A variational model of disjoining pressure: Liquid film on a nonplanar surface

Journal Article · Mon Jun 01 04:00:00 EDT 2009 · Transport in Porous Media

OSTI ID:979806

Silin, D; Virnovsky, G

Variational methods have been successfully used in modelling thin liquid films in numerous theoretical studies of wettability. In this paper, the variational model of the disjoining pressure is extended to the general case of a two-dimensional solid surface. The Helmgoltz free energy functional depends both on the disjoining pressure isotherm and 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 the 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.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: Earth Sciences Division
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 979806
• Report Number(s): LBNL-2854E
• Journal Information: Transport in Porous Media, Journal Name: Transport in Porous Media; ISSN TPMEEI
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
58 GEOSCIENCES
FREE ENERGY
FUNCTIONALS
ISOTHERMS
PARTIAL DIFFERENTIAL EQUATIONS
ROUGHNESS
RUPTURES
SHAPE
STABILITY
VARIATIONAL METHODS
WETTABILITY