MCT Research Talks – 24th March 2017
Prof. Eric S. G. Shaqfeh, Qin M. Qi, Departments of Chemical and of Mechanical Engineering, Stanford University
The inhomogeneous center-of-mass distribution of red blood cells and platelets normal to the flow direction in small vessels plays 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 characterised 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, “marginate” and thus develop a near-wall excess concentration. This margination controls the time it takes for the initial stages of platelet binding and clotting in response to trauma.
In this talk, we investigate the time-dependent concentration distribution of red blood cells and platelets in pressure-driven flow by developing and 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 equation for the distribution of red blood cells includes both lift flux away from the wall and shear-induced diffusion due to cell-cell “collisions”. On the other hand, the governing transport equation for platelets includes shear-induced diffusion from cell-platelet “collisions” and platelet-platelet “collisions”. We demonstrate that these predictions are in good agreement with full boundary element simulations of the margination process and we also compare directly to experimental results. We then examine, within this model and our full boundary element simulations, the time evolution and “entrance length” for red blood cell migration and platelet margination. The resulting complete model can serve as a fast and computationally efficient alternative to large-scale simulation with the application, for example, as a real-time computational tool for microfluidic blood assay systems.