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The analysis of axial dispersion of solute is presented in a pulsatile flow of Casson fluid through a tube in the presence of interfacial mass transport due to irreversible first-order reaction catalysed by the tube wall. The theory of dispersion is studied by employing the generalized dispersion model proposed by Sankarasubramanian & Gill (Proc. R. Soc. Lond. A, vol. 333 (1592), 1973). This dispersion model describes the whole dispersion process in terms of three effective transport coefficients, i.e. exchange, convection and dispersion coefficients. In the present study, the effects of yield stress of Casson fluid τ y , wall absorption parameter β, amplitude of fluctuating pressure component e and Womersley frequency parameter α on the dispersion process are discussed under the influence of pulsatile pressure gradient. In a pulsatile flow, the plug flow radius changes during the period of oscillation and it has an effect on the dispersion process. Even with the Casson fluid model also, in an oscillatory flow, for small values of α, the dispersion coefficient K 2 is positive, but when the value of α is as large as 3, K 2 takes both positive and negative values due to the fluctuations in the velocity profiles. This nature becomes more predominant for τ y , e and β. It is observed that initially, for small time, the amplitude and magnitude of fluctuations of K 2 becomes more rapid and increases with time but it decreases after certain time and reaches a non-transient state for large time. Like in the case of Newtonian model, double frequency period for K 2 is observed at small time for large values of α with the Casson model for blood. It is seen that critical time for which K 2 reaches a non-transient state is independent of τ y and e but is dependent on α. It is also observed that the axial distribution of mean concentration C m of solute depends on τ y and β. But the effect of e and α on C m is not very significant. This dispersion model in non-Newtonian pulsatile flow can be applied to study the dispersion process in the cardiovascular system and blood oxygenators.

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The theory of miscible dispersion in a straight circular pipe with interphase mass transfer that was investigated by Sankarasubramanian & Gill (1973

The effect of double dispersion on free convection heat and mass transfer from a vertical surface embedded in a non-Darcy electrically conducting fluid saturated porous medium with Soret and Dufour effects is studied using similarity solution technique. The heat and mass transfer coefficients are effected greatly due to these secondary effects and also due to the complex interaction among the dispersion parameters Raγ,Raξ, and Lewis number Le and buoyancy ratio N. In both aiding and opposing buoyancies, Df and Sr have significant influence on the Nusselt and Sherwood numbers in the presence and absence of thermal and solutal dispersion in the medium. It is also observed that the magnetic field parameter lowered heat and mass transfer coefficients. The results are presented through comparison tables and plots.

The axial dispersion of solute in a pulsatile flow of Herschel-Bulkley fluid through a straight circular tube is investigated considering absorption/reaction at the tube wall. The solute dispersion process is described by adopting the generalized dispersion model suggested by Sankarasubramanian and Gill [“Unsteady convective diffusion with interphase mass transfer,” Proc. R. Soc. A 333, 115–132 (1973)]. Firstly the exchange, convection, and dispersion coefficients are determined for small and large time, and then the axial mean concentration of a solute in the tube is determined. The effect of power-law index l, yield stress of fluid τy, wall absorption parameter β, amplitude of fluctuating pressure component e, and Womersley frequency parameter α on the convection, dispersion, and mean concentration of solute is discussed for a Herschel-Bulkley fluid in the tube. The single frequency period in the oscillation of dispersion coefficient K2 is observed for small values of α while the double frequency period is noticed for large values of α at small time. Only positive dispersion occurs for small values of α. Both positive and negative dispersion is seen for large values of α. Also, the occurrence of negative dispersion is influenced by the parameters l, τy, β, and e for large values of α. A comparative study of the convection, dispersion, and mean concentration of solute among the Newtonian and non-Newtonian Herschel-Bulkley, power-law, Bingham, and Casson [J. Rana and P. V. S. N. Murthy, “Solute dispersion in pulsatile casson fluid flow in a tube with wall absorption,” J. Fluid Mech. 793, 877–914 (2016)] fluid models is presented at small and large time. Also, large time behaviour of non-Newtonian Carreau and Carreau-Yasuda fluid models [J. Rana and P. V. S. N. Murthy, “Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption,” Proc. R. Soc. A 472, 20160294 (2016)] is considered for comparison with other discussed fluid models. It is noticed that these fluid models exhibit significant differences during the solute dispersion in the presence of wall absorption. These models are applied to study the dispersion process of a solute in blood flow. For a Herschel-Bulkley fluid, the critical value of α at which fluctuations of K2 attain negative magnitude increases as l increases. The critical value of α for a Herschel-Bulkley fluid (l = 0.9 with τy = 0.05) is 2.9 but it is equal to 3 for a Casson fluid (τy = 0.05) [J. Rana and P. V. S. N. Murthy, “Solute dispersion in pulsatile casson fluid flow in a tube with wall absorption,” J. Fluid Mech. 793, 877–914 (2016)] with non-zero β. It is noticed that the amplitude of fluctuations of both negative convection coefficient −K1 and dispersion coefficient K2 for a Casson fluid is lying below that of Herschel-Bulkley fluid at all times. Therefore, the peak of mean concentration Cm for the Casson model is higher than that of the Herschel-Bulkley model. The present study may be useful to know the transportation process of drugs in blood flow through the blood vessels.