Influence of membrane viscosity on capsule dynamics in shear flow

AbstractMost previous numerical studies on capsule dynamics in shear flow have ignored the role of membrane viscosity. Here we present a numerical method for large deformation of capsules using a Kelvin–Voigt viscoelastic model for the membrane. After introducing the model and the related numerical implementation, we present a comprehensive analysis of the influence of the membrane viscosity on buckling, deformation and dynamics. We observe that the membrane viscosity leads to buckling in the range of shear rate in which no buckling is observed for capsules with purely elastic membrane. For moderate to large shear rates, the wrinkles on the capsule surface appear in the same range of the membrane viscosity that was reported earlier for artificial capsules and red blood cells based on experimental measurements. In order to obtain stable shapes, it is necessary to introduce the bending stiffness. It is observed that the range of the bending stiffness required is also in the same range as that reported for the red blood cells, but considerably higher than that estimated for artificial capsules. Using the stable shapes obtained in the presence of bending stiffness, we analyse the influence of membrane viscosity on deformation, inclination and tank-treading frequency of initially spherical capsules. Membrane viscosity is observed to reduce the capsule deformation, and introduce a damped oscillation in time-dependent deformation and inclination. The time-averaged inclination angle shows a non-monotonic trend with an initial decrease reaching a minimum and a subsequent increase with increasing membrane viscosity. A similar non-monotonic trend is also observed in the tank-treading frequency. We then consider the influence of the membrane viscosity on the unsteady dynamics of an initially oblate capsule. The dynamics is observed to change from a swinging motion to a tumbling motion with increasing membrane viscosity. Further, a transient dynamics is also observed in which a capsule starts with one type of dynamics, but settles with a different dynamics over a long time.

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Red Blood Cells and Other Nonspherical Capsules in Shear Flow: Oscillatory Dynamics and the Tank-Treading-to-Tumbling Transition

Physical Review Letters ◽

10.1103/physrevlett.98.078301 ◽

2007 ◽

Vol 98 (7) ◽

Cited By ~ 188

Author(s):

J. M. Skotheim ◽

T. W. Secomb

Keyword(s):

Shear Flow ◽

Red Blood Cells ◽

Blood Cells ◽

Oscillatory Dynamics

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Blood Crystal: Emergent Order of Red Blood Cells Under Wall-Confined Shear Flow

Physical Review Letters ◽

10.1103/physrevlett.120.268102 ◽

2018 ◽

Vol 120 (26) ◽

Cited By ~ 7

Author(s):

Zaiyi Shen ◽

Thomas M. Fischer ◽

Alexander Farutin ◽

Petia M. Vlahovska ◽

Jens Harting ◽

...

Keyword(s):

Shear Flow ◽

Red Blood Cells ◽

Blood Cells ◽

Emergent Order

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Threshold shear stress for the transition between tumbling and tank-treading of red blood cells in shear flow: dependence on the viscosity of the suspending medium

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.496 ◽

2013 ◽

Vol 736 ◽

pp. 351-365 ◽

Cited By ~ 20

Author(s):

Thomas M. Fischer ◽

Rafal Korzeniewski

Keyword(s):

Shear Flow ◽

Red Blood Cells ◽

Blood Cells ◽

Theoretical Models ◽

Red Cells ◽

Theoretical Modelling ◽

Glass Capillary ◽

Basic Model ◽

A Value ◽

The Subject

AbstractRed blood cells are the subject of diverse studies. One branch is the observation and theoretical modelling of their behaviour in a shear flow. This work deals with the flow of single red cells suspended in solutions much more viscous than blood plasma. Below a critical shear rate (${\dot {\gamma } }_{t} $) the red cells rotate with little change of their resting shape. Above that value they become elongated and aligned in the shear field. We measured${\dot {\gamma } }_{t} $at viscosities (${\eta }_{0} $) ranging from 10.7 to 104 mPa s via observation along the vorticity of a Poiseuille flow in a glass capillary;${\eta }_{0} {\dot {\gamma } }_{t} $decreased steeply with increasing${\eta }_{0} $up to a value of 25 mPa s and remained constant for higher values. Present theoretical models are not in keeping with the measured data. Modifications of basic model assumptions are suggested.

