We report a molecular dynamics computation of the entropic depletion force induced between two large spheres (colloidal particles) immersed in a fluid of small spheres. The effective pair potential obtained by numerical integration of the force is used in a Monte Carlo study of the phase behaviour of the binary mixture. The simulation results are compared with the relevant theoretical predictions that follow from various integral equations for liquid mixtures. The simulations provide evidence for a spinodal instability in a liquid mixture of hard spheres with a size ratio of 0.1.