A Variational Model of Disjoining Pressure: Liquid Film on a Nonplanar Surface |
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Authors: | Dmitriy Silin George Virnovsky |
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Institution: | (1) Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India |
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Abstract: | Variational methods have been successfully used in modelling thin liquid films in numerous theoretical studies of wettability.
In this article, the variational model of the disjoining pressure is extended to the general case of a two-dimensional solid
surface. The Helmholtz free energy functional depends both on the disjoining pressure isotherm and on the shape of the solid
surface. The augmented Young–Laplace equation (AYLE) is a nonlinear second-order partial differential equation. A number of
solutions describing wetting films on spherical grains have been obtained. In the case of cylindrical films, the phase portrait
technique describes the entire variety of mathematically feasible solutions. It turns out that a periodic solution, which
would describe wave-like wetting films, does not satisfy Jacobi’s condition of the classical calculus of variations. Therefore,
such a solution is nonphysical. The roughness of the solid surface significantly affects liquid film stability. AYLE solutions
suggest that film rupture is more likely at a location where the pore-wall surface is most exposed into the pore space, and
the curvature is positive. |
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Keywords: | |
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