NUMERICAL SIMULATION OF PULSATILE MICROPOLAR BLOOD FLOW IN A VISCOELASTIC ARTERY AND COMPARISON WITH RIGID AND ELASTIC ARTERIES

Under normal physiological conditions, the transport of blood in the human circulatory system depends entirely on the pumping action of the heart producing a pulsatile pressure gradient throughout the arterial system. The theory of micro uids exhibits the microscopic eects arising from the local structure, and the micro-motion of the uid elements was developed. Such uids support stress and body moments, including rotary inertia. There is a subclass of micro uids, namely, micropolar uids, which support couple stress, body couples, microrotational eects and microrotational inertia. The micropolar uid, e.g. liquid crystals, suspensions and animal blood etc., consists of randomly oriented bar-like elements or dumbbell molecules, and each volume element has a microrotation about its centroid, described in an average sense by the skew-symmetric gyration tensor. From a continuum point of view, the classical Navier- Stokes equations are incapable of explaining the theory of micropolar uid as they contain no proper mechanism to account for the cellular microrotations. In this paper, an unsteady pulsatile laminar blood ow through a viscoelastic artery with large displacement and Cosserat continuum assumption has been developed and numerically investigated, where the blood was assumed to be a micropolar uid. A nite dierence Cosserat formulation is developed within the principles of continuum mechanics. Fluid ow simulation has been undertaken in dierent states, like a rigid exible wall, together with classical theory. By comparing experimental data with Cosserat theory results, some unknown coecients have been determined. The pressure and velocities of unsteady pulsatile blood ow have been obtained according to these coecients by using a pressure correction numerical solution approach for uid and coupling with solid equations. An arbitrary Lagrangian-Eulerian approach has been selected for uid-structure interaction in this paper. The achieved results are in good agreement with experiment data and other analytical solution results. Results in this paper show that the micropolar uid model of blood and the viscoelastic model of the artery, despite the existence of uid solid interaction, increase, in accordance with the numerical results of valid experimental data.