Bubble Control, Levitation, and Manipulation Using Dielectrophoresis

Bubbles attached to surfaces are ubiquitous in nature and in industry. However, bubbles are problematic in important technologies, including causing damage to the operation of microfluidic devices and being parasitic during heat transfer processes, so considerable efforts have been made to develop mechanical and electrical methods to remove bubbles from surfaces. In this work, liquid dielectrophoresis is used to force a captive air bubble to detach away from an inverted solid surface and, crucially, the detached bubble is then held stationary in place below the surface at a distance controlled by the voltage. In this “levitated” state, the bubble is separated from the surface by liquid layer with a voltage‐selected thickness at which the dielectrophoresis force exactly counterbalances the gravitational buoyancy force. The techniques described here provide exceptional command over repeatable cycles of bubble detachment, levitation, and reattachment. A theoretical analysis is presented that explains the observed detachment–reattachment hysteresis in which bubble levitation is maintained with voltages in an order of magnitude lower than those used to create detachment. The precision surface bubble removal and control concepts are relevant to situations such as nucleate boiling and microgravity environments and offer an approach toward “wall‐less” bubble microfluidic devices.

Bubbles attached to surfaces are ubiquitous in nature and in industry. However, bubbles are problematic in important technologies, including causing damage to the operation of microfluidic devices and being parasitic during heat transfer processes, so considerable efforts have been made to develop mechanical and electrical methods to remove bubbles from surfaces. In this work, liquid dielectrophoresis is used to force a captive air bubble to detach away from an inverted solid surface and, crucially, the detached bubble is then held stationary in place below the surface at a distance controlled by the voltage. In this "levitated" state, the bubble is separated from the surface by liquid layer with a voltage-selected thickness at which the dielectrophoresis force exactly counterbalances the gravitational buoyancy force. The techniques described here provide exceptional command over repeatable cycles of bubble detachment, levitation, and reattachment. A theoretical analysis is presented that explains the observed detachment-reattachment hysteresis in which bubble levitation is maintained with voltages in an order of magnitude lower than those used to create detachment. The precision surface bubble removal and control concepts are relevant to situations such as nucleate boiling and microgravity environments and offer an approach toward "wall-less" bubble microfluidic devices.

Introduction
In microfluidic systems, undesirable bubbles can often be nucleated inside the microchannels, or inadvertently introduced when connecting tubes. The motivation to develop through the displacement of the air-liquid interface. [26] While EWOD approaches have shown the ability to detach pinned bubbles, key issues were highlighted such as requiring direct electrical contact with the liquid, working only with electrically conducting liquids, not providing any precise control over the bubble once it has become detached, and devices only removing bubbles on the first actuation. [24,26] An alternative approach to reversibly modifying the wetting behavior of a liquid on a solid surface is dielectrowetting, which utilizes interface-localized liquid dielectrophoresis. [27,28] In this approach, dielectric liquid sessile droplets are deposited on a solid dielectric layer that over-coats interdigitated electrodes. By application of an A.C. voltage V 0 between interposing electrode fingers, a non-uniform electric field localized at the surface is generated which decays away from the surface exponentially characterized by a decay length, δ. The non-uniform electric field exerts a bulk force on the polarizable liquid which draws the liquid toward the region of highest electric field intensity. [29,30] Since the liquid is substantially more polarizable than vapor, surface-localized dielectrophoresis forces increase the area of the liquid-solid interface at the expense of the "dry" vapor-solid contact area which leads to a decreasing liquid droplet contact angle with increasing applied voltage. Dielectrowetting has been shown to promote reversible full film spreading and super-spreading overcoming the contact angle saturation present in EWOD. [28,31] Dielectrowetting has also found applications in a variety of optofluidic devices, [32] microfluidics, [33] and in improving heat transfer. [34] In this work we demonstrate how dielectrophoresis can be used not only to force bubble detachment, but crucially, to promote a state of voltage-controlled levitation where a captive bubble can be held indefinitely away from a solid surface with programmable separation distance down to the micrometer scale. We elucidate how localized electric field gradients at the surface both force the reduction in vapor-solid contact area leading to detachment, and then counterbalance buoyancy to maintain a state of levitation for single and multiple bubbles (Movies M1 and M2 †, Supporting Information). Furthermore, we show that at low voltages the same or other bubbles can be prevented from attaching or reattaching to the surface, even when a rising bubble meets the surface at speed or when mechanical force is applied to the bubble (Movies M3 and M4 †, Supporting Information). Lastly, we demonstrate that our bubble levitation technique is equally applicable to both insulating liquids and to de-ionised water.

