ABSTRACT

Blood is a highly viscous fluid with many different structural elements such as red blood cells (RBCs), white blood cells (WBCs), platelets and many macromolecules. Red blood cell aggregation and blood vessel geometry are two important determinants of the flow characteristics of blood in microvessels. Blood flow in venules is of particular interest to understand the vascular resistance. We have studied the effect of vessel bifurcation, red blood cell aggregation and leukocyte adhesion on blood flow by using computational models. The partial differential equations describing the flow are solved by using Galerkin finite element method. The calculations predict a complex three dimensional pattern of blood flow and generally nonaxisymmetric distribution of velocity, hematocrit, and shear stress in the collecting venule.

This talk will be devoted to the connection between kinetic theory and macroscopic fluid dynamics. We will start from the Boltzmann equation. Formally, we will derive the fluid equations under different scaling: Compressible Euler, acoustic, incompressible Navier-Stokes, Euler, Stokes, etc. Some rigorous results are introduced concerning the validity of these limits, including the long term program of Bardos-Golse-Levermore, followed by the work of Lions, Masmoudi and Saint-Raymond. In the last part, I will introduce my (small) result on the compressible Stokes limit using relative entropy method, which unify the acoustic and Stokes limits. Although the mathematical work of this field is highly technical, my talk will concentrate on the physical background and basic strategy of rigorous mathematical works, showing what hydrodynamic limit is.