  The Smoluchowski approach to diffusion-controlled reactions is generalized to
interacting substrate particles by including the osmotic pressure and
hydrodynamic interactions of the nonideal particles in the Smoluchoswki
equation within a local-density approximation. By solving the strictly
linearized equation for the time-independent case with absorbing boundary
conditions, we present an analytic expression for the diffusion-limited
steady-state rate constant for small substrate concentrations in terms of an
effective second virial coefficient B_2*. Comparisons to Brownian dynamics
simulations excluding HI show excellent agreement up to bulk number densities
of B_2* rho_0 < 0.4 for hard sphere and repulsive Yukawa-like interactions
between the substrates. Our study provides an alternative way to determine the
second virial coefficient of interacting macromolecules experimentally by
measuring their steady-state rate constant in diffusion-controlled reactions at
low densities.
