Dynamics of deformable straight and curved prolate capsules in simple shear flow

TL;DR

This study uses direct simulations to analyze how deformability and curvature affect the motion of prolate capsules, modeling sickle red blood cells, in shear flow, revealing complex dynamics and implications for blood disorders.

Contribution

It provides new insights into the dynamics of curved and deformable capsules, especially sickle-shaped red blood cells, in shear flow, highlighting the effects of deformability and curvature on their motion.

Findings

Straight capsules tumble in shear plane with low deformability.

Curved capsules exhibit complex initial behaviors, then settle into Jeffery-like orbits.

Deformability and curvature influence orbit parameters, affecting cell motion understanding.

Abstract

This work investigates the motion of neutrally-buoyant, slightly deformable straight and curved prolate capsules in unbounded simple shear flow at zero Reynolds number using direct simulations. The curved capsules serve as a model for the typical crescent-shaped sickle red blood cells in sickle cell disease (SCD). The effects of deformability and curvature on the dynamics are revealed. We show that with low deformability, straight prolate spheroidal capsules tumble in the shear plane as their unique asymptotically stable orbit, which contrasts with that for rigid spheroids where infinitely many neutrally stable Jeffery orbits exist. The dynamics of curved prolate capsules are more complicated due to a combined effect of deformability and curvature. At short times, depending on the initial orientation, slightly deformable curved prolate capsules exhibit either a Jeffery-like motion such as tumbling or kayaking, or a non-Jeffery-like behavior in which the end-to-end vector of the capsule crosses the shear-gradient plane back and forth. At long times, however, a Jeffery-like quasi-periodic orbit is taken regardless of the initial orientation. We further show that the average of the long-time trajectory can be well approximated using the analytical solution for Jeffery orbits with an effective orbit constant $C_{\textnormal{eff}}$ and aspect ratio $\ell_{\textnormal{eff}}$. As the capsule becomes more deformable or curved, $C_{\textnormal{eff}}$ decreases, indicating a shift of the orbit towards log-rolling motion, while $\ell_{\textnormal{eff}}$ increases weakly as the degree of curvature increases but shows negligible dependency on deformability. As cell deformability, cell shape, and cell-cell interactions are all pathologically altered in blood disorders such as SCD, these results will have clear implications on improving our understanding of the pathophysiology of hematologic disease.