An analysis of carrier-facilitated transport through thin films of hemoglobin and myoglobin

Abstract

The problem of carrier-facilitated transport through a thin film is examined in the asymptotic limit of small Damköhler number σ. In this limit, a regular perturbation solution is developed for the facilitated flux, correct to O(σ 6). The results are applied to the process of oxygen transfer through thin films of hemoglobin and myoglobin solutions. In these systems, the perturbation solution is found to be quite accurate for very thin films (i.e. small σ) with thickness substantially less than 1 μm; but it tends to diverge, leading to large errors, as the thickness increases. We have used the method of Padé approximants to accelerate the convergence of this series solution. The accelerated solution predicts the facilitated flux accurately for films of thickness up to about 3 μm in hemoglobin and about 5.5 μm in myoglobin.