Stick boundary condition at large hard sphere arising from effective attraction in binary hard-sphere mixtures

We have studied the diffusion of a large hard-sphere solute immersed in binary hard-sphere mixtures. We reveal how the boundary condition at the solute surface is affected by the solvent density around the solute. Solving equations for a binary compressible mixture by perturbation expansions, we obtain the boundary condition depending on the size ratio of binary solvent spheres. When the size ratio is 1:2, the boundary condition lies close to the slip boundary condition. By contrast, when the size ratio becomes large, the boundary condition approaches the stick boundary condition with the addition of larger solvent spheres. We find that the transition to the stick boundary condition is caused by the increase in the solvent density around the solute due to an entropic effect.