STABILIZING THE ADVANCING FRONT OF THERMALLY DRIVEN CLIMBING FILMS

As known from thermodynamic principles, the surface tension of a liqui d decreases with increasing temperature. This property can be used to force a liquid film to climb a vertical substrate whose lower end is h eld warmer than the top. The vertical gradient in surface tension gene rates a surface shear stress that causes the liquid film to spread upw ard spontaneously in the direction of higher surface tension. Experime ntal investigations have shown that the application of a large tempera ture gradient produces a thin climbing film whose leading edge develop s a pronounced capillary rim which breaks up into vertical rivulets. I n 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 l inear stability analysis that a climbing film can undergo a fingering instability at the leading edge when the him is sufficiently thin or t he shear stress sufficiently large for gravitational effects to be neg ligible. In this work we show that thicker films which experience sign ificant drainage cannot form a capillary rim and spread in stable fash ion. Gravitational drainage helps promote a straight advancing front a nd complete surface coverage. Our numerical predictions for the entire shape and stability of the climbing him are in good agreement with ex tensive experiments published years ago by Ludviksson and Lightfoot (A IChE J. 17, 1166 (1971)). We propose that the presence of a counterflo w which eliminates the capillary rim can provide a simple and general technique for stabilizing thermally driven films in other geometries. (C) 1998 Academic Press.