Computational study of the interaction between a newtonian fluid and a cellular biological medium in a straight vessel

Abstract

In this work, we solve numerically the governing equations for quasi-steady Newtonian flow past and through a cellular biological medium, which is attached to the surface of a straight vessel. The flow past the cellular biological medium is described by the Navier-Stokes equations. For the modeling of momentum transfer within the cellular biological medium, we consider that the cellular biological medium constitutes a biphasic fluid-solid mixture with poroelastic behaviour. The system of governing equations is solved numerically with the mixed finite element method. The computational domain is discretized using an unstructured, variable density triangular element mesh. From the numerical solution we obtain the spatial distributions of: (i) the fluid velocity and pressure, and (ii) the displacement and stresses of the solid matrix within the cellular biological medium. Also, the components of the overall hydrodynamic force exerted by the flowing fluid on the cellular biological medium are calculated. A parametric analysis is performed with regard to the Reynolds and Darcy numbers that characterize the flow past and through the cellular biological medium.