Film flow within an axially rotating horizontal cylinder and contact lines on an oscillating plate

A major difficulty in describing the interaction between surface waves and solid substrates is the unphysical stress singularity at the contact line that arises when the classical hydrodynamic assumptions are applied to the moving contact line. There are two primary methods to relieve the stress singularity. One constructs an “inner” region very near the contact line with slip and intermolecular forces. The other introduces a wetting-layer to alleviate the stress singularity at the moving contact line. In this work both methods are studied for flows in different geometries (oscillating contact lines on plates and film flow inside a cylinder).; To study the dynamic behavior of oscillating contact lines, stainless steel instead of glass (Ting & Perlin, 1995) minimizes the static meniscus in oscillating experiments. Previous experiments using a glass plate had similar dynamic behavior of oscillatory contact lines on a stainless steel plate. A pinned-edge condition appropriately describes the contact line motion for low Reynolds-number-oscillations. In high-Reynolds-number oscillations, the contact-line behavior becomes nonlinear though still periodic. Three types of motion associated with contact angle hysteresis occur: stick, partial stick, and slip. An edge condition allowing both the static range and dynamic behavior over one period is developed. Using this edge condition, I calculate the dynamic contact angle and the contact-line position for both stick and slip motion and compare them to the experimental data. Results show that the inviscid, linearized boundary-value problem combined with a slip coefficient model provides an improved prediction.; For film flow inside a rotating cylinder, the application of lubrication theory is revisited. High-order solutions based on the dimensionless film thickness are provided with capillary effects included. The results show that surface tension and higher-order terms allow better comparison with experiments, but significant differences still exist. A much-improved prediction of the thin film at both high and low rotation speed is achieved by introducing the centrifugal force in the r-momentum equation, and the pressure gradient term in the &thetas;-momentum equation. In addition, including the capillary effect and disjoining pressure in the dynamic boundary condition improves the model for slow rotation.