I have been thinking about this for quite some time: Given a foam or other absorbent material saturated with a solvent, how could you draw all the solvent to the top of the foam (basically how could you 'empty' the foam and draw all the liquid out of it)? I think a strong enough vacuum at the top of the foam should do the trick, but am not sure. If there are any publications regarding this problem, please link them in your answer as well; I have not been able to find any.
The vacuum could find easy pathways in the matrix of foam that could leave the hard-to-reach pockets alone like wet islands.
The best way is to take advantage of the gravity or centripetal force, acting on every single molecule of the fluid.
A container with porous bottom either tspinning by a machine or just sitting on top of a sloped drain would do.