged dielectric surface, and the interparticle electrostatic repulsion.29 For the colloidal droplets under consideration, the effect of the particle−dielectric surface electrostatic attraction dominates over the consequences of the interparticle electrostatic repulsion. This leads to net enhanced adsorption of the negatively charged microparticles at the dielectric−droplet interface, on top of the activated electrode, as compared to the

Fe̅ T = Fe̅ + Fe̅′ = +

eαAncp tc

eCeq 2tc

t = 2.3RC

∫t =0

[Veff (t )]2 dt

t = 2.3RC

∫t =0

Veff (t ) dt

(1)

Accordingly, the total force balance dictating the quasi-steady state motion of the colloidal droplets can be written as Fe̅ T −

3μπ(dc0)2 uref x uavg − BγCa xπdc0uavg − ζuref πdc0uavg ≈ 0    4href  cw cl Ffvs

Ff

Ff

where F̅ eT is defined by eq 1, u̅avg = uavg/uref is the nondimensionalized average droplet transport velocity, Fvs f is the friction force acting on the droplet due to the net viscous shear force at the dielectric surface, which in turn originates from the internal hydrodynamics of the droplet during motion (evaluated by considering a low Reynolds number flow of a Newtonian liquid),15 Fcw f is the additional friction force due to excitation of damped capillary waves along the liquid−vapor interface (here Ca = μuref/γ is the capillary number based on u ref ; B and x (x ≤ 0.5) are the pertinent model parameters)14,15,30 and Fclf is the contact line friction force (here ζ is the contact line friction coefficient).14,17,19,20 Furthermore, here d0c and href = d0c *[(1 − cos θ0eq)/2s in θ0eq] (θ0eq is the equilibrium droplet contact angle) are the reference droplet contact diameter and the reference droplet height, respectively (values of d0c and θ0eq are listed in Table S1 in the Supporting Information), while μ and γ are respectively the viscosity and surface tension of the colloidal suspensions (see Table S2 in the Supporting Information). Figure 7 shows the good agreement between the experimentally obtained values of u̅avg, for the 100 mM KCl drop, and the predictions of eq 2, G

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2γtc)∫ 2.3RC {Veff,max(t)}2 dt], where θs is the saturation contact 0 1 angle for the system under consideration, Veff,max(t) = V0eff,max(1 0 − e−t/RC) and Veff,max is the effective electrical voltage corresponding to the applied electrical voltage at which this particular value is attained; while for the colloidal droplet containing charged particles, it is the product αA that must satisfy the identical condition (see the discussion on the total electrical driving force for colloidal droplets in the Supporting Information). From a comparison of these two cases, for practically feasible values of the involved parameters, it can be inferred that O(α) ∼ 1.

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CONCLUSIONS AND SCOPE We have clearly shown here that the electrically modulated transport characteristics of colloidal droplets, on a hydrophobic dielectric film, are distinctly different from that of the droplets of the base liquid, under identical conditions. For colloidal droplets containing neutral suspended particles, the electrically triggered reduction in the dielectric-droplet local interfacial tension is significantly enhanced, in comparison to the classical electrocapillary phenomenon. This is achieved due to the additional interfacial adsorption of the suspended particles, in the immediate vicinity of the TPCL on top of the activated electrode pad, due to the electrically triggered reductions in the TPCL curvature and the liquid pressure at the TPCL. Such enhanced, asymmetric reduction in the dielectric−droplet interfacial tension culminates in an increased electrical driving force. This enhanced electrical driving force results in greater initial acceleration of the colloidal droplets. The imparted greater acceleration eventually results in steeper rate of increase of the instantaneous velocity, higher peak velocity during transfer, greater average droplet transport velocity, and higher maximum droplet transfer frequency for the colloidal droplets, as compared to that for the droplets of the base liquid, under a definite magnitude of the applied electrical voltage. Moreover, the total electrical driving force, due to this particle adsorption mediated electrocapillary phenomenon, increases with decreasing size of the suspended colloidal particles. On the other hand, for the colloidal droplets containing surface charged suspended particles, the extent of electrically triggered interfacial particle adsorption is also dictated by the additional interplay between the charged particle-dielectric surface electrostatic interaction and the interparticle electrostatic repulsion. Accordingly, for colloidal droplets containing negatively charged particles, the additional interfacial electrostatic attraction between the negatively charged particles and the positively charged dielectric surface, on top of the activated electrode pad, leads to enhanced particle adsorption and greater electrical driving force, as compared to that for colloidal droplets containing neutral particles of comparable size. Moreover, with decreasing magnitude of the negative particle ζ-potential, the involved interparticle electrostatic repulsion progressively weakens, thereby further augmenting the interfacial particle adsorption. Consequently, the electrical driving force, and the resulting average droplet transport velocity and the maximum droplet transfer frequency, further increase with decreasing magnitude of the negative particle ζ-potential. It is now clear that the analysis of the electrically actuated transport of colloidal droplets, by the classical electrocapillaritybased model, as percolated in the literature so far, will lead to severe under-estimation of the pertinent transport characteristics. In this regard, the physical model described in the present work, which takes in purview the alterations in the electrostatic

