Shell Balance Approach for One-Dimensional Biomass Transport

Abstract

Applications of the macroscopic species conservation equation discussed in Chap. 13 are used extensively in biotransport. However, the macroscopic approach has important practical restrictions. It is limited to predicting concentrations, fluxes, or flows that are spatially averaged. If concentrations or fluxes have significant spatial variations, a different approach must be applied. Rather than apply the species conservation principle to the entire system, a microscopic portion of the system is analyzed. The resulting expression will be a differential equation that is valid at any position within the boundaries of the system. Boundary conditions that are specific to the problem at hand must be applied to find a solution for a particular system. Applications include axial variations of oxygen and carbon dioxide in capillaries, axial variations in salt concentration in the Loop of Henle, radial concentration variations of urea in tissue or hemodialyzers, solute concentration variations in porous microcapsules, etc.