Unstable cellular flows

Global stability of confined, flowing red-blood-cells

Flowing trains of red blood cells are stable when tightly confined but can otherwise break down into an irregular flow. A linear stability formulation is developed to analyze this biological phenomena, advancing understanding of its origin and guiding the design of devices that process 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.


S. H. Bryngelson and J. B. Freund, “Global stability of flowing red blood cell trains,” Phys. Rev. Fluids 3, 073101 (2018)


Transient instabilities and transition of flowing capsule-trains

Highly confined capsules—most notably red blood cells—are observed to flow in a seemingly stable train. However, with less confinement this striking order is disrupted, and the train breaks apart into an apparently chaotic flow. Non-modal stability analysis of a model capsule train illuminates the mechanisms of the break-up.

Elastic capsules flowing in small enough tubes, such as red blood cells in capillaries, are well known to line up into regular single-file trains. The stability of such trains in somewhat wider    channels, where this organization is not observed, is studied in a two-dimensional model system that includes full coupling between the viscous flow and suspended capsules. A diverse set of linearly amplifying disturbances, both long-time asymptotic (modal) and transient (nonmodal) perturbations, is identified and analyzed. These have a range of amplification rates and their corresponding forms are wavelike, typically dominated by one of five principal perturbation classes: longitudinal and transverse translations, tilts, and symmetric and asymmetric shape distortions. Finite-amplitude transiently amplifying perturbations are shown to provide a mechanism that can bypass slower asymptotic modal linear growth and precipitate the onset of nonlinear effects. Direct numerical simulations are used to verify the linear analysis and track the subsequent transition of the regular capsule trains into an apparently chaotic flow.


S. H. Bryngelson and J. B. Freund, “Capsule-train stability,” Phys. Rev. Fluids 1, 033201 (2016)