Mass Transfer in a Rigid Tube With Pulsatile Flow and Constant Wall Concentration

Abstract

An approximate-analytical solution method is presented for the problem of mass transfer in a rigid tube with pulsatile flow. For the case of constant wall concentration, it is shown that the generalized integral transform (GIT) method can be used to obtain a solution in terms of a perturbation expansion, where the coefficients of each term are given by a system of coupled ordinary differential equations. Truncating the system at some large value of the parameter N, an approximate solution for the system is obtained for the first term in the perturbation expansion, and the GIT-based solution is verified by comparison to a numerical solution. The GIT approximate-analytical solution indicates that for small to moderate nondimensional frequencies for any distance from the inlet of the tube, there is a positive peak in the bulk concentration C1b due to pulsation, thereby, producing a higher mass transfer mixing efficiency in the tube. As we further increase the frequency, the positive peak is followed by a negative peak in the time-averaged bulk concentration and then the bulk concentration C1b oscillates and dampens to zero. Initially, for small frequencies the relative Sherwood number is negative indicating that the effect of pulsation tends to reduce mass transfer. There is a band of frequencies, where the relative Sherwood number is positive indicating that the effect of pulsation tends to increase mass transfer. The positive peak in bulk concentration corresponds to a matching of the phase of the pulsatile velocity and the concentration, respectively, where the unique maximum of both occur for certain time in the cycle. The oscillatory component of concentration is also determined radially in the tube where the concentration develops first near the wall of the tube, and the lobes of the concentration curves increase with increasing distance downstream until the concentration becomes fully developed. The GIT method proves to be a working approach to solve the first two perturbation terms in the governing equations involved.

Role of erythrocyte-released ATP in the regulation of microvascular oxygen supply in skeletal muscle

“…In arterioles in which flow velocities can be as high as 1 cm s −1 , the O 2 saturation of slow‐moving erythrocytes near the wall reflects tissue O 2 levels (Moschandreou et al . ) making them ideal sensors for regulating O 2 supply. As the plasma gap between the erythrocyte and the endothelium is <1 μ m, the erythrocyte would only travel ~0.5 mm before the ATP which was released from the erythrocyte reaches the purinergic receptor on the endothelium.…”