Diffusion-limited association of nanoparticles in fluid: Beyond the no-slip boundary conditions

In the treatments of diffusion-limited association of suspended nanoparticles (NPs), their diffusion coefficients are usually considered to be constant or depend on the interparticle distance as determined by fluid dynamics with the no-slip boundary condition. In the latter case, due to the corresponding slowdown of diffusion at short distances, the association rate constant is smaller than that calculated by ignoring this slowdown and using the diffusion coefficients corresponding to single NPs. The no-slip boundary condition can, however, be violated, and now there is evidence that it may happen more often than one could expect. In such situations, the partial-slip boundary condition is more suitable. Employing the latter boundary condition, I derive herein general integral expressions for the rate constant of association of spherically shaped NPs without and with the NP-NP interaction. Simple analytical results have been obtained in various situations.