| Περίληψη: | The scope of this work is the theoretical and computational modeling of the interaction between a Newtonian fluid and a cellular biological medium attached on the surface of a vessel. First and foremost, an extensive and comprehensive review is presented with regard to the available approaches for modeling momentum transfer within cellular biological media, including single-scale-single-phase approaches, Biot's poroelasticity, mixture theory, upscaling methods and multiscale computational equation free methods. Thereafter, at the cellular biological medium level, a theoretical model is developed for the description of momentum transfer within a poroelastic biomaterial, taking into account the interaction between the extracellular fluid and the solid skeleton that consists of cells and extracellular matrix (ECM). A continuum based formulation of momentum transport in a fluid-solid system at the finer spatial scale is used as starting point, and then the method of local spatial averaging with a weight function is implemented in order to establish the partial differential equations that describe the dynamics of fluid flow and matrix deformation at the coarser (macroscopic) spatial scale. In the special case of a homogeneous medium and under certain other conditions, the derived equations become similar to those which are postulated in the theory of interacting continua (mixture theory) and Biot's theory of poroelasticity. At the vessel level, the contribution of this work is twofold. First, a benchmark problem is developed for the validation of numerical methods used to solve problems that involve interactions between a fluid and a poroelastic material. Specifically, an analytical solution is developed for the problem of plane Couette-Poiseuille flow past a poroelastic layer. Second, a computational study is performed for plane Poiseuille flow past and through a semi-elliptical poroelastic biomaterial, which is attached to the surface of a straight vessel. Fluid flow in the clear fluid region is described by the Navier-Stokes equations, and momentum transfer within the biomaterial is described by the upscaled biphasic equations established in this work. The effect of the Reynolds and Darcy number that characterize the flow past and through the biomaterial, respectively, is investigated for obstacles with different configuration with respect to flow (semicircle, oblate semi-ellipse, prolate semi-ellipse). The distribution of the von Mises stress within the biomaterial is determined and, also, the drag and lift forces exerted by the fluid on the biomaterial are calculated.
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