Numerical Simulation of Red Blood Cells in Capillaries

A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the RBC rheology with an immersed boundary method. We combine the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the motion of a compound vesicle in a microchannel. We validate the methodology by comparing the numerical results of neutrally buoyant particle with the Jeffery's solutions. Numerical results with Stokes equations are compared with numerical results with Navier-Stokes equations. With Stokes equations, the motion of compound vesicle is determined by the part of vesicle; while with Navier equations, the motion of a compound vesicle is determined by the competition between the part of the vesicle and the particle inside. Computational modeling and simulation are also presented on the motion of red blood cells behind a moving interface in a capillary. As by the nature of the problem, the computational domain is moving with either a designated RBC or an interface in an infinitely long two--dimensional channel with an undisturbed flow field in front of the computational domain. The tank--treading and the inclination angle of a cell in a simple shear flow are briefly discussed for the validation purpose. We then present and discuss the results of the motion of red blood cells behind a moving interface in a capillary, which show that the RBCs with higher velocity than the interface speed form a concentrated slug behind the moving interface. The advancing velocity is slowed down to approximately one-fourth of the initial velocity when taking into the account the effective viscosity of the mixture of RBCs and fluid behind the moving interface. This indicates the reason of the penetration failure in a capillary.Mathematics, Department o