A Stochastic Simulation Method Using Constraints for the Modeling of Blood Rheology

In this dissertation, I present Brownian Dynamic simulation technique with constraint method to predict the movement of biological cells specifically focused on rheology of blood. Blood is often treated as continuum fluid or an empirical constitutive equation is used to study a blood flow. However, it would be impossible to observe neither the deformation nor the elasticity of the cell. The proposed method based on kinetic theory where the stress tensor and the stochastic differential equation (SDE) of motion depend on the configuration of the microstructure of the fluid will allow observing the movement as well as the material properties. In addition, the constraint method using Lagrange multiplier describes the effect of the biological cell conserving its overall size throughout the motion of flow while allowing the shape to deform. In this study, blood is considered as suspension of deformable red blood cells (RBCs) in a dilute solution of fluid. A discrete model of bead-spring RBC is constructed with linear Hookean spring to give flexibility to deform. To demonstrate the capability of the method, the minimalist bead-spring model to represent the RBC was simulated. Contraints used in this research are geometrical holonomic constraints. The RBC models are tested under shear and shear free flow. An assumption was made that the friction tensor is isotropic. The rheological material properties are obtained through simulations. A comparison is then made between predicted viscosity and experimental observations followed by discussion of the effects of constraint on each RBC models that are developed.