Dynamics of a single red blood cell in simple shear flow

Abstract

This work describes simulations of a red blood cell (RBC) in simple shear flow, focusing on the dependence of the cell dynamics on the spontaneous curvature of the membrane. The results show that an oblate spheroidal spontaneous curvature maintains the dimple of the RBC during tank-treading dynamics as well as exhibits off-shear-plane tumbling consistent with the experimental observations of Dupire et al. [J. Dupire, M. Socol, and A. Viallat, Proc. Natl. Acad. Sci. USA 109, 20808 (2012)] and their hypothesis of an inhomogeneous spontaneous shape. As the flow strength (capillary number Ca) is increased at a particular viscosity ratio between inner and outer fluid, the dynamics undergo transitions in the following sequence: tumbling, kayaking or rolling, tilted tank-treading, oscillating-swinging, swinging, and tank-treading. The tilted tank-treading (or spinning frisbee) regime has been previously observed in experiments but not in simulations. Two distinct classes of regime are identified: a membrane reorientation regime, where the part of membrane that is at the dimple at rest moves to the rim and vice versa, is observed in motions at high Ca such as tilted tank-treading, oscillating-swinging, swinging, and tank-treading, and a nonreorientation regime, where the part of the membrane starting from the dimple stays at the dimple, is observed in motions at low Ca such as rolling, tumbling, kayaking, and flip-flopping.

Inertial migrations of cylindrical particles in rectangular microchannels: Variations of equilibrium positions and equivalent diameters

“…Available experimental evidence later reveals that the RBC under rolling motion has a stabilized cell membrane and can maintain its biconcave disk-like shape. [58][59][60] Under physiological conditions, a mature RBC is about 6-8 µm in diameter and 2 µm in thickness. A smooth-edged disk-like particle with L/D = 4:15 is used to model the RBC with 7.5 µm in diameter and 2 µm in thickness.…”

High-throughput microfluidic characterization of erythrocyte shape and mechanical variability

“…The RBC model employs a stress-free shape of the elastic spring network, corresponding to a spheroidal shape with a reduced volume of 0.96, because recent simulation studies (36,39,40) suggest that a nearly spherical stress-free shape best reproduces experimental results for the tumbling-to-tank-treading transition at low viscosity contrasts (41,42). Alternatively, a stress-free condition can also be incorporated into the bending potential through an inhomogeneous spontaneous curvature (43). RBC size is characterized by the effective RBC diameter D r = A r /π, where A r is the RBC membrane area.…”

Effect of Cytoplasmic Viscosity on Red Blood Cell Migration in Small Arteriole-level Confinements

“…More symmetric shapes and tumbling motion are expected to reduce the lift velocity. For instance, at Ca = 0.25, an RBC is in the tumbling regime Sinha and Graham (2015) and therefore the migration is slower, whereas for Ca≥ 0.5, the RBC is in the tank-treading regime and lifts more quickly (Qi and Shaqfeh, 2017;Saadat et al, 2018). Slipper-like and parachute-like shapes for RBCs have been extensively reported in the literature Kaoui et al (2009) ;Quint et al (2017); Fedosov et al (2014); Tomaiuolo et al (2016); Guckenberger et al (2018).…”

“…al clearly revealed existence of more complicated multi-lobe shapes. Remarkably, there is a rich spectrum of shape states and motion that RBCs may undergo depending on the initial condition (Guckenberger et al, 2018), the ratio of convective forces to elastic restoring forces (denoted by the capillary number) (Sinha and Graham, 2015), and also the confinement level of the vessel (Reichel et al, 2018).…”

“…Due to the complexity of blood suspension dynamics, large scale simulation tools are required to understand much of the salient physics. Many approaches have been developed including the boundary integral method (Zhao et al, 2012;Sinha and Graham, 2015;Pozrikidis, 1992), the immersed boundary method coupled with the Lattice Boltzmann method (Shen et al, 2016;Krüger, 2012;Reasor et al, 2013;Závodszky et al, 2017;de Haan et al, 2018), and other immersed boundary approaches coupled to finite volume/difference/element solvers (Ye et al, 2016;Doddi, 2008;Balogh and Bagchi, 2018;Sigüenza et al, 2016;Saadat et al, 2018). The boundary integral method (BEM) has had great success in simulating smaller suspensions of cells, but poor scaling in particle number often reduces the ability to study larger suspensions via BEM.…”