Batchelorrsquo;s method of calculating the firsthyphen;order concentration dependence of the selfhyphen;diffusion coefficient of spherical Brownian particles is compared with our method devised previously. Both methods are based on the solution of the twohyphen;particle Smoluchowski equation as applied to a stationary state. It is shown that the difference between the methods resides only in one boundary condition which is imposed on solutions of a version of the Smoluchowski equation when two Brownian particles come into contact. Although the validity of Batchelorrsquo;s boundary condition is obvious, that of ours was not. We show how our boundary condition is justified and suggest that the two methods lead to identical results for the selfhyphen;diffusion coefficient in spite of the different boundary conditions. The suggestion is confirmed for the case of hard spheres. We also derive a boundary condition, corresponding to ours mentioned above, which is applicable to solutions of a version of the timehyphen;dependent Smoluchowski equation for an equilibrium state on the basis of which the selfhyphen;diffusion coefficient can also be obtained.
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