Nonlinear Diffusion and Transient Osmosis

We investigate both analytically and numericallythe concentration dynamics of a solution in two containers connected bya narrow and short channel, in which diffusion obeys a porous medium equation.We also consider the variation of the pressure in the containers due tothe flow of matter in the channel.
In particular, we identify a phenomenon, which depends on the transport of matteracross nano-porous membranes, which we call ``transient osmosis'.
We find that nonlinear diffusion of the porous medium equation type allows numerous differentosmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion.Experimental results suggest one possible candidate for transiently osmotic processes.