Facilitated diffusion of oxygen in red blood cell suspensions.

Abstract

A general model that treats the problem of diffusion with reversible chemical reaction in heterogeneous media has recently been developed (12, 11). This theory has been applied to the theoretical analysis of oxygen diffusion in red blood cell suspensions (13). Blood is modeled as a suspension of uniform spheres containing hemoglobin, which are suspended in a second continuous phase. In order to predict the steady state transport in such a medium, first the mass conservation equations are solved for a single reactive sphere located in an infinite nonreactive continuous medium in which a constant linear flux of the diffusing species A is imposed at a large distance from the center of the sphere. If the oxygen-hemoglobin reaction is modeled as a single step reaction of the form, $$ A + B\;\underset{{{k_{2}}}}{\overset{{{k_{1}}}}{\longleftrightarrow}}AB $$ (1) the equations inside the sphere and outside the sphere are nonlinear and must be linearized in order to be solved analytically. For a small sphere in a medium the partial pressure drop of A across an individual sphere is usually small so that a single point linearization technique is applicable (3). The equations are linearized about a single point by neglecting second order terms.