Figure 7. Experimental and theoretical variations of the nondimensional average droplet transport velocity (u̅avg) with increasing magnitude of the nondimensional electrowetting number η, for the 100 mM KCl droplet and for the droplets of colloidal suspensions containing negatively charged microparticles having different magnitudes of the negative surface charge, as represented by the different values of the ζ-potential.

obtained by numerically solving this equation, at different values of V, with F̅e′ = 0 and the physically consistent values of the other involved parameters:14,15,17,20,30 B = 2.8, x = 0.43 and ζ = 0.04 Pa·s. However, such classical electrocapillary-based description of the droplet transport dynamics (as established in the existing literature) fails to describe the electrically actuated transport characteristics of the colloidal droplets. The higher u̅avg values (not shown here) for the colloidal droplet containing neutral particles of dp = 1.1 μm are suitably addressed by eq 2 only on considering F̅e′, corresponding to A = 1.7 × 103 (C·m/mol) and α = 1; while the values of the other involved parameters are considered to be same as before. Similarly, the even higher values of u̅avg for the colloidal droplet containing smaller neutral particles of dp = 0.055 μm are described by eq 2, on considering the higher magnitude of F̅′e primarily due to the significantly higher value of npc (α = 1 for this case also). Interestingly, the higher experimental values of u̅avg for the colloidal droplet containing negatively charged particles (of dp = 1.1 μm) having ζp ≈ − 25.3 mV, at different values of η, are addressed by eq 2, only on considering F̅′e corresponding to A = 1.7 × 103(C·m/mol) (which is identical to that used for the colloidal droplet containing neutral particles of identical size) and α = 1.6 (and not 1; see Figure 7); while the u̅avg values for the colloidal droplet containing negatively charged microparticles having ζp ≈ − 5.3 mV are described by eq 2, on considering F̅e′ corresponding to the identical value of A, but an higher value of α (α = 3.6; see Figure 7). It must be noted here that for the colloidal droplets, O(F̅e/F̅′e) ∼ 10−1 − 1. Hence, it can be now concluded that the additional electrical driving force, stemming from the local attenuation of the dielectric surface−droplet interfacial energy, due to the electrically triggered and electrostatic interaction-mediated suspended particle adsorption, is responsible for the observed enhancement in the average transport velocity (and the droplet transfer frequency) of the colloidal droplets, as compared to that for the droplets of the base liquid. It is instructive to note here that for the colloidal droplet containing neutral particles, the value of A is physically restricted by the condition A ≤ (γtc/ 0 n cp ∫ 02.3RC V eff,max (t) dt)[(cos θ s − cos θ eq ) − (C eq / H

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and capillary interactions over interfacial scales in the presence of the suspended neutral/charged particles, can be used for a more accurate estimation of the average droplet transport velocity and the maximum droplet transfer frequency. Hence, the present work will provide a new guiding paradigm for the determination of more efficient design parameters (e.g., electrode dimensions) and optimal operational parameters (e.g., electrode switching rate, which is dependent on the maximum droplet transfer frequency) for digital microfluidic chips for manipulation of droplets containing suspended biological, synthetic or metallic particles. Therefore, the present endeavor will be beneficial for the efficient operation of a wide range of digital microfluidic applications: from immunoassays, point-of-care diagnostics to microparticle collection and sampling.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b01941. Characterization of the droplets of 100 mM KCl solution and the droplets of the colloidal suspensions on the hydrophobic dielectric layer; characterization of the thermophysical properties of the colloidal suspensions and the surface zeta potential values of the suspended particles; image sequence demonstrating a single droplet transfer under an applied electrical voltage; description of the involved image processing methodology, and subsequent postprocessing methodology of the experimental data; transport characteristics for the 100 mM KCl droplet and the droplets of different colloidal suspensions at η = 0.98; transport characteristics for the colloidal droplet containing positively charged microparticles; visual evidence for microparticle adsorption in the immediate vicinity of the colloidal droplet TPCL, on application of an electrical voltage; description of the time-averaged total electrical driving force for colloidal droplets (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; sunando.dasgupta@ gmail.com Ph: +91-3222-283922. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.D. and U.U.G. greatly acknowledge Mr. Subir DasGupta, in the Advanced Technology Development Center of IIT Kharagpur, for his help with the fabrication of the electrode chips. The authors gratefully acknowledge the financial support provided by the Indian Space Research Organization (Sanction Letter no.: IIT/KCSTC/STC/Chair/Appr/NEW/P/14-15/09, Dt. 22-08-2014).

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REFERENCES

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DOI: 10.1021/acs.langmuir.5b01941 Langmuir XXXX, XXX, XXX−XXX