<p>The transport of a reactive solute through a circular tube of finite radius is investigated mathematically using a two-layered macroscopic model that consists of a cell-rich core of suspension of all erythrocytes described as a particle-fluid suspension (Jeffrey fluid) and a peripheral zone of cell-free plasma (Newtonian fluid). At the tube wall, the solute may experience an irreversible absorptive response. The transport coefficients are computed both analytically and numerically (Crank–Nicholson finite difference method), and they are specified with the aid of Aris’s method of moments. Graphical analysis illustrates the effects of the Jeffreys parameter (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\lambda _{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>λ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>), wall absorption rate (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>), and volume fraction (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\phi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>) on key transport characteristics. The negative exchange coefficient, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$-K_0(t)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, rises with boundary absorption and stabilizes when diffusion balances solute transfer from the vessel wall to the core. Both the advection coefficient (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$K_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>) and dispersion coefficient (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$K_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>) increase significantly with the Jeffrey viscoelastic parameter (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\lambda _{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>λ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>) and volume fraction density (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\phi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>). The advection coefficient (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">$K_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>) exhibits the opposite behavior from the dispersion coefficient (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">$K_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>), which decreases with wall absorption rate (<InlineEquation ID="IEq11"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>). The mean axial concentration distribution and transverse concentration distribution of the solute are formulated using the Hermite polynomial representation of the central moments of the distribution. The axial mean concentration is significantly suppressed with an increment in particle volume fraction density (<InlineEquation ID="IEq12"> <EquationSource Format="TEX">$\phi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>) and also with higher values of the Jeffrey viscoelastic parameter (<InlineEquation ID="IEq13"> <EquationSource Format="TEX">$\lambda _{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>λ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>). However, it is very weakly increased with an increase in peripheral layer thickness. The transverse solute concentration decreases as <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$\phi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$\lambda _{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>λ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> increase. Axial concentration distribution is strongly affected by <InlineEquation ID="IEq16"> <EquationSource Format="TEX">$\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>, while transverse concentration distribution shows little variation with <InlineEquation ID="IEq17"> <EquationSource Format="TEX">$\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>. This study’s findings are particularly relevant to arterial pharmaco-hemodynamics.</p>

Unsteady Taylor–Aris dispersion in a Jeffery viscoelastic blood flow model with wall absorption

期刊论文
发表日期：

2025年12月8日

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Ashis Kumar Roy,
Sudip Debnath,
O. A. Bég,
T. A. Bég

摘要

The transport of a reactive solute through a circular tube of finite radius is investigated mathematically using a two-layered macroscopic model that consists of a cell-rich core of suspension of all erythrocytes described as a particle-fluid suspension (Jeffrey fluid) and a peripheral zone of cell-free plasma (Newtonian fluid). At the tube wall, the solute may experience an irreversible absorptive response. The transport coefficients are computed both analytically and numerically (Crank–Nicholson finite difference method), and they are specified with the aid of Aris’s method of moments. Graphical analysis illustrates the effects of the Jeffreys parameter ( $\lambda _{1}$ $λ_{1}$ ), wall absorption rate ( $\beta $ $β$ ), and volume fraction ( $\phi $ $ϕ$ ) on key transport characteristics. The negative exchange coefficient, $-K_0(t)$ $- K_{0} (t)$ , rises with boundary absorption and stabilizes when diffusion balances solute transfer from the vessel wall to the core. Both the advection coefficient ( $K_1$ $K_{1}$ ) and dispersion coefficient ( $K_2$ $K_{2}$ ) increase significantly with the Jeffrey viscoelastic parameter ( $\lambda _{1}$ $λ_{1}$ ) and volume fraction density ( $\phi $ $ϕ$ ). The advection coefficient ( $K_1$ $K_{1}$ ) exhibits the opposite behavior from the dispersion coefficient ( $K_2$ $K_{2}$ ), which decreases with wall absorption rate ( $\beta $ $β$ ). The mean axial concentration distribution and transverse concentration distribution of the solute are formulated using the Hermite polynomial representation of the central moments of the distribution. The axial mean concentration is significantly suppressed with an increment in particle volume fraction density ( $\phi $ $ϕ$ ) and also with higher values of the Jeffrey viscoelastic parameter ( $\lambda _{1}$ $λ_{1}$ ). However, it is very weakly increased with an increase in peripheral layer thickness. The transverse solute concentration decreases as $\phi $ $ϕ$ and $\lambda _{1}$ $λ_{1}$ increase. Axial concentration distribution is strongly affected by $\gamma $ $γ$ , while transverse concentration distribution shows little variation with $\gamma $ $γ$ . This study’s findings are particularly relevant to arterial pharmaco-hemodynamics.