ON THE DISPERSION OF A SOLUTE IN OSCILLATING FLOW-THROUGH A CHANNEL

The paper presents an exact analysis of the dispersion of a solute in an incompressible viscous fluid flowing slowly in a parallel plate cha nnel under the influence of a periodic pressure gradient. Using a gene ralised dispersion model which is valid for all times after the solute injection, the diffusion coefficients K-i(tau) (i=1,2, 3,...) are det ermined as functions of time tau when the initial distribution of the solute is in the form of a slug of finite extent. The second coefficie nt K-2(tau) gives a measure of the longitudinal dispersion of the solu te due to the combined influence of molecular diffusion and nonuniform velocity across the channel cross-section. The analysis leads to the novel result that K-2(tau) consists of a steady part S and a fluctuati ng part D-2(tau) due to the pulsatility of the flow. It is shown that S increases with increase in lambda (the amplitude of pressure pulsati on) for small values of omega (the frequency of the pulsation). But fo r large omega, S decreases with increase in lambda. It is also found t hat for fixed lambda, there is very little fluctuation in D-2(tau) for omega=1, but D-2 (tau) shows fluctuation with large amplitude when om ega slightly exceeds unity. The amplitude of D-2(tau) then decreases w ith further increase in omega. Thus the variation of both S and D-2(ta u) with omega is non-monotonic. Finally, theta(m), the average concent ration of the solute over the channel cross-section is determined for various values of lambda and omega.