Estimation of Mass Transfer Coefficients and Film Thickness. Transport in Blood Vessels

Illustration 1.5 Estimation of Mass Transfer Coefficients and Film Thickness, Transport in Blood Vessels 

The kc values given here represent the order cf magnitude of the outer limits of what can be accomplished, i.e., the maximum rate of mass transfer obtainable or the minimum time required to achieve the transfer of a given mass to or from a flat surface. 

Mass transfer by molecular diffusion resides at the other end of the spectrum. It yields the lowest possible mass transfer rate and sets an upper limit on time requirements. The solvent spill considered in Practice Problem 4.4, for example, requires several days to complete evaporation by diffusion into stagnant air. The same data applied to turbulent air flow at the same temperature yield an estimate of several minutes, lower by three orders of magnitude. The factor of 1000 can thus be viewed as separating the two extremes of diffusive and turbulent mass transfer. 

Transport in blood vessels presents another interesting subcase. Here the species involved in mass transfer, typically proteins, have much lower diffusivities than ordinary solutes, of the order 10 to 10 m /s. Flow is generally laminar, and of a pulsatile nature. A further departure from the norm is the complex geometry of the vascular systems, which involves multiple branchings, and constrictions in flow as well as expansions. Because of these complexities, it has become customary to measure local mass transfer coefficients confined to a typical wall area of 1 mm. A host of such measurements has by now been reported. The surprising fact that has emerged from these studies is that irrespective of location or configuration, the vast majority of kc values clusters around a value of IIP m/s. Thus, 

The studies referred to have been immensely helpful in analyzing tiie progress of vascular diseases, which are often associated with tiie migration of proteins to the vessel wall followed by an interaction with wall cells, leading, for example, to blood coagulation. Mass transfer is also important in the performance of vascular grafts and of controlled release devices (see Practice Problems 1.7 and 1.10). 

---