Dip coating with an interaction potential normal to the substrate

• Published in: Physics of fluids (1994) Vol. 24; no. 2; pp. 022107 - 022107-13
• Main Author: Vannozzi, C.
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.02.2012
• Subjects: Applied fluid mechanics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamics, hydraulics, hydrostatics; Physics; Liquid meniscus; Hydrodynamics; Modelling; Dip coating; Curvature; Digital simulation
• ISSN: 1070-6631; 1089-7666; 1527-2435; 1089-7666
• DOI: 10.1063/1.3680872

Dip coating in the presence of a substrate-liquid interaction potential normal to the substrate, previously theoretically investigated by R. Krechetnikov and G. M. Homsy [ Phys. Fluids 17 , 038101 ( 2005 )] , was revisited. Their solution procedure leads to predictions of the entrained film thickness $h_\infty ^*$ h ∞ * that deviate substantially from the classical Landau-Levich law because of the impossibility to identify meniscus solutions satisfying the proper boundary conditions of zero thickness and zero apparent contact angle on the solid substrate (L-L BC's). In contrast, in the present analysis, by choosing a different method of integration and requiring the satisfaction of the boundary condition of flat bath for large, but finite, meniscus thickness, we obtain solutions subject to L-L BC's for the same parameter range studied in Krechetnikov and Homsy's paper. Thus, the matching follows a modified Landau-Levich law, where $h_\infty ^*$ h ∞ * is inversely proportional to the meniscus curvature at the substrate. Since the interaction potential changes considerably this curvature, the entrained film significantly thickens for attractive interactions or thins for repulsive ones. Similar results are also found for a potential of the Debye-Hückel form.