(304g) Modeling And Analysis Of Non-Newtonian Fluid Flow In Flexible Structures

Fluid flow within a flexible structure such as a tube or channel is regulated by the stresses imposed upon the structure by the both the fluid and any external forces. Thus, the material properties of both the fluid and the conduit significantly influence the fluid flow in the system [1]. Additionally, the presence of an internal structure can impose further limitations on the fluid flow. When fluid properties exhibit non-Newtonian behavior, the viscosity becomes a function of the shear rate affecting the viscous forces [2]. Viscous forces together with the fluid pressure impose stresses on the boundaries of the conduit wall and on the internal structure. These forces cause the flexible structures to move resulting in continuous displacement of the flexible boundaries. In general, flexible structures exhibit anisotropic elastic properties [3] leading to nonlinear displacements. Furthermore, when the elastic properties of the conduit and internal structures are not at their nominal values, their flexibility is compromised, which affects fluid flow behavior. Systems consisting of a flexible conduit and internal flexible structures include venous vein and the venous bicuspid valves, bronchial air ways [4-7], peristaltic tubes, and micro-fluidic devices [8,9] .

The primary objective of this study is to model and analyze two-dimensional, non- Newtonian fluid flow within flexible structures; specifically fluid flow behavior under different flow conditions and different viscoelastic properties. Numerical solutions of non-Newtonian fluid flow within these systems provide a means of predicting the impact of these variables on the overall fluid dynamics. Such insights can provide useful design and performance information to the medical and pharmaceutical industries, industries involved in the development of polymer solutions and device manufacturers. For example, flow prediction within flexible micro-channels may assist in the design of new materials to lessen the stiffness of such systems.

The fluid domain is modeled using the conservation of momentum and mass while the viscous effects are modeled using non-Newtonian fluid properties. The induced stresses on the flexible structures, the forces acting upon the flexible structures, and the displacements are related by Newton's second law. Thus, the mathematical description of this system involves multi-dimensional fluid dynamics and nonlinear solid mechanics resulting in a system of nonlinear partial differential equations with moving boundary conditions. Initial numerical studies with collapsible channel flow [1,5] showed that there can be significant distortions in the both the fluid and flexible domains. To address these issues, an Arbitrary Lagrangian-Eulerian (ALE) method and a finite element description are used as the numerical method approaches to find a solution [10]. The ALE formulation combines the best features of both pure Lagrangian and pure Eulerian formulations. Thus, numerical computation with ALE formulation succeeds in eliminating computational burdens experienced with the former two formulations while capturing the fluid structure interaction dynamics in the presence of significant distortions.

For demonstration purposes, this study will focus on non-Newtonian fluid flow in a flexible tube with an internal, flexible one-way restriction. Such systems can be used to represent the venous vein and valve found in the legs of humans. The purpose of the venous valve is to guarantee the return of blood flow to the heart (venous return). Several factors may restrict the venous valve from functioning in the prescribed manner leading to undesirable retrograde (reverse blood flow) flow and liquid accumulation (blood pooling) in the venous valve sinus. In this study, flow patterns around the valves and a criteria for closing and opening dynamics of the flexible leaflets under different operating conditions will be the focus of the study.

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