The present article discusses the solute transport process in steady laminar blood flow through a non-Darcy porous medium, as a model for drug movement in blood vessels containing deposits. The Darcy–Brinkman–Forchheimer drag force formulation is adopted to mimic a sparsely packed porous domain, and the vessel is approximated as an impermeable cylindrical conduit. The conservation equations are implemented in an axisymmetric system (R, Z) with suitable boundary conditions, assuming constant tortuosity and porosity of the medium. Newtonian flow is assumed, which is physically realistic for large vessels at high shear rates. The velocity field is expanded asymptotically, and the concentration field decomposed. Advection and dispersion coefficient expressions are rigorously derived. Extensive visualization of the influence of effective Péclet number, Forchheimer number, reaction parameter on velocity, asymptotic dispersion coefficient, mean concentration, and transverse concentration at different axial locations and times is provided. Increasing reaction parameter and Forchheimer number both decrease the dispersion coefficient, although the latter exhibits a linear decay. The maximum mean concentration is enhanced with greater Forchheimer numbers, although the centre of the solute cloud is displaced in the backward direction. Peak mean concentration is suppressed with the reaction parameter, although the centroid of the solute cloud remains unchanged. Peak mean concentration deteriorates over time since the dispersion process is largely controlled by diffusion at the large time, and therefore the breakthrough curve is more dispersed. A similar trend is computed with increasing Péclet number (large Péclet numbers imply diffusion-controlled transport). The computations provide some insight into a drug (pharmacological agents) reacting linearly with blood.

本文讨论了通过非达西多孔介质的稳定层流中溶质的运输过程，作为药物在含有沉积物的血管中运动的模型。采用Darcy–Brinkman–Forchheimer拖曳力公式来模拟稀疏填充的多孔区域，该容器近似为不可渗透的圆柱形导管。守恒方程在轴对称系统（R，  Z）在适当的边界条件下，假设介质的曲率和孔隙率保持不变。假设采用牛顿流，这对于高剪切速率下的大型船舶在物理上是现实的。速度场渐近扩展，浓度场分解。严格推导对流和弥散系数表达式。提供有效的佩克利数，福希海默数，反应参数对速度，渐近弥散系数，平均浓度和不同轴向位置和时间的横向浓度的影响的广泛可视化。增加反应参数和Forchheimer数均会降低分散系数，尽管后者表现出线性衰减。最大的平均浓度随着更大的Forchheimer数而增加，尽管溶质云的中心向后移动。尽管溶质云的质心保持不变，但峰平均浓度却被反应参数所抑制。峰值平均浓度随着时间的流逝而变差，这是因为分散过程在很大程度上受到扩散的控制，因此，穿透曲线更加分散。随着Péclet数的增加，可以计算出类似的趋势（大的Péclet数意味着扩散控制的运输）。该计算提供了与血液线性反应的药物（药理学）的一些见识。峰值平均浓度随着时间的流逝而变差，这是因为分散过程在很大程度上受到扩散的控制，因此，穿透曲线更加分散。随着Péclet数的增加，可以计算出类似的趋势（大的Péclet数意味着扩散控制的运输）。该计算提供了与血液线性反应的药物（药理学）的一些见识。峰值平均浓度随着时间的流逝而变差，这是因为分散过程在很大程度上受到扩散的控制，因此，穿透曲线更加分散。随着Péclet数的增加，可以计算出类似的趋势（大的Péclet数意味着扩散控制的运输）。该计算提供了与血液线性反应的药物（药理学）的一些见识。