Date of Award
Doctor of Philosophy (PhD)
Mathematics and Statistics
Computational and Applied Mathematics
A description of the biomechanical character of red blood cells is given, along with an introduction to current computational schemes which use deformable capsules to simulate red blood cell shape change. A comprehensive two- and three-dimensional framework for the fluid-structure interaction between a deformable capsule and an ambient flow is provided. This framework is based on the immersed boundary method, using lattice Boltzmann and finite element methods for the fluid and structure, respectively. The characteristic response and recovery times of viscoelastic circular and spherical capsules are compared, and their dependence on simulation parameters is shown. The shape recovery of biconcave capsules in two and three dimensions is also considered, focusing on the role of simulation parameters and steady-state behaviour in two dimensions, while studying the capsule characteristics which lead to shape recovery and shape memory in three dimensions. Finally, the notion of interpreting membrane viscosity as an additional fluid viscosity is studied and a computational scheme based on power law fluids is described.
"Modeling and Simulation of Shape Changes of Red Blood Cells in Shear Flow"
(2014). Doctor of Philosophy (PhD), Dissertation, Mathematics and Statistics, Old Dominion University, DOI: 10.25777/frv3-m651