Geometry dependent critical exponents at complete wetting

We consider the complete wetting transition at nonplanar wall-fluid interfa ces, where the height of the substrate varies as a power-law proportional t o\x\(gamma) (with exponents 0 less than or equal to gamma less than or equa l to 1) in one direction (x). From a general scaling analysis, supported by numerical and analytical effective interfacial model calculations, we argu e that such power-law wedges can alter the growth law describing the diverg ence of the interfacial height l(0) (measured from the wedge bottom) and ot her length scales as the bulk saturation chemical potential is approached. For realistic experimental systems with dispersion forces, we predict that the complete wetting critical exponents are determined by gamma for wedge s hape with gamma > 1/2. For gamma < 1/2, the asymptotic growth of the film t hickness should be similar to that found for planar systems. Nevertheless, crossover behavior due to the influence of the geometry is still observable in adsorption isotherms. (C) 2000 American Institute of Physics. [S0021-96 06(00)70210-8].