Abstract
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 ${s=R}_{s}{/R}_{b}\ensuremath{\rightarrow}0$, we examine an exact expression for the depletion force and the corresponding potential for the range $0lhl{2R}_{s},$ 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 ${\ensuremath{\rho}}_{s}.$ In the limit ${\ensuremath{\rho}}_{s}\ensuremath{\rightarrow}0$ we recover the results of earlier low density theories. Comparison with recent computer simulations shows that the Derjaguin approximation is not reliable for $s=0.1$ and packing fractions ${\ensuremath{\eta}}_{s}=4\ensuremath{\pi}{\ensuremath{\rho}}_{s}{R}_{s}^{3}/3\ensuremath{\gtrsim}0.3$. 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 ${s=R}_{s}{/R}_{b}\ensuremath{\rightarrow}1$. Both improve upon the Derjaguin 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.
Published Version
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