Reactive solute transport in blood flow through a permeable capillary

Abstract

The present analysis discusses the solute transport process in a steady 2D (axial and radial) laminar flow of blood through a permeable, finite length capillary. Blood is treated as a homogeneous Newtonian fluid and the solute is absorbed at the capillary wall with a linear irreversible reaction rate. The velocity profile is obtained by a regular perturbation technique, whereas the transport coefficients depicted by the Gill generalized dispersion model are solved numerically. A number of different scenarios are considered, namely transport with no-reaction, weak absorption, strong absorption, low filtration or high filtration, etc. In the initial stages, the temporal behaviour of the dispersion coefficient is identical to those cases when there is no radial velocity. For the combined effect of radial and axial velocities, however, the dispersion coefficient is lower for a high absorption rate than for a weak absorption rate. Diffusion is accelerated with higher values of filtration coefficient. Owing to the opposite effects of radial diffusion and radial velocity, the solute particles require more time to reach the steady state. The analysis finds applications in, for example, reactive nutrient and pharmacological transport in capillary hemodynamics.