Complex interfacial and wetting dynamics

Abstract

Consider interface evolution in bounded and unbounded settings, namely in the spreading of droplets and stratified gas-liquid flows. A typical prototype consists of the surfacetension-dominated motion of a two-dimensional droplet on a substrate. The case of chemically heterogeneous substrates was examined here. Assuming small slopes, a single evolution equation for the droplet free surface was derived from the Navier-Stokes equations, with the singularity at the contact line being alleviated using the Navier slip condition. The chemical nature of the substrate is incorporated into the system by local variations in the microscopic contact angle. By using the method of matched asymptotic expansions, the flow in the vicinity of the contact lines is matched to that in the bulk of the droplet to obtain a set of coupled ordinary differential equations for the location of the two contact points. The solutions obtained by asymptotic matching are in excellent agreement with the solutions to the full governing evolution equation. The dynamics of the droplet is examined in detail via a phase-plane analysis. A number of interesting features that are not present in homogeneous substrates are observed: multiple droplet equilibria, pinning of contact points on localised heterogeneities, unidirectional motion of droplet and the possibility of stick-slip behaviour of contact points. Unbounded gas-liquid flows are also often encountered in natural phenomena and applications. The prototypical system considered here consists of a liquid film flowing down an inclined planar substrate in the presence of a co-flowing turbulent gas. The gas and liquid problems are solved independently by making certain reasonable assumptions. The influence of gas flow on the liquid problem is analysed by developing a weighted integralboundary-layer (WIBL) model, which is valid up to moderate Reynolds numbers. We seek solitary-wave solutions of this model using a pseudo-arclength continuation approach. As a general trend, it is found that the wave speed increases with increasing gas shear and the liquid flow rate. Further insight into the problem is provided by time-dependent computations of the WIBL model. Finally, the absolute-convective instability of a falling film that is in contact with a counter-current turbulent gas is analysed. The Orr–Sommerfeld (O-S) problem is formulated from the full governing equations and boundary conditions. The O-S problem along