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

• Type of Material: Article
• Authors: Xiao Zhang, University of Wisconsin; Wilbur Lam, Emory University; Malcolm D Graham, Emory University
• Language: English
• Date: 2019-04-18
• Publisher: American Physical Society
• Publication Version: Author Accepted Manuscript (After Peer Review)
• Copyright Statement: © 2019 American Physical Society..
• Final Published Version (URL): http://dx.doi.org/10.1103/PhysRevFluids.4.043103
• Title of Journal or Parent Work: Physical Review Fluids
• ISSN: 2469-990X
• Volume: 4
• Issue: 4
• Grant/Funding Information: This work was supported by NSF Grant No. CBET-1436082 and NIH Grant No. R21MD011590-01A1
• Keywords: Physical Sciences; Physics, Fluids & Plasmas; MECHANICAL-PROPERTIES; MOTION; ENERGY; PARTICLES; RED-BLOOD-CELLS; ROTATION; MEMBRANE; Science & Technology; SICKLE HEMOGLOBIN; Physics; RHEOLOGY
• Research Categories: Health Sciences, Medicine and Surgery; Engineering, Biomedical

Abstract

This work investigates the motion of neutrally buoyant, slightly deformable straight and curved prolate fluid-filled 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 exhibit tumbling in the shear plane as their unique asymptotically stable orbit. This result 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 director (end-to-end vector) of the capsule crosses the shear-gradient plane back and forth. At long times, however, a Jeffery-like quasiperiodic 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 Ceff and aspect ratio eff. These parameters are useful for characterizing the dynamics of curved capsules as a function of given deformability and curvature. As the capsule becomes more deformable or curved, Ceff decreases, indicating a shift of the orbit towards log-rolling motion, while eff increases weakly as the degree of curvature increases but shows negligible dependency on deformability. These features are not changed substantially as the viscosity ratio between the inner and outer fluids is changed from 1 to 5. 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.