We investigate solute dispersion in a two-phase system comprising a Casson fluid flowing in a tube and its surrounding wall phase that allows interphase solute exchange to mimic solute transport in blood and tissue phases. A pulsatile pressure gradient is imposed, and Gill’s classical methodology is extended to two-phase flows to analyse solute transport. The key parameters are the diffusivity ratio between wall and fluid phases (), the partition coefficient (ₚ), the Womersley number (), the yield stress (ᵧ), the wall thickness (ₕ) and the initial dimensionless radius of the solute source (a). In the long-time limit, increasing, ₚ and ₕ reduces the phase-averaged convection (K₁) and dispersion (K₂) coefficients, owing to solute accumulation in the wall where convective and shear-induced transport are absent. Short-time behaviour is dictated by the rate of solute transfer to the wall. Larger enhances both K₁ and K₂, while larger ᵧ suppresses them. The presence of a wall phase permits K₂ to reach O (10^0), compared with K₂ O (10^-3) without a wall, and can delay the onset of steady state to dimensionless time t O (10^2). Strong solute exchange and increasing wall thickness diminish downstream solute penetration, while non-Newtonian effects promote interphase transfer. These results provide mechanistic insight into solute exchange across fluid–wall interfaces, relevant to solute transport in blood flow and engineered permeable systems.
Rana et al. (Fri,) studied this question.