Dielectrophoresis Controlled Bubble Detachment, Levitation, and Reattachment
We pattern glass surfaces with a titanium-gold interdigitated microstripe electrode array capped with a thin planarizing dielectric layer and liquid-repellent coating of Teflon AF (Experimental and Methods Section). As the equilibrium Young's law contact angle of a sessile droplet of the dielectric liquid, trimethylolpropane triglycidyl ether (TMP-TG-E) on our Teflon coated surface is given by θ Y = 82° ± 1°, [35,36] TMP-TG-E would not spontaneously form a stable thin wetting film on our surface. [37,38] The patterned glass surfaces were inverted and submersed in liquid TMP-TG-E and air bubbles were then created and attached to the solid surface by a needle. Once the bubble is attached, a threephase contact line forms around the perimeter of the base of the captive bubble which encloses a circular "dry" vapor-solid base area, Figure 1a. The bubble contact angle is given at equilibrium by θ e = π − θ Y = 98° ± 1°, measured from inside the bubble.
When a voltage is applied between the interdigitated electrodes the surface-localized dielectrophoretic forces cause increased wetting of the dielectric liquid, i.e., dielectrowetting, increasing the area of the solid-liquid interface, while reducing the vapor-solid area in the base of the bubble which is accompanied by a concomitant increase in the bubble contact angle, θ(V 0 ), as shown in Figure 1b-d. During the dewetting process, we find the vapor-solid area at the base of the bubble exhibits a small deviation from a circular shape, and this deviation is more pronounced for the largest bubble sizes in our study at high applied voltages (see Figure S1 in the Supporting Information). At a critical detachment voltage, V D , the contact angle reaches θ = 180° and the dielectric liquid fully wets the surface, which detaches the bubble from the surface, Figure 1d,e. While bubbles can be detached in this manner via dielectrowetting for any orientation of the solid surface, if the surface is immersed in an inverted orientation liquid dielectrophoretic forces can counterbalance the buoyancy forces that would otherwise drive bubbles to attach to the surface, i.e., forcing a state of bubble levitation on an intervening liquid layer of thickness h. This situation is shown in the image in Figure 1e for an electrode voltage of V 0 = 270 V, which is slightly higher than the critical detachment voltage, V D = 269 ± 1 V. The thickness of the intervening liquid film in the gap between the bubble and the surface, h, varies monotonically as a function of the value of V 0 , as shown in Figure 1e-h, and Movie M1 † in the Supporting Information. As the value of V 0 is reduced below a threshold value, the reattachment voltage, V R (here V R = 30 ± 5 V), then h → 0 and the bubble reattaches back onto the surface, with a small gap shown in Figure 1h and then subsequent reattachment to produce a captive air bubble again, Figure 1a. There was no limit to the number of repeatable detachment, levitation, reattachment cycles that could be achieved.
It is remarkable that the reattachment voltage V R is almost an order of magnitude lower than the detachment voltage V D so detachment-reattachment hysteresis is exhibited for the system shown in Figure 1. Hence even low voltages are sufficient to prevent bubbles from attaching to the surface and, furthermore, at low voltages the same or other bubbles can be prevented from attaching or reattaching to the surface. This is demonstrated in Movie M3 † in the Supporting Information where a fast rising bubble is prevented from attaching to a surface, and in Movie M4 † in the Supporting Information where even a bubble that is mechanically squeezed to attempt to force it onto the surface is unable to attach to the surface, in both cases due to the surfacelocalized dielectrophoretic forces prevent bubble attachment while the voltage is applied.

Theoretical Analysis of the Attachment-Reattachment Hysteresis
We now develop an analytical model to describe the voltage dependence of surface-localized dielectrophoresis driven bubble "dewetting" and detachment θ(V 0 ), the subsequent suspended bubble vertical position control h(V 0 ), and which will further provide insight into the origin of the detachment-reattachment hysteresis. An illustration of the forces acting on a levitated bubble is shown in Figure 2a. A detailed description of the mathematical model and the key assumptions made is provided in File F1 † in the Supporting Information. Let the inverted solid surface be placed at position z = 0 in the x, y plane. Co-planar interdigitated microstripe electrodes with electrode linewidth, l e equal to the inter-electrode gap l g , are formed on this surface (see Figure 2b,c). An applied A.C. voltage of frequency f is applied between the electrode fingers, which we model as a simplified potential with a sinusoidal spatial dependence, where the angular frequency is ω = 2π/f and the spatial frequency is k = π/2l e = π/2l g . The electrodes are covered by a solid dielectric protection layer having thickness z d and dielectric constant ε d .
