Dispersion of a non-uniform solute slug in pulsatile viscoelastic fluid flow

Abstract

Solute transport in pulsatile viscoelastic fluid flow is relevant in nutrient transport and drug delivery in blood flow. Previous studies have extensively analyzed the effect of the shear-thinning nature of the blood but neglected the elastic property. The present study aims to fill this lacuna by analyzing the role of blood viscoelasticity on solute transport. To accomplish this, we study solute transport for a non-uniformly distributed solute slug in the pulsatile flow of an Oldroyd-B fluid through a tube in the presence of wall absorption. We employ Gill's procedure and Aris' method of moments to compute the transport coefficients Km(t) (m≤4). We also numerically solve the species transport equation using a finite difference scheme to directly determine local solute concentration C(t,z,r). Consistent results for a non-viscoelastic fluid predict a negative convection coefficient K1 and a positive effective diffusivity K2 for realistic values of the parameters. However, the present analysis predicts positive K1 and negative K2 for small tubes due to flow reversal caused by the fluid elasticity. For high Λ1, the amplitude of oscillation for K1 and K2 exhibits scaling K1∼Λ11.5 and K2∼Λ12 indicating an enhancement in the dispersion due to fluid elasticity, where Λ1 is the dimensionless relaxation time. The analysis of the skewness and (excess) kurtosis coefficients reveals inconsistency in previous studies on Newtonian fluids. Thus, we present consistent results not only for a viscoelastic fluid but also for a Newtonian fluid subjected to a pulsatile pressure gradient. In addition, the solute dispersion is significantly influenced by the non-uniformity of a solute slug. As the radius of a slug increases, solute dispersion reduces in short and moderate times; however, at large times, it is independent of the radius of a slug.