| Three-dimensional numerical simulations using immersed boundary/front-tracking method are considered to study the dynamics and deformation of microscopic deformable cells with elastic and viscoelastic membranes suspended in linear shear flow. The objective in this thesis is to understand the complex fluid/structure interaction problem for membrane-bound soft matter in dilute suspensions. The numerical model includes all essential properties of the cell membrane, namely, the resistance against shear deformation, area dilatation, and bending, as well as the viscosity difference between the cell interior and suspending fluids. In addition, the Kelvin–Voigt viscoelastic model is incorporated to account for the effect of membrane viscosity. Our numerical technique is able to simulate complex dynamics of vesicles, capsules, and red blood cells in the tank-treading, breathing, trembling, and tumbling modes.;A detailed comparison of the numerical results for vesicles is made with various theoretical models and experiments. It is found that the applicability of the theoretical models is limited to quasi-spherical vesicles. We show that near the transition between the tank-treading and tumbling dynamics, both the vacillating-breathing-like motion characterized by a smooth ellipsoidal shape, and the trembling-like motion characterized by a highly deformed shape are possible. We also present phase diagrams of the single red blood cell dynamics in linear shear flow. We find that the cell dynamics is often more complex than the well-known tank-treading, tumbling, and swinging motion and is characterized by an extreme variation of the cell shape. Identifying such complex shape dynamics termed here as breathing dynamics, is the focus of this study. Further, we find a very good agreement between our numerical and the theoretical and experimental results on the tank-treading frequency of red blood cells, which is often measured in experiments and used to extract the mechanical properties of the cell. A comprehensive analysis of the influence of the membrane viscosity on buckling, deformation and dynamics is given for initially spherical or oblate capsules. The major finding here is that the membrane viscosity leads to buckling in the range of shear rates in which no buckling is observed for capsules with purely elastic membrane. |
