HOW LIQUIDS SPREAD ON SOLIDS

Abstract

A theory of the wetting of solids by liquids is put forward. The theory accounts for capillary pressure gradient, gravitational potential gradient, surface tension gradient, disjoining pressure gradient driving forces of flow in thick thin-films and of surface diffusion in thin thin-films. Disjoining pressure stems from the way intermolecular forces aggregate in submicroscopically thin films. For thick thin-films of slowly varying thickness the lubrication approximation to velocity distributions is appropriate. With this approximation the spontaneous, unsteady, two-dimensional spreading of liquid is shown to be governed by a nonlinear convective-diffusion equation for the evolution of the film thickness profile. The predictions of the theory agree with Marmur and Lelah's (1980, 1981) observations of water drops spreading on glass and with Bascom, Cottington and Singleterry's (1964) and Ludviksson and Lightfoot's (1971) observations of oils spreading on high energy surfaces. The theory is used to analyze Derjaguin and co-workers' (1944, 1957, 1970) blowing-off experiments designed to measure thin-film rheology. The theory is also used to buttress the proposition that much contact angle hysteresis is due simply to slow attainment of equilibrium.

KEYWORDS:

• Capillary pressure
• Gravitational potential
• Surface tension
• Surface diffusion