A THEORETICAL-STUDY OF INSTABILITIES AT THE ADVANCING FRONT OF THERMALLY DRIVEN COATING FILMS

A thin liquid coating can spread vertically beyond the equilibrium men iscus position by the application of a temperature gradient to the adj acent substrate. So called super-meniscus fins experience a surface sh ear stress which drives how toward regions of higher surface tension l ocated at the cooler end of the substrate. The Marangoni stresses resp onsible for this spreading process can also be used to coat horizontal surfaces rapidly and efficiently. Experiments in the literature have shown that in either geometry, the advancing front can develop a prono unced ridge with lateral undulations that develop into long slender ri vulets. These rivulets, which prevent complete surface coverage, displ ay a remarkable regularity in height, width, and spacing which suggest s the presence of a hydrodynamic instability. We have performed a line ar stability analysis of such thermally driven films to determine the most dangerous wavenumber. Our numerical solutions indicate the presen ce of an instability at the advancing front of films which develop a s ufficiently thick capillary ridge. Our results for the film thickness profiles and spreading velocities, as well as the wavenumber correspon ding to the most unstable mode, compare favorably with recent experime ntal measurements. An energy analysis of the perturbed flow reveals th at the increased mobility in the thickened portions of the films stron gly promotes unstable flow, in analogy with other coating processes us ing gravitational or centrifugal forces. (C) 1997 Academic Press.