Cellular flow in a small blood vessel

n the smallest capillaries, or in tubes with diameter D ≲8 μ m, flowing red blood cells are well known to organize into single-file trains, with each cell deformed into an approximately static bullet-like shape. Detailed high-fidelity simulations are used to investigate flow in a model blood vessel with diameter slightly larger than this: D =11.3 μ m. In this case, the cells deviate from this single-file arrangement, deforming continuously and significantly. At the higher shear rates simulated (mean velocity divided by diameter U/≳50 s-1), the effective tube viscosity is shear-rate insensitive with μ _eff/μ _plasma=1.21. This matches well with the value μ _eff/μ _plasma =1.19 predicted for the same 30% cell volume fraction by an established empirical fit of high-shear-rate in vitro experimental data. At lower shear rates, the effective viscosity increases, reaching μ eff/μ plasma ̃1.65 at the lowest shear rate simulated (U/D̃3.7 s-1). Because of the continuous deformations, the cell-interior viscosity is potentially important for vessels of this size. However, most results for simulations with cell interior viscosity five times that of the plasma (.=5), which is thought to be close to physiological conditions, closely match results for cases with .=1. The cell-free layer that forms along the vessel walls thickens from 0.3 μ m for U/D=3.7 s-1 up to 1.2 μ m for U/D100 s-1, in reasonable agreement with reported experimental results. The thickness of this cell-free layer is the key factor governing the overall flow resistance, and this in turn is shown to follow a trend expected for lubrication lift forces for shear rates between U/D≳8 s^-1 and U/D∼100 s^-1. Only in this same range are the cells near the vessel wall on average inclined relative to the wall, as might be expected for a lubrication mechanism. Metrics are developed to quantify the kinematics of this dense cellular flow in terms of the well-known tank-treading and tumbling behaviours often observed for isolated cells in shear flows. One notable effect of .=5 versus .=1 is that it suppresses treading rotation rates by a factor of about 2. The treading rate is found to scale with the velocity difference across the cell-rich core and is thus significantly slower than the overall shear rate in the flow, which is presumably why the flow is otherwise insensitive to . The cells in all cases also have a similarly slow mean tumbling motion, which is insensitive to cell-interior viscosity and decreases monotonically with increasing U/D.