Does the CFL condition play any role in a pure Stokes flow, i.e. convective term is neglibile, or vanishing? If not, what is the "equivalent" condition for stability? I have read something about the diffusional time scale but it's quite vague. Anyone with in-depth insight?
And a quotation from a paper :
"The time step is $3.10^-3\dot\gamma^-1$, corresponding to a CFL number based on the diffusional time scale $CFL_d=v\Delta t/\Delta^2$ of 50."
 Gallier, S., Lemaire, E., Lobry, L., & Peters, F. (2014). A fictitious domain approach for the simulation of dense suspensions. Journal of Computational Physics, 256, 367-387.