Fingering instability of partially wetting evaporating liquids

• Published in: Journal of engineering mathematics 2012-04, Vol.73 (1), p.31-38
• Main Authors: Ajaev, Vladimir S., Klentzman, Jill, Gambaryan-Roisman, Tatiana, Stephan, Peter
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Theoretical and Applied Mechanics
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-010-9448-y

A numerical study of the fingering instability of the leading edge of a film of evaporating partially wetting liquid flowing down an inclined solid substrate is presented. The effects of capillarity, gravity, disjoining pressure, and evaporation are included in the formulation of our lubrication-type model. The disjoining pressure is assumed to be a linear combination of two components to account for both van der Waals forces and electrostatic effects. Consistent with previously published results, evaporation has a stabilizing effect on fingering instability and can completely suppress the instability if the evaporation number, a nondimensional measure of evaporation intensity, is above a critical value. The critical evaporation number decreases as the inclination angle is decreased. Increasing the apparent contact angle by suitable changes in the disjoining pressure parameters, has a destabilizing influence on the contact line. Also investigated is the length of the fingers in the regime when the instability develops, and it is found that this length decreases as the evaporation number is increased.