Stabilizing the Advancing Front of Thermally Driven Climbing Films.

As known from thermodynamic principles, the surface tension of a liquid decreases with increasing temperature. This property can be used to force a liquid film to climb a vertical substrate whose lower end is held warmer than the top. The vertical gradient in surface tension generates a surface shear stress that causes the liquid film to spread upward spontaneously in the direction of higher surface tension. Experimental investigations have shown that the application of a large temperature gradient produces a thin climbing film whose leading edge develops a pronounced capillary rim which breaks up into vertical rivulets. In contrast, smaller temperature gradients produce thicker films whose profiles decrease monotonically toward the substrate with no evidence of a rim or subsequent film breakup. We have previously shown within linear stability analysis that a climbing film can undergo a fingering instability at the leading edge when the film is sufficiently thin or the shear stress sufficiently large for gravitational effects to be negligible. In this work we show that thicker films which experience significant drainage cannot form a capillary rim and spread in stable fashion. Gravitational drainage helps promote a straight advancing front and complete surface coverage. Our numerical predictions for the entire shape and stability of the climbing film are in good agreement with extensive experiments published years ago by Ludviksson and Lightfoot (AIChE J. 17, 1166 (1971)). We propose that the presence of a counterflow which eliminates the capillary rim can provide a simple and general technique for stabilizing thermally driven films in other geometries. Copyright 1998 Academic Press.

A Theoretical Study of Instabilities at the Advancing Front of Thermally Driven Coating Films

A thin liquid coating can spread vertically beyond the equilibrium meniscus position by the application of a temperature gradient to the adjacent substrate. So called super-meniscus films experience a surface shear stress which drives flow toward regions of higher surface tension located at the cooler end of the substrate. The Marangoni stresses responsible 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 pronounced ridge with lateral undulations that develop into long slender rivulets. These rivulets, which prevent complete surface coverage, display a remarkable regularity in height, width, and spacing which suggests the presence of a hydrodynamic instability. We have performed a linear stability analysis of such thermally driven films to determine the most dangerous wavenumber. Our numerical solutions indicate the presence of an instability at the advancing front of films which develop a sufficiently thick capillary ridge. Our results for the film thickness profiles and spreading velocities, as well as the wavenumber corresponding to the most unstable mode, compare favorably with recent experimental measurements. An energy analysis of the perturbed flow reveals that the increased mobility in the thickened portions of the films strongly promotes unstable flow, in analogy with other coating processes using gravitational or centrifugal forces. Copyright 1997Academic Press