AN ADVANCING FRONT MODEL OF TRANSPORT INTO PULSATING LAMINAR FLOW

The diffusion and transport of a gas species is analyzed for a slowly pulsating fluid in laminar tube flow. It is assumed that the fluid velocity is in phase with the pulsating pressure gradient. A reversible chemical reaction within the fluid is modeled using advancing front theory. The pulsation is assumed to affect only the diffusion boundary layer thickness, which may be out of phase with the flow pulsation. The solution is approximate for small perturbations of the boundary layer thickness. With these assumptions a closed form solution for the bulk transport is obtained. The results are expressed as differences in the bulk transport relative to a steady flow having the same average flow conditions. The pulsation effect is expressed as a function of the non-dimensional flow amplitude and frequency parameters for various average conditions. Comparison with experimental measurements of oxygen diffusing into water and hemoglobin solutions shows good agreement. For the range of parameters used for the measurements, there is no effect of the pulsation on time-averaged transfer rates.