# Chaos and spatial complexity of flowing red blood cells

The flow of red blood cells within cylindrical vessels is often complex and irregular, so long as the vessel is somewhat larger than the cells. We statistically analyze the kinematic behavior of a model of this flow, which includes full coupling between the elastic red cell membranes and surrounding viscous fluid. The flow is shown to be extremely sensitive to the initial flow configuration, the hallmark of a chaotic system and so-called Lagrangian turbulence. Phase-space reconstructions of the long-time flow data show that a low-dimensional attractor does not exist, so the observed long-time dynamics are indistinguishable from those generated by a stochastic system. Based on this stochasticity, a reduced-order Markov chain model for the dynamics is shown to quantitatively reproduce statistics of the full dynamical system.

**S. H. Bryngelson**and J. B. Freund, “Capsule-train stability,”*Physical Review Fluids***1**, 033201 (2016)- J. B. Freund and
**S. H. Bryngelson**, "The stability of ﬂowing trains of conﬁned red blood cells,"*XXIV International Conference of Theoretical and Applied Mechanics*, Montreal, Canada (2016) **S. H. Bryngelson**and J. B. Freund, “Global stability of ﬂowing red blood cell trains,”*Physical Review Fluids***3**, 073101 (2018)**S. H. Bryngelson**, F. Guéniat, J. B. Freund, "Irregular dynamics of cellular blood flow in a model microvessel,"*Physical Review E***100**, 012203 (2019)

# A buckling mechanism for confined suspension flows: Rheology and dynamics

The rheology of confined flowing suspensions, such as blood, depends upon the dynamics of the components, which can be particularly rich when they are elastic capsules. Using spectral boundary integral methods, we simulated a two-dimensional model channel through which flows a dense suspension of fluid-filled capsules. A parameter of principal interest is the equilibrium membrane perimeter, which ranges from round capsules to capsules with a dog-bone-like equilibrium shape. We showed that the minimum effective viscosity occurs for a biconcave equilibrium shape, similar to a red blood cell. The rheological behavior changes significantly over this range; transitions are linked to specific changes in the capsule dynamics. Most noteworthy was an abrupt change in behavior when the capsule at-rest shape is sufficiently slender, correlating with the onset of capsule buckling. Buckled capsules have a more varied orientation and make significant rotational (rotlet) contributions to the capsule–capsule interactions.

**S. H. Bryngelson**and J. B. Freund, “Buckling and its eﬀect on the conﬁned ﬂow of a model capsule suspension,”*Rheologica Acta***55**, 451–464 (2016)