tension gradient, which depends on the particular tempera-As known from thermodynamic principles, the surface tension ture distribution along the substrate, creates a surface shear of a liquid decreases with increasing temperature. This property stress that forces the liquid film to climb above the position can be used to force a liquid film to climb a vertical substrate of the equilibrium meniscus. Concentration variations at an whose lower end is held warmer than the top. The vertical gradient air-liquid interface, which are more difficult to control, can in surface tension generates a surface shear stress that causes the produce a similar shear stress which causes a liquid coating liquid film to spread upward spontaneously in the direction of to spread upward against gravity. Such ''supermeniscus'' higher surface tension. Experimental investigations have shown films have been shown to be important in the operation of gas that the application of a large temperature gradient produces a thin climbing film whose leading edge develops a pronounced cap-diffusion electrodes in which the oxidation reaction occurs illary rim which breaks up into vertical rivulets. In contrast, almost exclusively in the region above the normal meniscus smaller temperature gradients produce thicker films whose profiles position (1). Enhanced spreading behavior has also been decrease monotonically toward the substrate with no evidence of observed in boundary lubrication problems in which the a rim or subsequent film breakup. We have previously shown evaporation of volatile impurities in the spreading films eswithin linear stability analysis that a climbing film can undergo a tablishes a spontaneous concentration gradient (2). Flows fingering instability at the leading edge when the film is sufficiently created by gradients in surface tension, whether induced by thin or the shear stress sufficiently large for gravitational effects temperature or concentration variations, are commonly to be negligible. In this work we show that thicker films which called thermocapillary or Marangoni-driven flows. These experience significant drainage cannot form a capillary rim and types of flows, which become dominant in situations where spread in stable fashion. Gravitational drainage helps promote a straight advancing front and complete surface coverage. Our the surface-to-volume ratio of the liquid film is large, are numerical predictions for the entire shape and stability of the receiving increased attention as technological advances enclimbing film are in good agreement with extensive experiments courage the production of smaller and lighter componentry.
published years ago by Ludviksson and Lightfoot (AIChE J. 17, Although temperature or concentration gradients can 1166 (1971)). We propose that the presence of a counterflow therefore be used very effectively to guide a spreading film which eliminates the capillary rim can provide a simple and gento coat a substrate, the coating process will be unsuccessful eral technique for stabilizing thermally driven films in other geomif the liquid spreads nonuniformly and suffers any instability etries. α§ 1998 Academic Press at the leading edge. Several groups have shown that ther-Key Words: drainage; thermally driven spreading; coating films; mally driven films are subject to a fingering instability at Marangoni forces.
the advancing front. In coating experiments of horizontal (3) or vertical substrates (4, 5), thermally driven films were observed to develop a pronounced capillary rim at the lead-