Solute dispersion in Phan-Thien–Tanner (PTT) fluid flows

To understand the effect of viscoelasticity and finite extensibility of polymer chains on solute dispersion, the present study analyses the unsteady solute transport in a steady pipe flow of the exponential Phan-Thien–Tanner (PTT) fluid. We utilize Gill's procedure and homogenization method to determine the coefficients characterizing solute transport. In the large time limit, both methods yield the same result. The PTT fluid introduces two dimensionless parameters, viz., Deborah number (De) characterizing fluid elasticity and polymer chain extensibility (ϵ). An increasing De and ϵ leads to increasing shear-thinning of the PTT fluid. Owing to the average velocity scale for non-dimensionalization, the convection transport coefficient (K1) in Gill's procedure has unity magnitude. The diffusion transport coefficient (K2) in Gill's procedure or effective diffusivity predicted by the homogenization method drastically decreases with increasing De and ϵ. This prediction is explained on the basis of shear-thinning-induced reduction in the velocity gradient. Following the trend shown by K2, the mean concentration Cm(t,z) shows an increased tendency of a higher peak as De and ϵ increase, implying slower axial spreading. Additionally, contours obtained for the local concentration C(t,r,z) further confirm the reduction in the solute dispersion for increasing De and ϵ. Thus, the present study demonstrates a reduction in the solute dispersion due to fluid elasticity and shear-thinning.