Spreading of Thin Droplets of Perfect and Leaky Dielectric Liquids on Inclined Surfaces

Abstract

The spreading of droplets may be influenced by electric fields, a situation that is relevant to applications such as coating, printing, and microfluidics. In this work we study the effects of an electric field on the gravity-driven spreading of two-dimensional droplets down an inclined plane. We consider both perfect and leaky dielectric liquids, as well as perfectly and partially wetting systems. In addition to the effects of electric fields, we examine the use of thermocapillary forces to suppress the growth of the capillary ridge near the droplet front. Lubrication theory is applied to generate a set of coupled partial differential equations for interfacial height and charge, which are then solved numerically with a finite-difference method. Electric fields increase the height of the capillary ridge in both perfect and leaky dielectric droplets due to electrostatic pressure gradients that drive liquid into the ridge. In leaky dielectrics, large interfacial charge gradients in the contact-line region create shear stresses that also enhance ridge growth and the formation of trailing minor ridges. The coalescence of these ridges can significantly affect the long-time thinning rate of leaky dielectric droplets. In partially wetting liquids, electric fields promote the splitting of smaller droplets from the primary droplet near the receding contact line due to the interplay between electrostatic forces and disjoining pressure. Cooling from below and heating from above generates thermocapillary forces that counteract the effects of electric fields and suppress the growth of the capillary ridge. The results of this work have important implications for manipulating the spreading of droplets down inclined surfaces.

Accurate low-order modeling of electrified falling films at moderate Reynolds number

“…This has included work on the full leaky dielectric formulation [17,18] 40 as well as the simpler situations where both regions have large conductivities [19], or indeed where 41 one region is a perfect conductor [20]. Notably, given a permittivity ratio R and a conductivity ratio…”

“…This is complemented by no-slip and no-penetration, the kinematic equation (12), and the tangential 133 stress equation (18). Equations (25) and (18) are now solved by use of the method of weighted 134 residuals.…”

Influence of Surface Roughness on Droplet Evaporation and Absorption: Insights into Experiments from Lubrication-Theory-Based Models

“…A principal advantage of lubrication-theory-based models is that numerous physical effects (e.g., surfactants, thermocapillarity, electrostatics 76 ) can readily be incorporated and the resulting equations can be solved with much less computational effort compared to models that do not employ the lubrication approximation. This enables the efficient exploration of various phenomena, which is helpful in deciding how to employ resources for more detailed modeling and complementary experiments.…”