Short-distance expansion for the local susceptibility and pair correlation function at continuous wetting transitions

Abstract

A scaling ansatz is proposed for the density profile rho (z) (with z the distance normal from the substrate) for a fluid undergoing a continuous wetting transition at a wall. The ansatz predicts that, in the fluctuation dominated regime, the local susceptibility ( delta rho (z)/ delta mu )T, with mu the chemical potential, has a simple power law position dependence for short distances z<< zeta perpendicular to , the perpendicular correlation length. The power law is determined by the wetting critical exponents, which is different for complete and critical wetting. The scaling predictions are confirmed in dimension d=2 by explicit analysis for an interfacial Hamiltonian model of the wetting transition. For critical wetting a scaling ansatz for the form of the transverse moments of the two-point correlation function G is postulated which now yields the z1, z2 dependence of G in terms of critical exponents. Calculations again confirm the scaling theory for d=2. The analysis highlights the different qualitative and quantitative features of the response functions for critical and complete wetting for fluids with short-ranged forces.