Layer-adapted meshes for solute dispersion in a steady flow through an annulus with wall absorption: Application to a catheterized artery

Abstract

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.