Polarization of disk electrodes in high-conductivity electrolyte solutions.

We investigate the polarization of disk electrodes immersed in an electrolyte solution and subjected to a small external AC voltage over a wide range of frequencies. A mathematical model is developed based on the Debye-Falkenhagen approximation to the coupled Poisson-Nernst-Planck equations. Analytical techniques are used for predicting the spatial distribution of the electric potential and the complex impedance of the system.

Evaporation and fluid flow near the boundary of a stationary dry patch.

We consider an isolated circular dry patch formed in an evaporating liquid layer and investigate local viscous flows in both liquid and air near the contact line which is the boundary of the dry patch. Flow patterns in the liquid deviate significantly from the predictions of single-phase models even when the air-to-liquid dynamic viscosity ratio is small. In particular, the separatrices in the liquid flow patterns at large contact angles disappear completely for a range of realistic viscosity ratios when the shear stress on the air side of the interface is accounted for.

Levitation conditions for condensing droplets over heated liquid surfaces.

We report experimental studies and develop mathematical models of levitation of microscale droplets over an evaporating liquid layer. The maximum size of droplets is estimated from the balance between gravity and Stokes force due to the action of upward Stefan flow generated by evaporation. Mathematical models of diffusion around levitating droplets allow us to determine Stefan flow velocity at the liquid layer surface.

Interaction of advancing contact lines with defects on heated substrates.

We consider an advancing contact line traveling over a region of locally modified wetting or thermal substrate properties. A lubrication-type model is developed to account for coupling of viscous flow, evaporation, surface tension, and disjoining pressure. Stick-slip-type behavior is found for a range of conditions as the contact line passes over the defect and explained by a temporary increase in the local stresses disrupting the liquid supply into the contact line region.

Levitation and Self-Organization of Liquid Microdroplets over Dry Heated Substrates.

Levitating droplets of liquid condensate are known to organize themselves into ordered arrays over hot liquid-gas interfaces. We report experimental observation of similar behavior over a dry heated solid surface. Even though the lifetime of the array is shorter in this case, its geometric characteristics are remarkably similar to the case of droplets levitating over liquid-gas interfaces.

Stability and break-up of thin liquid films on patterned and structured surfaces.

Solid surfaces with chemical patterning or topographical structure have attracted attention due to many potential applications such as manufacture of flexible electronics, microfluidic devices, microscale cooling systems, as well as development of self-cleaning, antifogging, and antimicrobial surfaces. In many configurations involving patterned or structured surfaces, liquid films are in contact with such solid surfaces and the issue of film stability becomes important. Studies of stability in this context have been largely focused on specific applications and often not connected to each other.

Significance of electrically induced shear stress in drainage of thin aqueous films.

We develop a novel model of drainage of microscale thin aqueous film separating a gas bubble and a solid wall. In contrast to previous studies, the electrostatic effects are accounted for not only in the normal but also in the shear stress balance at the liquid-gas interface. We show that the action of the tangential component of the electric field leads to potentially strong spatially variable shear stress at the deforming charged interface.

Effect of charge regulation on the stability of electrolyte films.

The stability of a thin liquid film of an electrolyte on a solid substrate is investigated. In the framework of the Debye-Hückel approximation, we show that the commonly used approximation of fixed potential at the solid-liquid interface does not lead to predictions of film rupture. To reconcile the model with experimental observations, we consider the constant charge density approximation for the solid substrate and then proceed to systematically investigate the effects of charge regulation based on a linear relationship between charge density and potential.

Rupture of thin liquid films on structured surfaces.

We investigate stability and breakup of a thin liquid film on a solid surface under the action of disjoining pressure. The solid surface is structured by parallel grooves. Air is trapped in the grooves under the liquid film.

Static and dynamic contact angles of evaporating liquids on heated surfaces.

We studied both static and dynamic values of the apparent contact angle for gravity-driven flow of a volatile liquid down a heated inclined plane. The apparent contact line is modeled as the transition region between the macroscopic film and ultra-thin adsorbed film dominated by disjoining pressure effects. Four commonly used disjoining pressure models are investigated.

Ripples in a wetting film formed by a moving meniscus.

We carry out a theoretical investigation of the evolution of a wetting film formed by pressing a bubble against a solid substrate. Our model incorporates the effects of capillarity and Derjaguin-Landau-Verwey-Overbeek (DLVO) (van der Waals and electrostatic) components of the disjoining pressure. Rapid changes in the relative position of the bubble and the substrate are shown to result in surprisingly rich dynamics of wetting film deformations.

Evolution of dry patches in evaporating liquid films.

We investigate evolution of dry patches in a thin film of a volatile liquid on a heated plate in the framework of a model that accounts for the effects of surface tension, evaporation, thermocapillarity, and disjoining pressure. Dry areas on the plate are modeled by isothermal microscopic films which are in thermodynamic equilibrium with the vapor. For nonpolar liquids such equilibrium is achieved due to van der Waals forces, well-defined capillary ridges are formed around growing dry patches, contact line speed increases with time.

Viscous flow of a volatile liquid on an inclined heated surface.

We investigate the effects of evaporation on a gravity-driven flow of a viscous liquid on a heated solid surface. Vapor molecules are adsorbed on the dry areas of the solid and form a microscopic adsorbed film. The thickness of this film is calculated from the formulas for disjoining pressure and the principles of equilibrium thermodynamics.

Dynamic response of geometrically constrained vapor bubbles.

We consider a two-dimensional model of a vapor bubble between two horizontal parallel boundaries held at different temperatures. When the temperatures are constant, a steady state can be achieved such that evaporation near the contact lines at the hot bottom plate is balanced by condensation in colder areas of the interface near the top. The dynamic response of the bubble is probed by treating the case of time-dependent wall temperatures.

Steady Vapor Bubbles in Rectangular Microchannels.

We consider vapor bubbles in microchannels in which the vapor is produced by a heater element and condenses in cooler parts of the interface. The free boundary problem is formulated for a long steady-state bubble in a rectangular channel with a heated bottom. Lubrication-type equations are derived for the shape of the liquid-vapor interface in a cross-sectional plane and in the regime for which the vapor phase fills most of the cross section.