Displacement of Fluid Droplets From Solid Surfaces

Abstract

The displacement of fluid droplets from solid substrates is a fundamental problem of fluid mechanics. This problem has application in coating operations, enhanced oil recovery and vapor condensation. Our goal is to predict the yield conditions (capillary number Ca) as a function of physical parameters including viscosity ratio lambda, Bond number B d and advancing and receding contact angles thetaA and thetaR. To determine the yield conditions, we conduct a computational study employing a spectral implementation of the boundary integral method for Stokes flow. In these computations, we develop a novel Newton iteration algorithm which allows us to determine equilibrium interfaces in low Re flows. In earlier studies, the treatment of the contact line has been simplified by assuming fixed geometrical shapes such as circles or ellipses. In our study, we model the true physics by solving for the actual contour of the contact line as determined by the contact angle hysteresis thetaA -- thetaR. This model requires the solution of a nonlinear optimization problem: search over all possible contact line profiles to determine the configuration which minimizes the contact angle hysteresis for a given flow rate or gravitational force. Results are presented for the yield conditions for four model problems: drop displacement from plane solid substrates in low Re shear flows, gravitational displacement of droplets from inclined planes and the displacement of droplets and fluid bridges in pressure-driven flows. The study covers a wide range of all the parameters which affect the three problems. A number of significant results concerning the fundamental physics are revealed.