Diffusion-limited reactions are usually described within the Smoluchowski theory, which neglects interparticle interactions. We propose a simple way to incorporate excluded-volume effects building on simulations of hard sphere in the presence of a sink. For large values of the sink-to-particle size ratio Rs, the measured encounter rate is in good agreement with a simple generalization of the Smoluchowski equation at high densities. Reducing Rs, the encounter rate is substantially depressed an...