Non-modal stability of flowing red blood cells
A train of red blood cells flowing in a round tube will either advect steadily or break down into a complex and irregular flow, depending upon its degree of confinement. We analyze this apparent instability, including full coupling between the viscous fluid flow and the elastic cell membranes. A linear stability analysis is constructed via a complete set of orthogonal perturbations to a boundary integral formulation of the flow equations. Both transiently and asymptotically amplifying disturbances are identified. Those that amplify transiently have short-wavelength shape distortions that carry significant membrane strain energy. In contrast, asymptotic disturbances are primarily rigid-body-like tilts and translations. It is shown that an intermediate cell-cell spacing of about half a tube diameter suppresses long-time train instability, particularly when the vessel diameter is relatively small. Altering the viscosity ratio between the cytosol fluid within the cell and the suspending fluid is found to be asymptotically destabilizing for both higher and lower viscosity ratios. Altering the cytosol volume away from that of a nominally healthy discocyte alters the stability with complex dependence on train density and vessel diameter. Several of the observations are consistent with a switch from predominantly cell-cell interactions for dense trains and predominantly cell-wall interactions for less dense trains. Direct numerical simulations are used to verify the linear stability analysis and track the perturbation growth into a self-sustaining disordered regime.
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- S. H. Bryngelson and J. B. Freund, “Global stability of ﬂowing red blood cell trains,” Physical Review Fluids 3, 073101 (2018)