Transmembrane Pressure is the net hydrostatic driving force pushing solvent through the porous membrane wall. In crossflow filtration, pressure declines along the feed channel due to friction, so TMP is calculated as the average of feed inlet and retentate outlet pressures minus permeate backpressure: TMP = (Pfeed + Pret)/2 - Pperm.

Hermia unified membrane blocking kinetics into four distinct mathematical mechanisms based on particle size relative to pore dimensions: Cake / Gel Filtration (n = 0, particles deposit on surface), Intermediate Blocking (n = 1, particles either seal open pores or stack on existing deposits), Standard Pore Constriction (n = 1.5, internal adsorption narrows pore throat), and Complete Blocking (n = 2, every particle blocks a pore entrance).

Concentration polarization is the accumulation of rejected solutes and colloids in a stagnant boundary layer directly against the membrane surface (Cm > Cb). High crossflow velocity induces wall shear stress that sweeps away accumulated particles and promotes Brownian back-diffusion into the bulk stream, preventing premature gel layer collapse.

Critical flux is the maximum permeate flux threshold below which hydraulic fouling remains minimal and reversible via standard crossflow shear. Operating above critical flux causes rapid, irreversible compaction of the cake layer, causing TMP to spike uncontrollably.

Permeate flux is inversely proportional to liquid dynamic viscosity (J = TMP / [μ * R]). Because water viscosity decreases by roughly 2.4% for every 1°C increase in temperature, warming feed slurry from 20°C to 40°C increases permeate flux by nearly 50% under identical operating TMP.