2-DIMENSIONAL AND 3-DIMENSIONAL INSTABILITIES AND RUPTURE OF THIN LIQUID-FILMS FALLING ON HEATED INCLINED PLATE

Long-wave instabilities in thin viscous films draining down heated inclined planes are studied. Linear stability analysis and nonlinear computations are performed via a long-wave evolution equation, which describes the effects of mass loss, wave propagation, mean flow, hydrostatic pressure, thermocapillarity, vapor recoil, and mean surface tension. Mean flow, thermocapillarity, and vapor recoil destabilize the flow, and give, respectively, surface-wave, thermocapillary, and evaporative instabilities. Nonlinear flow developments, examined by numerically integrating the evolution equation, show interesting interactions of the instabilities, including generation of longitudinal patterns.