Analytical Form of Forces in Hydrophobic Collapse

We calculate analytically the forces between two solvophobic solutes, considering a model system. We show that the effective interaction forces between two solvophobic solutes, mediated by the solvent, is attractive for short ranges, which decreases linearly with surface-to-surface separation s between the solutes and repulsive in the long range falling off as 1 / s 4 . The attraction originates from the unbalanced Laplace force at the liquid-gas interface, generated by the repulsive interaction with the solvent particles, around the solutes at small s. The long range part arises due to unbalanced osmotic pressure. We illustrate the calculations for the Lennard-Jones solvent. We discuss the general implication of our results in the context of hydrophobic collapse.