MODELING AND NUMERICAL SIMULATION OF THE BIO-FLUID-DYNAMICS OF RED BLOOD CELLS
Prof. C. Pozrikidis
Department of Mechanical & Aerospace Engineering
Red blood cells are liquid capsules containing a viscous fluid that is enclosed by a biological membrane consisting of a lipid bilayer and a supporting network of proteins. In the absence of flow, the cells assume the equilibrium shape of a biconcave disk. When subjected to flow, the cells deform in a way that is determined by the type and strength of the flow and the mechanical properties of the membrane. In this presentation, an integrated mathematical framework for the equations governing the fluid dynamics and membrane mechanics is discussed under the auspices of low-Reynolds-number hydrodynamics and nonlinear theory of thin shells. The governing equations are solved using a novel implementation of the boundary-element method in global Cartesian coordinates, accounting for the membrane incompressibility, elasticity, and bending stiffness. Numerical simulations are carried out to investigate the deformation of a cell in simple shear flow in the physiological range of physical properties and flow conditions. The cells are found to perform flipping motion accompanied by periodic deformation in which the cross-section of the membrane in the plane of the flow alternates between the nearly biconcave resting shape and a reverse S shape. The period of the overall rotation is in good agreement with experimental observations of red blood cells suspended in plasma. The numerical results illustrate in quantitative terms the distribution of the membrane tensions developing due to the flow-induced deformation, and reveal that the membrane is subjected to stretching and compression in the course of the rotation. The success of these simulations motivates the development of further computational techniques, with the long-term goal of being able to simulate particulate blood flow under a broad range of conditions.