The solid dielectric is covered by a layer of thickness l 1 and dielectric constant ε 1 , which is in turn covered by further layer having thickness l 2 and dielectric constant ε 2 . Below these layers lies the oil reservoir. Our geometry, in which we are exponentially decaying strong electric field gradients localized to the surface, is hence very different from the normal electric field destabilization of spontaneously wetting liquid film described by Schäffer et al. [39,40] The general form of the electric potential in each of the regions of the system described above can be written in the form shown in Equation (1) , , The non-uniform electric field produced by this potential, which has both normal and tangential in-plane spatially varying periodic components, is responsible both for generating and stabilizing the liquid film intervening between the bubble and the surface for bubble "dewetting" and the voltage control of bubble position, respectively.
The electric energy density at any position in the system is given by 1/2D · E per unit volume, where E = −∇V is the electric field, and D = εE is the displacement field. The electrostatic energy can be calculated using Equation (1) by applying appropriate electrostatic continuity conditions at the boundaries between the different regions, and integrating the electric energy density over a time period of the applied A.C. voltage, and over space for one period of the potential at the surface and from z = 0 to z = ∞. In the limits where l 1 ≫ l e and l 2 ≫ l e , the electrostatic energy per unit surface area, W e of the solid surface for this 3-layer system is given, to leading order, by Equation (2) where, ε 0 is the permittivity of free space. First, we consider the electric field gradient forced bubble "dewetting" case corresponding to the experimental results shown in the images in Figure 1a-d. Equation (2) can be applied to this situation by assuming only a 2-layer system in which the solid dielectric is covered either by vapor or else by liquid, and so ε 1 = ε 2 , l 1 → ∞ and b = 0. Inside the base of the attached bubble the vapour is in contact with the solid dielectric surface, and so the electrostatic energy is given by Equation (2) with ε 1 = ε V and the expression for the coefficient in Equation (2b) will be denoted by a V . It will be assumed that the height of the bubble is large and that the entire region above the solid dielectric is effectively filled with vapor. Outside the base of the attached bubble the liquid is in contact with the solid dielectric surface, and so the electrostatic energy is given by Equation (2) with ε 1 = ε L and the expression for the coefficient in Equation (2b) will be denoted by a L . It will be assumed that for all values of the contact angle θ(V 0 ) the liquid layer is thick, so that the entire region above the solid dielectric is effectively filled with liquid. Consider a sessile bubble on an activated interdigitated electrode array after a voltage-driven small change in the position of the contact line around the perimeter of the base of the bubble, resulting in a change ΔA in the bubble base area. Adding the electrostatic energy, Equation (2), to the unbalanced interfacial tension energies at the contact line provides the surface localized dielectrophoresis modified form of the change in the energy ΔW as a function in the change in bubble base area, Equation (3) cos c os 1 8 Here θ e is the equilibrium contact angle inside the bubble, which is related to the Young's law angle θ Y , [35,36] by θ e = π − θ Y radians as discussed in Section 2.1, γ LV is the surface energy of the liquidvapor interface, and k is the spatial frequency, k = π/2l e = π/2l g . The equilibrium situation can be found by setting ΔW/ΔA = 0, which yields a surface localised dielectrophoresis modified version of Young's law for bubble "dewetting", Equation (4) cos c os 8 where, θ(V 0 ) is the voltage dependent contact angle of the bubble and V 0 is the applied voltage at the electrodes. By substituting θ = 180° into Equation (4) an analytical expression for the critical detachment voltage V D can be derived, given in Equation (5) Equation (5) for the detachment voltage V D , a ratio of surface tension and interfacial energy parameters in the numerator over dielectric terms in the denominator, expresses how the voltage induced polarization of the liquid adjacent to the surface needs to be sufficient to overcome surface energy forces to produce bubble detachment. Figure 3a shows how the value of the bubble contact angle θ(V 0 ) increases as the voltage V 0 is quasi-statically incremented. Up until V 0 = 100 V the contact angle does not change significantly because the dielectrophoresis force is insufficient to overcome contact line pinning effects. For voltages of 100 V and above the value of the contact angle increases monotonically and super linearly as a function of voltage V 0 . The solid line in Figure 3a shows the fitting to Equation (4) (see Figure S3 in the Supporting Information). Hence we predict and experimentally observe the same cos 0 2 V θ ∝ relationship for our liquid dielectrophoresis controlled bubble "dewetting" technique that has also previously also been found both for liquid EWOD, [11][12][13][14] and for liquid dielectrowetting. [28] This relationship may be used to extrapolate from the data to predict an experimentally derived value for the critical detachment voltage V D at which the bubble contact angle would reach θ = 180°. This is shown on Figure 3a by the vertical dashed line at V 0 = V D = 269 ± 1 V. Above this voltage, the greyed area in Figure 3a, the bubble is detached and enters the levitating state as shown in Figure 1e.
