Nonlinear Analysis for Shear Augmented Dispersion of Solutes in Blood Flow through Narrow Arteries

Abstract

The shear augmented dispersion of solutes in blood flow (i) through circular tube and (ii) between parallel flat plates is analyzed mathematically, treating blood as Herschel-Bulkley fluid model. The resulting system of nonlinear differential equations are solved with the appropriate boundary conditions, and the expressions for normalized velocity, concentration of the fluid in the core region and outer region, flow rate, and effective axial diffusivity are obtained. It is found that the normalized velocity of blood, relative diffusivity, and axial diffusivity of solutes are higher when blood is modeled by Herschel-Bulkley fluid rather than by Casson fluid model. It is also noted that the normalized velocity, relative diffusivity, and axial diffusivity of solutes are higher when blood flows through circular tube than when it flows between parallel flat plates.

Mathematical analysis for unsteady dispersion of solute with chemical reaction in blood flow

“…The solute dispersion of nanoparticles within the tumor in blood vessels with permeable wall has been studied by many researchers [12][13][14][15]. Sankar et al [16] and Jaafar et al [17] analyzed the steady dispersion of solute in blood flow through pipe and channel for Herschel-Bulkley fluid using the approach of Taylor-Aris and GDM, respectively. In the studies mentioned so far, it is assumed that the solute does not chemically react with fluid.…”

Mathematical modeling of shear augmented dispersion of solute in blood flow

“…(6) and (7) subject to boundary conditions (8), the expressions for and can be obtained. The complete expression for and are given in Sankar et al [12]. The flow rate is obtained using the approach of Sharp [3] and the effective axial diffusivity is as follows:…”

“…He corrected the Taylor's formula for the effective axial diffusivity as . The Taylor-Aris's theory had been extensively studied by several researchers [8][9][10][11][12][13] to extend their studies either theoretically or experimentally. The whole process of the solute dispersion in laminar fluid flow by considering diffusion in both radial and axial directions was analyzed by Ananthakrishnan et al [14].…”

“…Sharp [3] applied the Taylor-Aris's dispersion theory to study the steady dispersion of solute in Casson fluid flow through pipe and channel and pointed out that the effective axial diffusivity is strongly dependent on the yield stress of the solvent fluid. Sankar et al [12] investigated the dispersion of solute in blood flow, modeling blood as Herschel-Bulkley (H-B) fluid. In the present paper, the expressions obtained for the flow quantities by Sankar et al [12] are used to extend their results and obtain some new useful results.…”

“…Sankar et al [12] investigated the dispersion of solute in blood flow, modeling blood as Herschel-Bulkley (H-B) fluid. In the present paper, the expressions obtained for the flow quantities by Sankar et al [12] are used to extend their results and obtain some new useful results.…”