Liquid film entrainment during dip coating on a saturated porous substrate
The present work examines the effect of substrate surface porosity on the coating thickness and meniscus profile during dip coating under saturated porous media conditions. The classical Landau-Levich formulation is modified by encoding the influence of porosity in an effective Navier slip boundary condition at the porous substrate surface. It is shown that simplified Navier slip-based model works well for creeping flow through the porous medium. The film height profile equation is derived as a function of a rescaled capillary number (Ca‾) and a substrate permeability factor, with inertial effects neglected. Numerical solutions show that the classical 2/3rd power dependence of film thickness on capillary number is recovered only at sufficiently high Ca‾ values. As Ca‾ is decreased, a marked deviation is seen. The shrinking of the entrainment meniscus and the change in meniscus curvature are analyzed in detail. The theoretical results are also validated with a suitable experimental system.
Switching the Roles of Wettability-based Patterns Through Solutal Marangoni Effect
Controlling the dynamics of thin liquid films on solid surfaces is illustrated by a combination of substrate patterning and solutal Marangoni effect. A solid surface, patterned based on wettability differences, can trigger film instability due to wettability gradient-driven flows. Additionally, if insoluble surfactants are introduced at the liquid film surface, the surfactant transport can cause surface-tension gradients across the film, and a solutal Marangoni flow results. By using suitable non-uniform initial surfactant concentration distributions, the rate and direction of Marangoni flow can be manipulated to compete with the wettability gradient-driven flows. It is found that film dewetting can be reversed in selected problem parameter space. Dewetting can be engendered on more wettable patches of the bounding solid, with a consequent accumulation of the liquid on less wettable regions. The importance of length scales of the less and more wettable patches on switching the roles of wetting behaviour is also investigated.
Interplay of substrate wettability and surfactant distributions in controlling interfacial instability
The current work investigates the combined effects of substrate wettability patterns and preset surfactant distributions on the dynamics and rupture of thin liquid films. The configuration considered here is a liquid film with a free surface above, and bounded below by a solid substrate with alternate zones of less and more wettable areas. This wettability-based patterning triggers an instability of the liquid film, caused by the outward flow from less to more wettable regions at the liquid–substrate interface. Introducing surfactants in the liquid film also affects the interfacial dynamics through Marangoni flow at the air–liquid interface. A variety of distribution functions are used as initial conditions for the surfactant concentration, to suitably modify the final configuration of a flat film. A set of two evolution equations for the film height and surfactant concentration are developed as partial differential equations to be solved numerically and simultaneously. Results indicate that the interplay between substrate wettability and surfactant distributions may significantly alter the ruptured film configurations. Typical scenarios include multiple near-rupture events in place of a single rupture, asymmetry in the ruptured film profile, and reversal of flow leading to film rupture on a more wettable region of the substrate. The results also provide insights into the dependence of rupture time scales on the inherent length scales in the problem, such as the pattern feature widths and the size of the surfactant-depleted zones.