(230aj) Time Evolution of Shear-Induced Particle Margination and Migration in a Cellular Suspension

The inhomogeneous center-of-mass distributions of red blood cells and platelets normal to the flow direction in small vessels play a significant role in hemostasis, drug delivery and microfluidics. Under pressure-driven flow in channels, the migration of deformable red blood cells at steady state is characterized by a concentration peak at the channel center and a cell-free layer or Fahraeus-Lindqvist layer near the vessel wall. Rigid particles such as platelets, however, â??marginateâ? and thus develop a near-wall excess concentration. Though many efforts have been invested into determining these steady state behaviors of shear-induced migration and margination, little progress has been made on the time evolution of such processes. In the vascular system, branching occurs on the length scale of approximately 1mm for arterioles. In the design of microfluidic devices, short flow paths are preferred in order to reduce the volume of blood used for diagnostic purposes. Therefore, it is worth investigating the time evolution of particle margination and migration from a non-equilibrium state and determine the corresponding entrance lengths.

In this talk, we investigate the time-dependent concentration distribution of red blood cells and platelets in pressure-driven flow by solving a Boltzmann model, advection-diffusion equation for both species. From a fluid mechanics point of view, deformability-induced hydrodynamic lift and shear-induced diffusion are essential mechanisms for the cross-flow particle migration and margination. The governing Boltzmann equation for red blood cells includes both lift flux away from the wall and shear-induced diffusion due to cell-cell â??collisionsâ?. On the other hand, the governing transport equation for platelets includes shear-induced diffusion from cell-platelet â??collisionsâ? and platelet-platelet â??collisionsâ?. We verify our model by, first, solving for the steady concentration profile of red blood cells and platelets, and demonstrating that these predictions are in good agreement with full boundary element simulation and experimental results. We then explore the time evolution and report entrance lengths for red blood cell migration and platelet margination. Our theory serves as a fast and computationally-efficient alternative to large-scale simulation.