Abstract

The unsteady dispersion of a solute has been discussed by the method of generalized dispersion technique in a blood-like liquid flowing through a pipe under the combined effects of finite yield stress and irreversible absorption into the wall.The solvent is enacted as a three-layered liquid by considering the center liquid as a Casson liquid (a core of red blood cell suspension) and a peripheral layer of plasma as a Newtonian liquid. An asymptotic representation for the convection and dispersion coefficients has been shown only for large values of time, which will not hamper the study of physical behavior of the system. The objective of the present study is to examine the nature of exchange coefficient, convective coefficient and in particular, dispersion coefficient together with mean concentration distribution under the effect of absorption parameter (​β)​, yield stress (​​τ​y​​​) (equivalently the plug radius (​​Rp​​​)) and peripheral layer variation (i.e., ratio of central core radius to normal artery radius (​​Ro​​​)). It is found that the presence of peripheral layer makes some important increment in dispersion coefficient compared to single phase Casson liquid for small absorption. Increase in both diffusivity (D*​​) and Peclet number (Pe) make a significant decrement in the magnitude of dispersion coefficient with respect to absorption rate. The decrease in peak of the mean concentration distribution with the increase in reaction rate is found irrespective of the nature of reaction.

Highlights

  • The rate of broadening of a cloud of matter in a flowing stream is due to dispersion phenomena and it can be utilized as an efficient means to accomplish dilution or mixing

  • 6 Results and Discussion The present analysis mainly deals with the dispersion of a solute in a blood-like liquid flowing through a narrow pipe under the effect of peripheral layer variation and irreversible absorption into the wall

  • It was already discussed that the unsteady dispersion coefficient has to be analyzed by generalized dispersion technique, so the entire process is based on three effective transport coefficient, viz. exchange coefficient (M0​ ), convection coefficient (M1​ ) and dispersion coefficient (M2​ )

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Summary

Introduction

The rate of broadening of a cloud of matter in a flowing stream is due to dispersion phenomena and it can be utilized as an efficient means to accomplish dilution or mixing. Because of its wide applications in the arena of chemical engineering, physiological fluid dynamics, environmental sciences, bio medical engineering etc., investigations of longitudinal dispersion of a solute in an exceedingly solvent flowing through a conduit (pipe/channel) is gaining additional attention among the scientific community. The first fundamental study on dispersion was initiated by Taylor [1], discussing the dispersion of a soluble matter in a viscous liquid flowing through a circular pipe under laminar condition. He observed that the spreading of solute under the joint effects of the lateral molecular diffusion and the radial velocity distribution over the cross section is symmetrical about a point moving with the average velocity of the liquid. A lot of researchers added their valuable contribution to understand dispersion process more and more precious way

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