Multi-scale analysis of solute dispersion in non-Newtonian flows in a tube with wall absorption

Abstract

This study presents the two-dimensional concentration distribution of a solute cloud for non-Newtonian fluid in a tube flow with wall absorption. The non-Newtonian fluid models, such as the Carreau–Yasuda and Carreau fluid models, are helpful in investigating solute dispersion in the bloodstream and have also been effective in understanding hemodynamics. The multi-scale method of homogenization is used here to analyze the dispersion of solute through a straight tube for Carreau–Yasuda and Carreau fluids, which represents the shear-thinning nature. Most of the previous studies are mainly focused on determining the dispersion coefficient and mean concentration distribution for non-Newtonian fluids. Apart from those in our study, we also derived analytical expressions for the two-dimensional concentration distribution for Carreau–Yasuda and Carreau fluids. As the exact peak position of the two-dimensional concentration is a concern in real-life applications rather than that of mean concentration, the effects of wall absorption parameter (α*), the Weissenberg number (We), Yasuda parameter (a), and power-law index (n) on solute concentration distribution are discussed. Comparison between the present results and previous results of solute dispersion for non-Newtonian as well as Newtonian fluids are also enclosed in this study. Results reveal that the mean concentration decreases with increasing values of We because of an increase in the dispersion coefficient. Carreau–Yasuda and Carreau fluids act like Newtonian fluid for very small values of We. At the initial stage, the solute concentration exhibits transverse non-uniformity and then becomes uniform over a larger timescale. The effects of non-Newtonian parameters such as We, a, and n on transverse variation are also studied. It is noted that parameters n, We, and a have no significant impacts on the non-uniformity of the transverse concentration variation on both sides of the tube centroid, but that is not the case for the wall absorption parameter. It is observed that wall absorption results in significant transverse concentration non-uniformity across the tube cross section even after large times.