On Dispersion in Oscillatory Annular Flow Driven Jointly by Pressure Pulsation and Wall Oscillation

Abstract

Longitudinal dispersion of solute released in an unsteady flow between two coaxial cylinders is re-examined in the presence of first order chemical kinetics in the bulk flow. The flow unsteadiness is caused by the oscillation of the outer tube around its axis as well as by a periodic pressure gradient. Unlike some previous works, the gap width of the annular tube is used as the typical length scale which is physically meaningful to a greater extent. In order to employ the method of moment, a finite difference implicit scheme has been adopted to solve the Aris integral moment equations arising from the unsteady convective diffusion equation for all time periods. The individual and combined effects of different velocity components resulting from steady and timedependent parts of the driving forces are examined and they are identified based on their functionality. In any flow situation, wall factor is found to have a larger contribution in velocity as well as in dispersion compared to the pressure factor. The behaviour of dispersion coefficient with the variation of radius ratio, bulk flow reaction parameter, and frequency parameters have been examined. Dispersion coefficient is found to diminish with the increase of the reaction-rate in the bulk flow, whereas the effect of the radius ratio on the dispersion coefficient is fixed by the form of the velocity distribution. The axial distributions of mean concentration are approximated using Hermite polynomial representation from the first four central moments for a range of different reaction-rate parameters. It has been found that, irrespective of the flow situation, the peak of the concentration distribution decreases with the increase in reaction rate parameter.

Moment analysis of unsteady bi-component species (drug) transport with coupled chemical reaction in non-Newtonian blood flow

“…( 42) i.e., the p th order moment general concentration partial differential equation under boundary conditions ( 43) and ( 44), a finite difference method based on the Crank Nicholson implicit scheme is employed. Further details of numeric are given in [56,57].…”