Off-plane motion of a prolate capsule in shear flow

Abstract

The objective of this study is to investigate the motion of an ellipsoidal capsule in a simple shear flow when its revolution axis is initially placed off the shear plane. We consider prolate capsules with an aspect ratio of two or three enclosed by a membrane, which is either strain-hardening or strain-softening. We seek the equilibrium motion of the capsule as we increase the capillary number $\mathit{Ca}$, which measures the ratio between the viscous and elastic forces. The three-dimensional fluid–structure interaction problem is solved numerically by coupling a boundary integral method (for the internal and external flows) with a finite element method (for the wall deformation). For any initial inclination with the flow vorticity axis, a given capsule converges towards a unique equilibrium configuration which depends on $\mathit{Ca}$. At low capillary number, the stable equilibrium motion is the rolling regime: the capsule aligns its long axis with the vorticity axis, while the membrane tank-treads. As $\mathit{Ca}$ increases, the capsule takes a complex wobbling motion at equilibrium, precessing around the vorticity axis. As $\mathit{Ca}$ is further increased, the capsule long axis oscillates about the shear plane, while the membrane rotates around a capsule cross-section that also oscillates over time (oscillating–swinging regime). The amplitude of the oscillations about the shear plane decreases as $\mathit{Ca}$ increases and the capsule finally takes a swinging motion in the shear plane. It is found that the transitions from rolling to wobbling and from wobbling to oscillating–swinging depend on the mean energy stored in the membrane.

Red cells’ dynamic morphologies govern blood shear thinning under microcirculatory flow conditions

“…However, during each tumbling period the membrane elements oscillate around a given position and this local oscillatory strain seems to destabilize RBCs from tumbling toward rolling (27) instead of tank treading. Although not fully settled, this phenomenon is well captured by our simulations and is described as a stable motion in several recent numerical simulations of capsules (28) and RBCs (29).…”

Mechanical response of red blood cells entering a constriction

“…For example, RBCs have been shown to display shape memory 11 and exhibit motions such as swinging 5 and rolling. [12][13][14] These motions have been interpreted in terms of the elasticity and stored energy in the membrane, 12,15 and modifications to the KS model by Abkarian, Faivre, and Viallat 5 and Skotheim and Secomb 16 (the AFV-SS model) now recognize an elastic component that contributes to mode transition. While the model takes into account both the viscous and elastic components, recent work by Dupire et al 12 suggests that the shear elasticity is a key determinant of RBC deformation, motion, and orientation.…”

Numerical Simulation of the Motion of Inextensible Capsules in Shear Flow Under the Effect of the Natural State

“…Lipid vesicles ( [1]- [9]), non-spherical capsules ( [10]- [14]), and red blood cells ([15]- [23]) show phenomenologically similar behavior in shear flows, which are (i) an unsteady tumbling motion, (ii) a tank-treading rotation with a stationary shape and a fixed inclination angle with respect to the flow direction, and (iii) while tank-treading (TT), the long axis oscillates about a fixed inclination angle which is called swinging mode in [9] (but it is still called the tank-treading in [11]). The aforementioned motions depend on the shear rate, viscosity ratio between internal fluid and external fluid, membrane viscosity and other parameters.…”