Next, we turn our attention to the voltage control of the vertical position of a suspended bubble, corresponding to the images in Figure 1e-h. Once the bubble has detached the surface is covered by an intervening liquid film layer with thickness z 1 = h(V 0 ) and dielectric constant ε 1 = ε L . The suspended bubble has a vertical height z 2 = H b and dielectric constant ε 2 = ε V . The gravitational potential energy associated with the buoyancy of the bubble relative to the surface is given by Equation (6) below, where Δρ is the density difference between the liquid and air and g is the acceleration due to gravity The total energy of the system is described by the sum of the gravitational potential energy associated with the buoyancy of the bubble, W g Equation (6) Where the reattachment voltage, V R , is given in Equation (8) Equation (8) for the reattachment voltage V R , a ratio dominated by gravity related parameters in the numerator over dielectric terms dominating the denominator, expresses how the bubble can only reattach when the buoyancy then overcomes the polarization of the liquid film in place between the bubble and the surface when the voltage is reduced. Figure 3b shows how h(V 0 ) decreases monotonically as the voltage V 0 is quasi-statically reduced where the solid line shows the fitting to Equation (7) (see Figure S3 in the Supporting Information ). By extrapolation we are able to predict the experimentally derived value for the critical "touchdown voltage" V R at which the thickness becomes zero, i.e., h (V R ) = 0 when V R = 30 ± 5 V. At, and below, this reattachment voltage V R the electrostatic forces are no longer sufficient to counterbalance the buoyancy force which then pushes the bubble to reattach back onto the surface, the greyed area on Figure 3b. The reattachment mechanism that we have observed is that the liquid film punctures as the gap between the top of the bubble and the surface reduces toward zero.
Our theoretical model has successfully described the analytical voltage dependence of surface-localized dielectrophoresis driven bubble "dewetting" and detachment θ(V 0 ), the subsequent suspended bubble vertical position control h(V 0 ). However, the measured and predicted numerical values of V D , and of V R , are not in quantitative agreement. The detachment voltage from the theory (Equation (5)) over-predicts the experimental value, V D (theory) = 355 V compared with V D = 269 ± 1 V from extrapolation of the cos 0 2 V θ ∝ fit to the experimental data shown in Figure 3a, and the reattachment voltage (Equation (8)) is under predicted, with V R (theory) = 11 V compared with the value V R = 30 ± 5 V obtained by extrapolation from a h∝log e V 0 fit to the experimental data shown in Figure 3b. These differences can be attributed to small deviations away from ideal circular base area during dewetting (see Figure S1 in the Supporting Information) and the sinusoidal potential function approximation that we used to describe the periodic surface potential produced by microstripe co-planar electrodes at z = 0, which is more complex in reality. [41,42] A complete theoretical treatment of the voltage control of bubble position would require numerical solution of the 3D electric fields in the system and the Maxwell and LaPlace contributions to the vapor-liquid interfacial stress, [43,36,44] to account for a non-spherical bubble shape and for the periodic deformation of the liquid film surface as thickness h → 0. [45] Furthermore, we have used a flat liquid-vapor interface at the underside of the bubble, while the curved surface shape of the bubble and voltage induced periodic deformation of the liquid film surface will influence the actual reattachment voltage.
