Smoluchowski association rate
= Smoluchowski association rate
{c}
{title2=$k=4\pi D_{\rm rel}a$}
For an absorbing spherical target of radius $a$ in an infinite uniform reservoir, steady <diffusion> gives $c(r)=c_\infty(1-a/r)$. Integrating the inward flux yields $k=4\pi D_{\rm rel}a$, where $D_{\rm rel}=D_A+D_B$ if both partners diffuse. Here $k$ multiplies <number densities>; its units are volume per time. Molecular orientation, finite-domain transients and imperfect capture require corrections.