This paper describes the longitudinal dispersion of passive tracer molecules injected in a steady, fully developed, viscous, incompressible, laminar flow through an annular pipe with a first order heterogeneous boundary absorption at the outer wall, numerically using layer-adapted meshes. The model is based on steady advection-diffusion equation with Dirichlet and Robin boundary conditions. The solutions are discussed in the form of iso-concentration contours of the tracer molecules in the vertical plane. An artanh transformation is used to convert the infinite domain into a finite one. A combination of central finite difference and 2-point upwind scheme is adopted to solve the governing advection-diffusion equation. It is shown that how the mixing of tracers is affected by the shear flow, aspect ratio and the first-order boundary absorption. When the flow becomes convection dominated, the monotone finite difference on a uniform mesh does not work properly, so a layer-adapted mesh, namely a “Shishkin” mesh, is used to capture the layer phenomena at the different downstream stations. The present results are compared with existing experimental and numerical data and we have earned an excellent agreement with them. It is observed that, due to the use of layer adapted mesh, we have achieved a better agreement with the experimental data than some other previous results available in the literature, especially in the closest downstream location. The results of this study are likely to be of interest to understand the basic mechanism of dispersion process of solute in blood through a catheterized artery with an absorptive arterial wall.

本文描述了通过在环形管中稳定，充分发展，粘性，不可压缩的层流中注入的被动示踪剂分子的纵向分散，该流在外壁具有一阶异质边界吸收，数值上使用了层自适应网格。该模型基于具有Dirichlet和Robin边界条件的稳定对流扩散方程。以示踪剂分子在垂直平面上的等浓度轮廓的形式讨论了这些解决方案。一个artanh转换用于将无限域转换为有限域。结合中心有限差分和两点迎风方案求解控制对流扩散方程。结果表明，示踪剂的混合如何受到剪切流，长宽比和一阶边界吸收的影响。当流动成为对流主导时，均匀网格上的单调有限差分将无法正常工作，因此使用了层自适应网格（即“ Shishkin”网格）来捕获不同下游站的层现象。目前的结果与现有的实验和数值数据进行了比较，我们已经与他们取得了很好的协议。可以观察到，由于使用了适应层的网格，与文献中可获得的其他一些先前结果相比，我们在实验数据上取得了更好的一致性，尤其是在最近的下游位置。这项研究的结果可能有助于了解溶质通过具有吸收性动脉壁的导管动脉在血液中的弥散过程的基本机制。