CONTINUUM SHARP INTERFACE MODELS FOR CONTACT LINES: ANALYSES AND SIMULATIONS

Abstract

When two immiscible fluids flow on a solid substrate, a moving contact line (MCL) forms at where the fluid-fluid interface meets the solid surface. The MCL problem has been an issue of debate for decades. This thesis covers four relevant topics. First, we prove by complex analysis the non-existence of the solution to Stokes equations with the no-slip condition, showing the inconsistency of the classical model applied to MCLs. Next, we present an implementation-friendly model, following the energy law, and its fast solver for general multi-phase incompressible flows with the appearance of MCLs. Thereafter, we study the boundary conditions of fluid-structure systems along the MCL, highlighting the essentially different behavior of 3-D and 2-D hyper-elastic materials at this location. Finally, we explore with asymptotic analysis the definition of the apparent contact angle in electro-wetting on dielectric, showing that this well-defined angle can be taken as the one observed in experiments.