Dispersion in core–annular flow with a solid annulus

Authors


Abstract

The Taylor dispersion of a solute is studied in a core–annular geometry. The fluid flows only through the core, but the solute can diffuse into the solid annulus. The long time limit of the dispersion coefficient D* is derived by a regular expansion in the aspect ratio for two different scalings of the Biot number (Bi), which is the dimensionless interfacial mass-transfer resistance. The results for the case of O(1) Bi match those obtained by Aris and a number of other researchers. In the case of O(ε) Bi, where ε is the aspect ratio, the average mass-transfer equations for the core and the annulus are coupled and do not simplify to a simple convection–dispersion form. The average mass-transfer equations are derived for two velocity profiles: Poiseuille flow and plug flow. The dispersion coefficient for the limiting case when both the core and the annulus are radially well mixed at all times is also determined for the case of O(1) Bi. For O(1) Bi, the dispersion of the solute arises as a result of molecular diffusion, interfacial mass-transfer resistance, and convective flow, and the contribution from interfacial mass-transfer resistance is independent of the velocity profile. This dispersion coefficient reduces to the classical result of fluid flow through a tube in the limit of vanishing annulus thickness and also for the case when the solute has zero solubility in the solid. The core–annular geometry mimics the Krogh cylinder, which is a model used for analyzing mass transfer from capillaries into surrounding tissue. The model predictions for the dispersion coefficients in different tissues agree reasonably with the experimentally reported values, and the agreement is the best for muscles, where the Krogh cylinder model is expected to most closely resemble the actual physiology. © 2005 American Institute of Chemical Engineers AIChE J, 2005

Ancillary