Crater Formation on Electrodes during Charge Transfer with Aqueous Droplets or Solid Particles.

We report that metallic electrodes are physically pitted during charge transfer events with water droplets or other conductive objects moving in strong electric fields (>1 kV/cm). Post situ microscopic inspection of the electrode shows that an individual charge transfer event yields a crater approximately 1-3 µm wide, often with features similar to a splash corona. We interpret the crater formation in terms of localized melting of the electrode via resistive heating concurrent with dielectric breakdown through the surrounding insulating fluid. A scaling analysis indicates that the crater diameter scales as the inverse cube root of the melting point temperature T_{m} of the metal, in accord with measurements on several metals (660 °C≤T_{m}≤3414 °C). The process of crater formation provides a possible explanation for the longstanding difficulty in quantitatively corroborating Maxwell's prediction for the amount of charge acquired by spheres contacting a planar electrode.

Hexatic-to-disorder transition in colloidal crystals near electrodes: rapid annealing of polycrystalline domains.

Colloids are known to form planar, hexagonal closed packed (hcp) crystals near electrodes in response to electrohydrodynamic (EHD) flow. Previous work has established that the EHD velocity increases as the applied ac frequency decreases. Here we report the existence of an order-to-disorder transition at sufficiently low frequencies, despite the increase in the attractive EHD driving force. At large frequencies (~500 Hz), spherical micron-scale particles form hcp crystals; as the frequency is decreased below ~250 Hz, however, the crystalline structure transitions to randomly closed packed (rcp). The transition is reversible and second order with respect to frequency, and independent measurements of the EHD aggregation rate confirm that the EHD driving force is indeed higher at the lower frequencies. We present evidence that the transition is instead caused by an increased particle diffusivity due to increased particle height over the electrode at lower frequencies, and we demonstrate that the hcp-rcp transition facilitates rapid annealing of polycrystalline domains.

Electrically tunable partial coalescence of oppositely charged drops.

We report the existence of a critical ionic conductivity below which oppositely charged drops only partially coalesce. The extent of coalescence between dissimilarly sized water drops in oil can be tuned from complete coalescence at low electric field strengths to complete noncoalescence at high field strengths, thus providing external control over the daughter droplet size. Strikingly, the size and charge of the daughter droplet are both independent of the ionic conductivity. We present evidence suggesting the charge transfer is instead strongly influenced by convection associated with the capillary-driven penetration of a vortex into the larger drop, and we demonstrate that the size of the daughter droplet is consistent with a scaling model based on a balance between capillary-driven inertia and electrostatic repulsion.

Michaelis-Menten kinetics in shear flow: Similarity solutions for multi-step reactions.

Models for chemical reaction kinetics typically assume well-mixed conditions, in which chemical compositions change in time but are uniform in space. In contrast, many biological and microfluidic systems of interest involve non-uniform flows where gradients in flow velocity dynamically alter the effective reaction volume. Here, we present a theoretical framework for characterizing multi-step reactions that occur when an enzyme or enzymatic substrate is released from a flat solid surface into a linear shear flow. Similarity solutions are developed for situations where the reactions are sufficiently slow compared to a convective time scale, allowing a regular perturbation approach to be employed. For the specific case of Michaelis-Menten reactions, we establish that the transversally averaged concentration of product scales with the distance x downstream as x(5/3). We generalize the analysis to n-step reactions, and we discuss the implications for designing new microfluidic kinetic assays to probe the effect of flow on biochemical processes.

Aggregation and coalescence of oil droplets in water via electrohydrodynamic flows.

Electrohydrodynamic (EHD) flows are known to cause rigid colloids to aggregate near electrodes. Here we report that EHD flows also induce immiscible oil droplets to aggregate and, for sufficiently strong field strengths, to coalesce. We measure the aggregation and coalescence rates of micrometer-scale oil droplets in water, and we find that the most effective way to induce coalescence is by suddenly decreasing the applied frequency. We interpret the results in terms of a balance between EHD flow and colloidal forces, and we discuss the implications for using EHD flows to separate trace oils from solution.

Non-coalescence of oppositely charged drops.

Electric fields induce motion in many fluid systems, including polymer melts, surfactant micelles and colloidal suspensions. Likewise, electric fields can be used to move liquid drops. Electrically induced droplet motion manifests itself in processes as diverse as storm cloud formation, commercial ink-jet printing, petroleum and vegetable oil dehydration, electrospray ionization for use in mass spectrometry, electrowetting and lab-on-a-chip manipulations. An important issue in practical applications is the tendency for adjacent drops to coalesce, and oppositely charged drops have long been assumed to experience an attractive force that favours their coalescence. Here we report the existence of a critical field strength above which oppositely charged drops do not coalesce. We observe that appropriately positioned and oppositely charged drops migrate towards one another in an applied electric field; but whereas the drops coalesce as expected at low field strengths, they are repelled from one another after contact at higher field strengths. Qualitatively, the drops appear to 'bounce' off one another. We directly image the transient formation of a meniscus bridge between the bouncing drops, and propose that this temporary bridge is unstable with respect to capillary pressure when it forms in an electric field exceeding a critical strength. The observation of oppositely charged drops bouncing rather than coalescing in strong electric fields should affect our understanding of any process involving charged liquid drops, including de-emulsification, electrospray ionization and atmospheric conduction.

