Contact Angles and Inertia for Liquid Bounded by an Oscillating Plate

Abstract

The contact angle between a liquid and a solid varies with the speed of the contact line, and has been much studied for zero Reynolds numbers. In order to examine how this behaviour is affected by inertia, the contact line between a pool of liquid and an oscillating bounding plate is studied. If the boundary is nearly horizontal, the simplification afforded by lubrication theory is possible. If small-amplitude oscillations are considered, the problem is governed by a linear differential equation. The contact-line speed and the contact angle are obtained for all Reynolds numbers. For moderate Reynolds numbers the contact line is fixed in the plate, and the contact angle has a constant magnitude, but there is a phase difference between the angle and the plate speed that depends on the slip coefficient and the Reynolds number. The oscillation produces an outward capillary-gravity wave on the free surface of the liquid. The amplitude of this wave does not depend significantly on the slip coefficient, but increases linearly with the Reynolds number