NONISOTHERMAL SPREADING OF A THIN LIQUID-FILM ON AN INCLINED PLANE

A thin layer of liquid advancing over a dry, heated, inclined plate is studied. A lubrication model with contact line motion is derived. The plate is at constant temperature, and the surface Biot number is spec ified. The steady-state solution is obtained numerically. In addition, the steady-state solution is studied analytically in the neighbourhoo d of the contact line. A linear stability analysis about the steady st ate is then performed. The effects of gravity, thermocapillarity and c ontact line motion are discussed. In particular, we determine a band o f unstable wavenumbers, and the maximum growth rate as a function of t hese parameters.