Effects of flow on solute exchange between fluids and supported biosurfaces

Uptake of nutrients by cultured cells on solid supports, conversion of substrates by surface-bound catalysts and binding of antibodies to microtitre plates are examples of transport processes that are strongly influenced by the flow conditions in the surrounding fluid. The literature on this subject is scattered over widely different research fields and is often found in dated, and not generally available, treatises. Also, the subject is inherently complicated from a mathematical viewpoint, because even the simplest experimental configurations will usually not allow analytical solutions for the diffusion-convection equations describing the solute mass transport in the system. Fortunately, however, relatively simple expressions for the rates of mass transport can often be obtained in physically realistic limiting cases. The present study attempts to give a short overview of the main experimental models used in this field and presents simple equations for the estimation of solute exchange rates between surfaces and fluids. The models considered are: (1) uptake from an unstirred solution; (2) reversible binding from a perfectly stirred solution; (3) reversible binding through an unstirred fluid layer; (4) catalytic conversion at the internal surface of a tube or a slit with laminar flow; (5) adsorption by a surface opposite a rotating stirrer; (6) adsorption from an impinging fluid jet; and (7) uptake by the surface of a rotating disc. In practical situations the property of uniform accessibility proves to be of crucial importance. Stirring by ultrasound, more specifically the use of acoustic streaming in nano-devices, is also discussed.