= Smoluchowski diffusion-controlled encounter rate
{c}
{title2=$k_{12}=4\pi(D_1+D_2)(a_1+a_2)$}
For two dilute spherical species with absorbing contact and negligible interaction barriers, relative <diffusion> has coefficient $D=D_1+D_2$ and contact radius $R=a_1+a_2$. The steady concentration outside one target is $c(r)=c_\infty(1-R/r)$, solving the radial <Laplace equation> with zero contact concentration. Its inward diffusive flux is $4\pi DRc_\infty$, proving the displayed bimolecular rate coefficient. For identical particles, converting this encounter coefficient into a rate of loss of cluster number additionally needs the factor that prevents counting the same pair twice.
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