On solute dispersion in pulsatile flow through a channel with absorbing walls

Abstract

The paper presents the longitudinal dispersion of passive tracer molecules released in an incompressible viscous fluid flowing through a channel with reactive walls under the action of a periodic pressure gradient. A finite-difference implicit scheme is adopted to solve the unsteady advection–diffusion equation based on the Aris–Barton method of moments for all time period. Here it is shown how the spreading of tracers is influenced by the shear flow, lateral diffusion about its mean position due to the action of absorption at both the walls. The analysis has been performed for three different cases: steady, periodic and the combined effect of steady and periodic currents, separately. The results show that for all cases the dispersion coefficient asymptotically reaches a stationary state after a certain critical time and it achieves a stationary state at earlier instant of time, when absorption at the walls increases. The axial distributions of mean concentration are determined from the first four central moments by using Hermite polynomial representation for all three different flow velocities.