Transient convective mass transfer in Krogh tissue cylinders

Abstract

A compact economical description of transient mass transport in Krogh tissue cylinders is devised. It is based on extensions of the Gill-Subramanian dispersion technique and Sturm-Liouville theory to two-phase systems and takes into account the following aspects of convective mass transfer simultaneously: radial and axial diffusion in both blood and tissue, a localized mass-transfer resistance at the capillary membrane, and an axial diffusion barrier at each end of the cylinder. Numerical examples are provided for two situations of physiological interest: (i) Small lipid-soluble solutes encountering no localized barrier at the capillary membrane, and (ii) hydrophilic solutes, which encounter a very substantial barrier. It is shown that existing one-dimensional chromatographic models are satisfactory for the lipophilic solutes, for what is generally considered a satisfactory set of parameters for describing Krogh cylinders. However, the limitations on this treatment are emphasized, and it is shown how convective dispersion may complicate this picture. For the hydrophilic solutes Taylor dispersion is shown to be much more important than hitherto believed. It appears that existing methods of estimating capillary membrane permeabilities should be revised in the light of these findings.