Our theory also provides meaningful insight into the detachment-reattachment hysteresis, notwithstanding these approximations, because we have retained the key geometrical and material parameter dependences of the system. An expression for the ratio of the detachment voltage to the reattachment voltage, is the capillary length for the liquid, is found by making the approximations z d → 0, cos (θ) ≈ −1, and ε L ≫ ε V . Hence, the key determining factor of the relative magnitudes of V D and V R is the comparison between the capillary length of the liquid, and the geometric mean of two key length-scales; the bubble vertical height, H b and the electrode linewidth l e . In our experiments depicted in Figure 1, Λ C ≈ 2 × 10 −3 m, H b ≈ 1.5 × 10 −3 m, and l e = 20 × 10 −6 m, and so V D is over an order of magnitude larger than V R and we observe significant hysteresis. So for a centimeter scale bubble on electrodes with millimeter linewidth the detachment-reattachment hysteresis would disappear, although both voltages would significantly increase, and if V R ≥ V D electrostatic bubble detachment would not be possible.  bubble detachment, levitation and reattachment of multiple bubbles with different volumes. Repeated and reproducible cycling between detachment and reattachment at the region of the inverted surface is demonstrated. In the detached levitated state, as discussed above, the bubble is separated from the surface by liquid layer with a voltage-selected thickness at which the dielectrophoresis force exactly counterbalances the gravitational buoyancy force, and the latter depends on the vertical height and volume of a bubble. Hence, for a given constant voltage V 0 , larger bubbles will be held suspended at a smaller levitation height h(V 0 ). This is demonstrated in Figure 4d, where the largest levitation height is exhibited for the bubble on the left that has the smallest vertical height H b (and smallest volume Ω), compared to the smallest levitation height which is exhibited for the bubble on the right that has the largest vertical height H b . Figure 5 shows the results of dielectrophoresis bubble levitation control experiments for seven different bubbles. This detailed study provides data for a ranges of voltages V 0 in each case, and for two different dielectric liquids (TMP-TG-E with ε L = 13.7, and propylene glycol PG with ε L = 35), two different electrode linewidths (l e = 20 and 40 µm), and multiple bubble volumes (in the range over two decades, Ω = 0.015 µL to Ω = 3.46 µL). The levitation height h(V 0 ) is plotted against (2l e /π)log e (V 0 /V R ), where the value of V R is separately experimentally determined for each data set. We find that all of the data is well represented by a common unity gradient, shown by the solid line on the graph in Figure 5. Hence we observe that the gradient of h versus log e (V 0 /V R ) shows linear dependence on only one parameter, the linewidth l e of the interdigitated microelectrodes that are buried within the surface. The gradient is found to be independent of the size of the bubble and independent of the dielectric constant of the liquids used in the system, in agreement with the prediction of Equation (7).

Future Prospects for Further Development of Our Levitation Concepts
Once the bubbles are in the voltage-controlled levitation state we find that they are constrained to remain within the electrode boundary, as shown in Movie M5 † in the Supporting Information. As a levitated bubble approaches the edge of the underlying electrode structure the bubble is repelled from the extremities of the structure leading to a lateral confinement of the bubble which is entirely electrically controlled. Once the applied voltage is removed the electrostatic potential barrier is also removed and the bubble can cross outside the electrode area. This indicates that guidance of levitated bubbles is possible in a "wall-less" configuration, where electrostatic potential barriers can be placed and removed at will to control bubble trajectories without any solid or moving parts.
While the focus of the current work has been on bubble detachment, levitation and reattachment in non-conducting dielectric liquids, our concepts are also applicable to conducting liquids. This is illustrated by the experiment shown in Movie M6 † in the Supporting Information which shows the dielectrophoresis forced detachment, levitation with movement under gravity (the surface was not completely horizontal), and reattachment of an air bubble in de-ionized water with a conductivity of 1.7 µS m −1 . We also demonstrate  in de-ionized water the ability to prevent attachment of large approaching bubbles to the surface, due to the localized electric field gradient, and to vary the voltage to alter the separation distance of a large levitated bubble (Movies M7 and M8 †, Supporting Information). Theoretical description of these results will require the development of models that include the effects of finite conductivity, which may be possible by extending the current model to include the polarization effects associated with lossy dielectrics in the case of relatively low conductivity liquid systems.

