Solute dispersion in transient Casson fluid flow through stenotic tube with exchange between phases

Abstract

A mathematical study on solute dispersion has been carried out in a stenotic tube having an absorptive wall—a study relevant to arterial pharmacokinetics. The rheology of blood is represented by Casson model and the solute is introduced at a point that is uniformly distributed over the cross section. The two-dimensional fluid flow is considered in this study. The governing equations of motion for the flow of Casson fluid, for the transport of solute in the lumen as well as in the tissue along with appropriate initial and boundary conditions, are numerically solved by leveraging the Marker and Cell method and the immersed boundary method in staggered grids formulation. Following the introduction of solute, we provide a comprehensive investigation of the influence of the wall absorption parameter (κ), yield stress (τy), and the severity of the stenosis (ξ) on the three transport coefficients, namely, the fraction of solute remaining in the fluid phase, the apparent convection velocity, and the dispersion coefficient. Simulated results predict the diminishing magnitudes of the transport coefficients with the increase in the values of yield stress and absorption parameter. Moreover, the transport coefficients and the axial mean concentration get significantly perturbed by the severity of the stenosis. Obtained results presented graphically concur with existing steady-state results in the literature. The present study would certainly be of some use in the case of targeted drug delivery and in treatment related to microvascular disease.

Exact Analysis of Unsteady Convective Diffusion in Herschel-Bulkley Fluid Flow- Application to Catheterised Stenosed Artery

“…The transport of a reactive solute in the bloodstream in dimensionless form is governed by the convection-diffusion equation [18], which is expressed as (6) where Pe is the Peclet number, t is the dispersion time, 𝐷 . is molecular diffusivity of the solute which is assumed as constant.…”

“…The formation of such lesion or plaque started blocking the artery and reducing the normal blood flow, medically termed as atherosclerosis or stenosis. It is important for clinicians to analyse the rate of dispersion of an injected drug associated with intravenous drug delivery into an affected artery because of its therapeutic nature and also to measure the amount of drug in the system for better efficacy as well as the effectiveness of the delivery [6]. In this situation, a long thin tube called a catheter is inserted into the veins to refine the flow.…”

Unsteady solute dispersion in the presence of reversible and irreversible reactions

“…Some recent eminent works demonstrating the impact of irreversible wall reaction on the transport process are Rana & Murthy [19,20], Debnath et al [21,22], Rana & Liao [23], Tiwari et al [24], Shah et al [25], and Roy & Shaw [26]. Recently, solute dispersion in Casson fluid flow through a stenosed artery was investigated by Das et al [27,28] incorporating the effect of the first-order irreversible absorption. Also, Biswas et al [29,30] explored drug transportation in lumen and tissue considering a patient-specific atherosclerotic artery with the irreversible absorption.…”

“…Recently, solute dispersion in Casson fluid flow through a stenosed artery was investigated by Das et al. [27,28] incorporating the effect of the first-order irreversible absorption. Also, Biswas et al.…”

Advection and dispersion induced by an interface between two immiscible fluids in a laminar flow

“…phase systems, a theoretical understanding of the advective-dispersive mixing in multiphase systems is relatively less developed. [14][15][16][17] There are a variety of natural and manufactured systems, where two immiscible and incompressible Newtonian fluids unevenly fill the space between two parallel plates. For instance, conditions at which a stable laminar flow without recirculation or instabilities at the interface between phases can be formed in microfluidic devices are ubiquitous.…”