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The steady motion of a closely fitting vesicle in a tube

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.743 ◽

2017 ◽

Vol 835 ◽

pp. 721-761 ◽

Cited By ~ 9

Author(s):

Joseph M. Barakat ◽

Eric S. G. Shaqfeh

Keyword(s):

Red Blood Cells ◽

Blood Cells ◽

Steady Motion ◽

Bending Stiffness ◽

Singular Perturbation Theory ◽

Bending Elasticity ◽

Theoretical Predictions ◽

Bending Stresses ◽

Membrane Bending ◽

Lipid Bilayer Vesicle

A singular perturbation theory is developed for the steady, inertialess motion of a lipid-bilayer vesicle flowing through a narrow tube. The vesicle is treated as a sac of fluid enclosed by an inextensible membrane that admits a bending stiffness. Matched asymptotic expansions are developed in terms of a clearance parameter $\unicode[STIX]{x1D716}\ll 1$ in order to calculate the flow field and vesicle shape. Mild restrictions are applied to the ratio of viscosities $\unicode[STIX]{x1D705}$ and the ratio of bending stresses to viscous stresses $\unicode[STIX]{x1D6FD}$; in particular, the theory holds for $\unicode[STIX]{x1D705}=o(\unicode[STIX]{x1D716}^{-1/2})$ and $\unicode[STIX]{x1D6FD}=O(\unicode[STIX]{x1D716}^{-1})$. The ratio of the vesicle length to the tube radius $\ell$ is included as a parameter and asymptotic solutions in the limit of negligible bending stiffness are developed for long, cylindrical vesicles and short, spherical vesicles. The main result of the theory is a prediction for the vesicle speed and extra pressure drop due to the presence of the vesicle in the tube. The effects of confinement, vesicle length, and membrane bending elasticity are examined. The theoretical predictions show good agreement with experimental measurements reported for vesicles and red blood cells in highly confined channel flow. Previously reported models for red blood cells (Secomb et al., J. Fluid Mech., vol. 163, 1986, pp. 405–423; Halpern & Secomb, J. Fluid Mech., vol. 203, 1989, pp. 381–400) are clarified and extended in light of the new theory.

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Role of membrane viscosity in the orientation and deformation of a spherical capsule suspended in shear flow

Journal of Fluid Mechanics ◽

10.1017/s002211208500341x ◽

1985 ◽

Vol 160 ◽

pp. 119-135 ◽

Cited By ~ 96

Author(s):

D. Barthes-Biesel ◽

H. Sgaier

Keyword(s):

Relaxation Time ◽

Shear Flow ◽

Red Blood Cells ◽

Blood Cells ◽

Liquid Droplets ◽

Regular Perturbation ◽

Shear Rates ◽

Freely Suspended ◽

Spherical Capsule

Red blood cells or artificial vesicles may be conveniently represented by capsules, i.e. liquid droplets surrounded by deformable membranes. The aim of this paper is to assess the importance of viscoelastic properties of the membrane on the motion of a capsule freely suspended in a viscous liquid subjected to shear flow. A regular perturbation solution of the general problem is obtained when the particle is initially spherical and undergoing small deformations. With a purely viscous membrane (infinite relaxation time) the capsule deforms into an ellipsoid and has a continuous flipping motion. When the membrane relaxation time is of the same order as the shear time, the particle reaches a steady ellipsoidal shape which is oriented with respect to streamlines at an angle that varies between 45° and 0°, and decreases with increasing shear rates. Furthermore it is predicted that the deformation reaches a maximum value, which is consistent with experimental observations of red blood cells.

