The effect of evaporation on fingering instabilities

• Published in: Physics of fluids (1994) 2009-12, Vol.21 (12), p.122101-122101-9
• Main Authors: Klentzman, Jill, Ajaev, Vladimir S.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Interfacial instability; Physics; Surface-tension-driven instability
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3271826

We investigate the flow of evaporating thin films of viscous liquid on inclined solid substrates under the influence of gravity. A lubrication-type approach is used to develop a three-dimensional model of the flow including physical effects such as capillarity, gravity, Marangoni stresses, disjoining pressure, and evaporation. Numerical simulations are then carried out based on the model. The effect of evaporation on the so-called fingering instability that develops along the contact line in the transverse direction of the flow is studied. It is found that evaporation acts to suppress the instability if the evaporation number, a nondimensional measure of the mass flow rate across the interface, is above a critical value. The critical value decreases as the inclination angle is decreased. For the values of evaporation number below the critical one, the fingers grow initially but then saturate at a length that depends on the evaporation conditions. It is also shown that thermocapillarity acts to enhance the instability.