Conclusions and Discussion
In this work, we have shown how a vapor filled bubble can be "dewetted" and detached from a solid surface by dielectrowetting with an applied voltage V D which exceeds a critical value. Once the bubble is free from an inverted surface, it enters a state of voltage-controlled levitation where changing the voltage allows precise, micrometer scale control over the separation distance. We further demonstrate how a localized electric field gradient prevents other approaching rising bubbles from attaching to the surface. For the system demonstrated here, the electrostatic pressure remains sufficient to maintain a stable liquid film, preventing bubble reattachment to the surface, even for voltages of a few tens of volts-almost an order of magnitude lower than the initial detachment voltage. At or below a critical touchdown voltage V R puncturing of the intervening liquid film between the bubble and the surface occurs, precipitating the buoyancy driven reattachment of the bubble to the surface. Hence cycling the voltage to above the critical detachment voltage, and then to below the critical touchdown voltage, provides repeatable bubble detachment-reattachment control (Movies M1 and M2 †, Supporting Information). Our theoretical model successfully describes the dependence of the contact angle during electric field gradient forced bubble "dewetting," and the dependence of the liquid film thickness on the voltage and the electrode linewidth during controlled levitation. The geometry of the system is shown to play a key role in determining the value of both the detachment and reattachment touchdown voltages. We have further demonstrated switchable "wall-less" voltage-controllable lateral confinement of levitated bubbles, potentially reducing the level of intricacy required for microfluidic devices. Finally, we have demonstrated that our concepts of dielectrophoresis controlled bubble detachment, levitation and reattachment apply equally to dielectric liquids and to conducting liquids.
We note how our dielectrophoresis controlled vapor filled bubble detachment and reverse "levitation" mirrors the Leidenfrost effect, which has previously been shown to levitate and transport liquid droplets on a vapor layer above a structured surfaces. [46,47] However, unlike Leidenfrost droplet transport where the direction is fixed by the structure of the solid surface, our vapor-filled bubble held detached below a surface by an electric field gradient stabilized liquid layer can be actuated on demand by using sets of interdigitated fingers which have a small overlap, [33] where by application of different voltages to the sets, a reprogrammable spatially varying h 0 can be created. This creates spatial variation of the magnitude of the electric field gradients in the plane of the surface which the bubble responds to due to buoyancy, hence permitting directional bubble actuation.
Hence the ability described in this work to electrostatically detach, i.e., to dislodge and control bubbles at will in dielectric and conducting liquids has potential applications in; improving efficiency by rapidly removing nucleated bubbles in immersion heat transfer, [48][49][50] as an active "debubbler" in conventional microfluidics, for controlling bubbles in microgravity environments, [7] as well as opening up new avenues to achieving "wallless" surface driven bubble-microfluidics with the intervening liquid layer avoiding the issues associated with moving contact lines. [51]

Experimental Section
The experiments were carried out on air bubbles deposited onto solid surfaces immersed within one of two different dielectric liquids, trimethylolpropane triglycidyl ether (TMP-TG-E, CAS: 3454-29-3, dielectric constant, ε = 13.7, density, ρ = 1160 kg m −3 , surface tension γ LV = 44 mJ m −2 ) and propylene glycol (CAS: 57-55-7 dielectric constant, ε = 35, density, ρ = 1040 kg m −3 , surface tension, γ LV = 38.6 mJ m −2 ). Bubbles of volume in the range of 0.4-2.4 µL were created by injecting air onto the underside of the solid surface using a syringe. An array of interdigitated co-planar parallel microstripe electrodes fabricated from gold on titanium was patterned on the solid surface. The electrode linewidths equaled the electrode gaps, and two linewidths were used in the experiments, 20 and 40 µm. The surface and the electrodes were coated with a SU-8 dielectric layer (Microchem Corp., thickness 1 µm, dielectric constant 3.2) to prevent any conduction through the liquid. A final capping layer of Teflon AF was added to the device to promote retraction of the liquid from the surface, which imparted an equilibrium contact angle of 95° measured inside a bubble in TMP-TG-E, and 95° measured inside a bubble in PG. To coat the devices in Teflon AF, a solution was made from 0.5% w.t. of Poly[4,5-difluoro-2,2bis(trifluoromethyl)-1,3-dioxole-co-tetrafluoroethylene] (CAS: 37626-13-4) in the solvent Octadecafluorodecahydronaphthalene (CAS: 306-94-5). Substrates were dip-coated in the solution, allowed to dry at room temperature before baking at 155 °C for 20 min to cure.
The localized electric field gradient at the solid surface was produced by applying a sinusoidal A.C. voltage (V 0 ) at 10 kHz to alternate fingers of an interdigitated microstripe electrode array within the solid surface, with the interposed electrode fingers at earth potential.
For the DI water experiments, an electrode linewidth and gap of 200 µm was used with a PDMS dielectric layer (Sylgard-184., thickness 12 µm) to prevent any conduction through the liquid.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.