Solvation force for long ranged wall-fluid potentials

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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→ ∞, 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 fsolv for the Ising film is repulsive and decays for large wall separations L in the same fashion as the boundary field fsolv L⁻ᵖ, whereas for temperatures larger than the bulk critical temperature fsolv is attractive and the asymptotic decay is fsolv L⁻⁽ᵖ⁺¹⁾. For the LJ fluid system fsolv 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.