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Dynamics of Individual Red Blood Cells Under Shear Flow: A Way to Discriminate Deformability Alterations

Frontiers in Physiology ◽

10.3389/fphys.2021.775584 ◽

2022 ◽

Vol 12 ◽

Author(s):

Scott Atwell ◽

Catherine Badens ◽

Anne Charrier ◽

Emmanuèle Helfer ◽

Annie Viallat

Keyword(s):

Shear Stress ◽

Shear Flow ◽

Red Blood Cells ◽

Sickle Cell ◽

Blood Cells ◽

Center Of Mass ◽

Shear Plane ◽

Shear Stresses ◽

Cell Axis ◽

Lower Shear

In this work, we compared the dynamics of motion in a linear shear flow of individual red blood cells (RBCs) from healthy and pathological donors (Sickle Cell Disease (SCD) or Sickle Cell-β-thalassemia) and of low and high densities, in a suspending medium of higher viscosity. In these conditions, at lower shear rates, biconcave discocyte-shaped RBCs present an unsteady flip-flopping motion, where the cell axis of symmetry rotates in the shear plane, rocking to and fro between an orbital angle ±ϕ observed when the cell is on its edge. We show that the evolution of ϕ depends solely on RBC density for healthy RBCs, with denser RBCs displaying lower ϕ values than the lighter ones. Typically, at a shear stress of 0.08 Pa, ϕ has values of 82 and 72° for RBCs with average densities of 1.097 and 1.115, respectively. Surprisingly, we show that SCD RBCs display the same ϕ-evolution as healthy RBCs of same density, showing that the flip-flopping behavior is unaffected by the SCD pathology. When the shear stress is increased further (above 0.1 Pa), healthy RBCs start going through a transition to a fluid-like motion, called tank-treading, where the RBC has a quasi-constant orientation relatively to the flow and the membrane rotates around the center of mass of the cell. This transition occurs at higher shear stresses (above 0.2 Pa) for denser cells. This shift toward higher stresses is even more remarkable in the case of SCD RBCs, showing that the transition to the tank-treading regime is highly dependent on the SCD pathology. Indeed, at a shear stress of 0.2 Pa, for RBCs with a density of 1.097, 100% of healthy RBCs have transited to the tank-treading regime vs. less than 50% SCD RBCs. We correlate the observed differences in dynamics to the alterations of RBC mechanical properties with regard to density and SCD pathology reported in the literature. Our results suggest that it might be possible to develop simple non-invasive assays for diagnosis purpose based on the RBC motion in shear flow and relying on this millifluidic approach.

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Dynamics of a large population of red blood cells under shear flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.42 ◽

2019 ◽

Vol 864 ◽

pp. 408-448 ◽

Cited By ~ 8

Author(s):

C. Minetti ◽

V. Audemar ◽

T. Podgorski ◽

G. Coupier

Keyword(s):

Flow Stress ◽

Shear Flow ◽

Red Blood Cells ◽

Blood Cells ◽

Rate Increase ◽

Large Population ◽

Experimental Studies ◽

Hysteresis Loops ◽

Fluid Viscosity ◽

Characteristic Parameters

An exhaustive description of the dynamics under shear flow of a large number of red blood cells in a dilute regime is proposed, which highlights and takes into account the dispersion in cell properties within a given blood sample. Physiological suspending fluid viscosity is considered, a configuration surprisingly seldom considered in experimental studies, as well as a more viscous fluid that is a reference in the literature. Stable and unstable flipping motions well described by Jeffery orbits or modified Jeffery orbits are identified, as well as transitions to and from tank-treading motion in the more viscous suspending fluid case. Hysteresis loops upon shear rate increase or decrease are highlighted for the transitions between unstable and stable orbits as well as for the transition between flipping and tank-treading. We identify which of the characteristic parameters of motion and of the transition thresholds depend on flow stress only or also on suspending fluid viscosity.

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