where γ is the shear rate (s−1), q

where γ is the shear rate (s−1), q is the flow rate per lumen (cm3/s), R is the lumen radius (cm).In the absence of specific data pertaining to the effect of shear on the product stability, testing might begin using the following shear rate, γ, conditions: (i) shear sensitive, 0–4000s−1; (ii) moderate shear tolerance, 4000–8000s−1; and (iii) little to no shear sensitivity, 8000–16,000 s−1.In addition to the mechanical sweeping action bringing matter off of the membrane surface and back into the bulk flow, there is a more subtle contribution from the chemical equilibrium. The flow of liquid out of the fluid path through the membrane creates a concentration gradient from the center of the flow path to the membrane wall-the concentration at the membrane surface being greater. This concentration gradient then instils a “back-diffusion” of the material into the bulk flow. This force is designated as the “pinch effect” in Fig. 15.17. This principle is more applicable to dissolved molecules rather than particles.Smaller molecules, being more nimble, can readily migrate off of the membrane surface and be carried away in the bulk flow while larger molecules may tend to form complex gel layers and remain affixed to the membrane surface. Early work using rigid-model particles suggests that this same “back-diffusion” can occur with particles [5], although characterization of this behavior with cell suspension processes may be difficult to prove.