Solvation force for long ranged wall-fluid potentials

The solvation force of a simple fluid confined between identical planar walls is studied in two model systems with short ranged fluid-fluid interactions and long ranged wall-fluid potentials decaying as $-Az^{-p}, z\to \infty$, for various values of $p$. Results for the Ising spins system are obtained in two dimensions at vanishing bulk magnetic field $h=0$ by means of the density-matrix renormalization-group method; results for the truncated Lennard-Jones (LJ) fluid are obtained within the nonlocal density functional theory. At low temperatures the solvation force $f_{solv}$ for the Ising film is repulsive and decays for large wall separations $L$ in the same fashion as the boundary field $f_{solv}\sim L^{-p}$, whereas for temperatures larger than the bulk critical temperature $f_{solv}$ is attractive and the asymptotic decay is $f_{solv}\sim L^{-(p+1)}$. For the LJ fluid system $f_{solv}$ is always repulsive away from the critical region and decays for large $L$ with the the same power law as the wall-fluid potential. We discuss the influence of the critical Casimir effect and of capillary condensation on the behaviour of the solvation force.