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 channel under the influence of a periodic pressure gradient. Using a generalised dispersion model which is valid for all times after the solute injection, the diffusion coefficientsK _i (τ)(i=1,2,3,…) are determined as functions of timeτ when the initial distribution of the solute is in the form of a slug of finite extent. The second coefficientK ₂(τ) gives a measure of the longitudinal dispersion of the solute due to the combined influence of molecular diffusion and nonuniform velocity across the channel cross-section. The analysis leads to the novel result thatK ₂(τ) consists of a steady partS and a fluctuating partD ₂(τ) due to the pulsatility of the flow. It is shown thatS increases with increase inλ (the amplitude of pressure pulsation) for small values ofω (the frequency of the pulsation). But for largeω, S decreases with increase inλ. It is also found that for fixedλ, there is very little fluctuation inD ₂(τ) forω=1, butD ₂(τ) shows fluctuation with large amplitude whenω slightly exceeds unity. The amplitude ofD ₂(τ) then decreases with further increase inω. Thus the variation of bothS andD ₂(τ) withω is non-monotonic. Finally,? _m , the average concentration of the solute over the channel cross-section is determined for various values ofλ andω.