Geometry dependent critical exponents at complete wetting

We consider the complete wetting transition at nonplanar wall–fluid interfaces, where the height of the substrate varies as a power-law ∝|x|γ (with exponents 0⩽γ⩽1) in one direction (x). From a general scaling analysis, supported by numerical and analytical effective interfacial model calculations, we argue that such power-law wedges can alter the growth law describing the divergence of the interfacial height l0 (measured from the wedge bottom) and other 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 γ for wedge shape with γ>1/2. For γ<1/2, the asymptotic growth of the film thickness 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.