ANALYSES AND COMPUTATIONS OF CONTACT LINES ON AN ELASTIC MEMBRANE

Abstract

When the substrate is soft, its deformation near the contact line will effectively affect the static and dynamic behaviors of the system. This thesis is devoted to our study of the static and dynamic contact line problems on an elastic membrane. An energy-based framework is considered to derived models for these problems. Asymptotic solutions are obtained and numerically verified for static systems in the limits as the positive bending modulus tends to infinity and zero, respectively. A FEM-based numerical method is designed with proved well-posedness and the numerical convergence. Two applications of the model are considered, including the relaxation dynamics of a droplet on a membrane and the spontaneous droplet transport driven by bendotaxis in a channel bounded by two membranes. The numerical simulation results are consistent with the phenomena observed in experiments. Furthermore, the physical processes and the relevant forces are analyzed theoretically and numerically.