Frenkel's method and the dynamic wetting of heterogeneous planar surfaces

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McHale, G ; Newton, MI (2002)

The relationship between the edge velocity, vE, and the dynamic contact angle, #, for the spreading of a small spherical cap type droplet on chemically and geometrically heterogeneous surfaces is examined using Frenkel's method. In this method, the change in surface free energy is equated to the viscous dissipation caused by Poiseuille flow inside the spherical cap. To describe dynamic wetting of a surface that is heterogeneous due to small variations in the local surface geometry of the solid, we introduce a simple Wenzel type correction for the ratio of the actual to geometric surface areas, r. The rate of change of surface free energy is then (2izr0)yLy{Q,osd-rr)VE where r0 is the drop base radius, I={y^v- "^L)I%V and the %'s are the interfacial tensions. For partial wetting, I=cos&e where 6e is the equilibrium contact angle and when the viscous dissipation vanishes, Wenzel's relationship linking the equilibrium contact angle on a rough surface to that on a smooth surface is obtained.
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