Mixing involves inducing flow in a liquid medium and this is generally captured by the convection-diffusion equation. However, if your are only interested in for instance colloidal (nanoparticle) aggregation, you may use shortcuts by Smoluchowski who derived times scales for orthokinetic and perikintec aggregation.
The keywords you need to look for is 'convection diffusion' or 'advection diffusion' (I don't understand if there is any real difference). There are textbooks and lots of downloadable PDFs to learn how to solve the diffusion (Smoluchowski) equation in a flow (start from Wikipedia).