Electrohydrodynamic flow and colloidal patterning near inhomogeneities on electrodes.

Current density inhomogeneities on electrodes (of physical, chemical, or optical origin) induce long-range electrohydrodynamic fluid motion directed toward the regions of higher current density. Here, we analyze the flow and its implications for the orderly arrangement of colloidal particles as effected by this flow on patterned electrodes. A scaling analysis indicates that the flow velocity is proportional to the product of the applied voltage and the difference in current density between adjacent regions on the electrode. Exact analytical solutions for the streamlines are derived for the case of a spatially periodic perturbation in current density along the electrode. Particularly simple asymptotic expressions are obtained in the limits of thin double layers and either large or small perturbation wavelengths. Calculations of the streamlines are in good agreement with particle velocimetry experiments near a mechanically generated inhomogeneity (a "scratch") that generates a current density larger than that of the unmodified electrode. We demonstrate that proper placement of scratches on an electrode yields desired patterns of colloidal particles.

Electrically driven flow near a colloidal particle close to an electrode with a Faradaic current.

To elucidate the nature of processes involved in electrically driven particle aggregation in steady fields, flows near a charged spherical colloidal particle next to an electrode were studied. Electrical body forces in diffuse layers near the electrode and the particle surface drive an axisymmetric flow with two components. One is electroosmotic flow (EOF) driven by the action of the applied field on the equilibrium diffuse charge layer near the particle. The other is electrohydrodynamic (EHD) flow arising from the action of the applied field on charge induced in the electrode polarization layer. The EOF component is proportional to the current density and the particle surface (zeta) potential, whereas our scaling analysis shows that the EHD component scales as the product of the current density and applied potential. Under certain conditions, both flows are directed toward the particle, and a superposition of flows from two nearby particles provides a mechanism for aggregation. Analytical calculations of the two flow fields in the limits of infinitesimal double layers and slowly varying current indicate that the EOF and EHD flow are of comparable magnitude near the particle whereas in the far field the EHD flow along the electrode is predominant. Moreover, the dependence of EHD flow on the applied potential provides a possible explanation for the increased variability in aggregation velocities observed at higher field strengths.

Influence of substrate conductivity on circulation reversal in evaporating drops.

Nonuniform evaporation from sessile droplets induces radial convection within the drop, which produces the well-known "coffee-ring" effect. The evaporation also induces a gradient in temperature and consequently a gradient in surface tension, generating a Marangoni flow. Here we investigate theoretically and experimentally the thermal Marangoni flow and establish criteria to gauge its influence. An asymptotic analysis indicates that the direction of the flow depends on the relative thermal conductivities of the substrate and liquid, k_{R} identical withk_{S}/k_{L}, reversing direction at a critical contact angle over the range 1.45

Coalescence of spreading droplets on a wettable substrate.

We investigate experimentally and theoretically the coalescence dynamics of two spreading droplets on a highly wettable substrate. Upon contact, surface tension drives a rapid motion perpendicular to the line of centers that joins the drops and lowers the total surface area. We find that the width of the growing meniscus bridge between the two droplets exhibits power-law behavior, growing at early times as t1/2. Moreover, the growth rate is highly sensitive to both the radii and heights of the droplets at contact, scaling as ho3/2/Ro. This size dependence differs significantly from the behavior of freely suspended droplets, in which the coalescence growth rate depends only weakly on the droplet size. We demonstrate that the scaling behavior is consistent with a model in which the growth of the meniscus bridge is governed by the viscously hindered flux from the droplets.

Assembly of colloidal aggregates by electrohydrodynamic flow: Kinetic experiments and scaling analysis.

Electric fields generate transverse flows near electrodes that sweep colloidal particles into densely packed assemblies. We interpret this behavior in terms of electrohydrodynamic motion stemming from distortions of the field by the particles that alter the body force distribution in the electrode charge polarization layer. A scaling analysis shows how the action of the applied electric field generates fluid motion that carries particles toward one another. The resulting fluid velocity is proportional to the square of the applied field and decreases inversely with frequency. Experimental measurements of the particle aggregation rate accord with the electrohydrodynamic theory over a wide range of voltages and frequencies.

Electrically guided assembly of planar superlattices in binary colloidal suspensions.

Binary colloidal suspensions are assembled into planar superlattices using ac electric fields. Either triangular or square-packed arrays form, depending on the frequency and relative particle concentrations. The frequency dependence is striking since superlattices develop at low and high frequencies but not at intermediate frequencies. We explain the low frequency behavior (<3 kHz) in terms of induced-dipole repulsion balanced by attraction resulting from electrohydrodynamic (EHD) flow. At high frequencies (20-200 kHz), EHD flow is negligible but aggregation occurs since dipole-dipole interactions become attractive.