Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption

The theory of miscible dispersion in a straight circular pipe with interphase mass transfer that was investigated by Sankarasubramanian & Gill (1973 Proc. R. Soc. Lond. A 333, 115-132. (doi: 10.1098/rspa.1973.0051); 1974 Proc. R. Soc. Lond. A 341, 407408. (doi: 10.1098/rspa.1974.0195)) in Newtonian fluid flow is extended by considering various non-Newtonian fluid models, such as the Casson (Rana & Murthy 2016 J. Fluid Mech. 793, 877914. (doi: 10.1017/jfm.2016.155)), Carreau and Carreau-Yasuda models. These models are useful to investigate the solute dispersion in blood flow. The three effective transport coefficients, i.e. exchange, convection and dispersion coefficients, are evaluated to analyse the dispersion process of solute. The convection and dispersion coefficients are determined asymptotically at large time which is sufficient to understand the nature of the solute dispersion process in a tube. The axial mean concentration is analysed, using the asymptotic expressions for these three coefficients. The effect of the wall absorption parameter, Weissenberg number, power-law index, Yasuda parameter and Peclet number on the dispersion process is discussed clearly in this study. A comparative study of the solute dispersion among the Newtonian and all other non-Newtonian models is presented. At low shear rate, it is observed that Carreau fluid behaves like Newtonian fluid, whereas the other fluids exhibit significant differences during the solute dispersion. This study may be applicable to understand the dispersion process of drugs in the blood stream.