Depletion forces between two spheres in a rod solution

We study the depletion interaction between spherical particles of radius R immersed in a dilute solution of rigid rods of length L. The computed interaction potential is, within numerical accuracy, exact for any value of L/R. In particular we find that for L similar to R, the depth of the depletion well is smaller than the prediction of the Derjaguin approximation. Our results bring new light into the discussion on the lack of phase separation in colloidal mixtures of spheres and rods.