Depletion forces in fluids

We investigate the entropic depletion force that arises between two big hard spheres of radius R-b, mimicking colloidal particles, immersed in a fluid of small hard spheres of radius R-s. Within the framework of the Derjaguin approximation, which becomes exact as s=R-s/R-b-->0, we examine an exact expression for the depletion force and the corresponding potential for the range 0<h<2R(s), where h is the separation between the big spheres. These expressions, which depend only on the bulk pressure and the corresponding planar wall-fluid interfacial tension, are valid for all fluid number densities rho(s). In the limit rho(s)>0 we recover the results of earlier low density theories. Comparison with recent computer simulations shows that the Dejaguin approximation is not reliable for s=0.1 and packing fractions eta(s)=4 pi rho(s)R(s)(3)/3 greater than or similar to 0.3. We propose two new approximations, one based on treating the fluid as if it were confined to a wedge and the other based on the limit s=R-s/R-b-->1. Both improve upon the Dejaguin approximation for s=0.1 and high packing:fractions. We discuss the extent to which our results remain valid for more general fluids, e.g., nonadsorbing polymers near colloidal particles, and their implications for fluid-fluid phase separation in a binary hard-sphere mixture.