Thanks for your responses!
Martin, in answer to your question, both the solids and the liquids discharge to pipes that are still under some pressure (usually just a few psi but can be up to 50 depending on how we are running our experimental process). Basically, it means we are running the process normally otherwise with spring loaded pressure on the solid phase, just everything is shifted up 50 psi or so, both the inlets and the outlets.
The purpose for this is that we are trying to separate a slurry with the main liquid component being a fairly high vapor pressure hydrocarbon.
So if I understand you correctly you have to balance the pressure diff. such that you don't wan't to push too fine of solids through? From our experience the higher pressure differential means higher solids concentration of the back end solids output, which is preferential to us. I guess that makes sense those two things would be inversely proportional.