Flux Behavior in Membrane Processes

In pressure driven membrane processes, flux is related to pressure as follows

J = P-∆π/(ηRtot)

where:
P: pressure exerted on the membrane
η: feed viscosity
Rtot: the sum of resistances

In an ideal scenario, such as in the case of a feed solution comprised solely of pure water, we would expect that pressure and flux to follow a direct and linear relationship.In this case, the total resistance is equal to only the resistance exerted by the membrane, which would remain constant, as would the feed viscosity at constant temperature. However, with the addition solutes to the feed stream, the total resistance increases. This can be attributed to a number of factors, such as concentration polarization andfouling via pore blockage or cake layer formation. For this reason, flux behavior in pressure driven membrane processes typically decreases over time (see figure below).