In this thesis, three-dimensional simulations are performed to investigate the effects of membrane viscosity on behaviors of red blood cells (RBCs) in simple shear flow and the migration processes of viscoelastic capsules in tube flow. The lattice Boltzmann method is used as the fluid solver, whereas the immersed boundary method is employed to capture the dynamic interaction between the flow and membrane. The RBC membrane follows the Skalak constitutive law for elasticity, and the resistances to area dilation and bending deformation are also included. In addition, the membrane viscosity is incorporated using the recently developed finite difference scheme. The methodology and computer programs are validated carefully by conducting several benchmark test simulations.
The lateral migration of viscoelastic capsules in tube flow is investigated in details with various combinations of viscosity ratio, membrane shear viscosity and capillary number. In general, the migration process starts with an initial transient phase, where the capsule deformation and migration velocity suddenly increase from zero to a maximum value. Following that, the deformation and migration velocity gradually reduce as the capsule moves toward the tube centerline. The capsule also performs continuous rotation during the migration, and the rotation gradually slows down with the capsule migration. The interior-exterior fluid viscosity contrast and the membrane viscosity have similar effects in reducing the capsule deformation and inclination angle to the flow direction; however, a strong membrane viscosity may introduce significant oscillations in the capsule deformation, inclination, and migration velocity. Due to the reduced capsule deformation, the migration velocity and capsule rotation become slower for capsules with higher viscosity contrast and/or membrane viscosity. Moreover, the influence of membrane viscosity on the migration dynamics intensifies at higher capillary number.
In addition, tank-treading behaviors of RBC in simple shear flow is scrutinized over a wide range of shear rate and exterior fluid viscosity. Detailed comparisons of the tanktreading frequency, deformation, and inclination angle of the cell with experiments are conducted by considering different combinations of membrane and interior fluid viscosities. According to the results, tank-treading frequency diminishes with both membrane viscosity and internal fluid viscosity, although elevating the interior viscosity alone does not sufficiently retard the tank-treading motion to achieve favorable agreement with experimental results. This stronger impact of membrane viscosity has also been noticed for the cell deformation and inclination angle. In particular, including membrane viscosity is essential to reproduce experimental results for the cell orientation. Furthermore, the results indicate that a reasonable agreement can be obtained in comparison to experiments even without applying the shear-thinning model for membrane viscosity. Hence, more supporting evidence is required to justify necessity and applicability of shear-thinning models for membrane viscosity of RBCs. Suggestions for future research have been proposed as well.