Time-dependent particle migration and margination in the pressure-driven channel flow of blood

Qin M. Qi and Eric S. G. Shaqfeh
Phys. Rev. Fluids 3, 034302 – Published 7 March 2018

Abstract

We present a theory to describe the time evolution of the red blood cell (RBC) and platelet concentration distributions in pressure-driven flow through a straight channel. This model is based on our previous theory for the steady-state distributions [Qi and Shaqfeh, Phys. Rev. Fluids 2, 093102 (2017)] and captures the flow-induced nonuniformity of the concentrations of RBCs and platelets in the cross-flow direction. Starting with a uniform concentration, RBCs migrate away from the channel walls due to a shear-induced lift force and eventually reach steady state due to shear-induced diffusion, i.e., hydrodynamic “collisions” with other RBCs. On the other hand, platelets exit the cell-laden region due to RBC-platelet interactions and enter the cell-free layer, resulting in margination. To validate the theory, we also perform boundary integral simulations of blood flow in microchannels and directly compare various measureables between theory and simulation. The timescales associated with RBC migration and platelet margination are discussed in the context of the simulation and theory, and their importance in the function of microfluidic devices as well as the vascular network are elucidated. Due to the varying shear rate in pressure-driven flow and the wall-induced RBC lift, we report a separation of timescales for the transport in the near-wall region and in the bulk region. We also relate the transient problem to the axial variation of migration and margination, and we demonstrate how the relevant timescales can be used to predict corresponding entrance lengths. Our theory can serve as a fast and convenient alternative to large-scale simulations of these phenomena.

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  • Received 14 September 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.034302

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Qin M. Qi* and Eric S. G. Shaqfeh

  • Chemical Engineering, Stanford University, Stanford, California 94305, USA

  • *qinq@stanford.edu
  • Also at Mechanical Engineering, Stanford University, and Institute for Computational and Mathematical Engineering, Stanford University; esgs@stanford.edu

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Issue

Vol. 3, Iss. 3 — March 2018

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