Spreading fronts and fluctuations in sedimentation

While the average settling velocity of particles in a suspension has been successfully predicted, we are still unsuccessful with the r.m.s velocity, with theories suggesting a divergence with the size of

the container and experiments finding no such dependence. A possible resolution involves stratification originating from the spreading of the front between the clear liquid above and the suspension below. One theory describes the spreading front by a nonlinear diffusion equation

$\frac{\partial \phi}{\partial t} = D \frac{\partial }{\partial z}(\phi^{4/5}(\frac{\partial \phi}{\partial z})^{2/5})$.

\\

\\

Experiments and computer simulations find differently.