6 results
Assessment of coupled bilayer–cytoskeleton modelling strategy for red blood cell dynamics in flow
- V. Puthumana, P.G. Chen, M. Leonetti, R. Lasserre, M. Jaeger
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- Journal:
- Journal of Fluid Mechanics / Volume 979 / 25 January 2024
- Published online by Cambridge University Press:
- 22 January 2024, A44
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The red blood cell (RBC) membrane is composed of a lipid bilayer and a cytoskeleton interconnected by protein junction complexes, allowing for potential sliding between the lipid bilayer and the cytoskeleton. Despite this biological reality, it is most often modelled as a single-layer model, a hyperelastic capsule or a fluid vesicle. Another approach involves incorporating the membrane's composite structure using double layers, where one layer represents the lipid bilayer and the other represents the cytoskeleton. In this paper, we computationally assess the various modelling strategies by analysing RBC behaviour in extensional flow and four distinct regimes that simulate RBC dynamics in shear flow. The proposed double-layer strategies, such as the vesicle–capsule and capsule–capsule models, account for the fluidity and surface incompressibility of the lipid bilayer in different ways. Our findings demonstrate that introducing sliding between the layers offers the cytoskeleton a considerable degree of freedom to alleviate its elastic stresses, resulting in a significant increase in RBC elongation. Surprisingly, our study reveals that the membrane modelling strategy for RBCs holds greater importance than the choice of the cytoskeleton's reference shape. These results highlight the inadequacy of considering mechanical properties alone and emphasise the need for careful integration of these properties. Furthermore, our findings fortuitously uncover a novel indicator for determining the appropriate stress-free shape of the cytoskeleton.
Influence of surface viscosity on droplets in shear flow
- J. Gounley, G. Boedec, M. Jaeger, M. Leonetti
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- Journal:
- Journal of Fluid Mechanics / Volume 791 / 25 March 2016
- Published online by Cambridge University Press:
- 22 February 2016, pp. 464-494
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The behaviour of a single droplet in an immiscible external fluid, submitted to shear flow is investigated using numerical simulations. The surface of the droplet is modelled by a Boussinesq–Scriven constitutive law involving the interfacial viscosities and a constant surface tension. A numerical method using Loop subdivision surfaces to represent droplet interface is introduced. This method couples boundary element method for fluid flows and finite element method to take into account the stresses due to the surface dilational and shear viscosities and surface tension. Validation of the numerical scheme with respect to previous analytic and computational work is provided, with particular attention to the viscosity contrast and the shear and dilational viscosities characterized both by a Boussinesq number $B_{q}$. Then, influence of equal surface viscosities on steady-state characteristics of a droplet in shear flow are studied, considering both small and large deformations and for a large range of bulk viscosity contrast. We find that small deformation analysis is surprisingly predictive at moderate and high surface viscosities. Equal surface viscosities decrease the Taylor deformation parameter and tank-treading angle and also strongly modify the dynamics of the droplet: when the Boussinesq number (surface viscosity) is large relative to the capillary number (surface tension), the droplet displays damped oscillations prior to steady-state tank-treading, reminiscent from the behaviour at large viscosity contrast. In the limit of infinite capillary number $Ca$, such oscillations are permanent. The influence of surface viscosities on breakup is also investigated, and results show that the critical capillary number is increased. A diagram $(B_{q};Ca)$ of breakup is established with the same inner and outer bulk viscosities. Additionally, the separate roles of shear and dilational surface viscosity are also elucidated, extending results from small deformation analysis. Indeed, shear (dilational) surface viscosity increases (decreases) the stability of drops to breakup under shear flow. The steady-state deformation (Taylor parameter) varies nonlinearly with each Boussinesq number or a linear combination of both Boussinesq numbers. Finally, the study shows that for certain combinations of shear and dilational viscosities, drop deformation for a given capillary number is the same as in the case of a clean surface while the inclination angle varies.
Tank-treading of microcapsules in shear flow
- C. de Loubens, J. Deschamps, F. Edwards-Levy, M. Leonetti
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- Journal:
- Journal of Fluid Mechanics / Volume 789 / 25 February 2016
- Published online by Cambridge University Press:
- 26 January 2016, pp. 750-767
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We investigated experimentally the deformation of soft microcapsules and the dynamics of their membrane in simple shear flows. Firstly, the tank-treading motion, i.e. the rotation of the membrane, was visualized and quantified by tracking particles included in the membrane by a new protocol. The period of membrane rotation increased quadratically with the extension of the long axis. The tracking of the distance between two close microparticles showed membrane contraction at the tips and stretching on the sides, a specific property of soft particles such as capsules. The present experimental results are discussed in regard to previous numerical simulations. This analysis showed that the variation of the tank-treading period with the Taylor parameter (deformation) cannot be explained by purely elastic membrane models. It suggests a strong effect of membrane viscosity whose order of magnitude is determined. Secondly, two distinct shapes of sheared microcapsules were observed. For moderate deformations, the shape was a steady ellipsoid in the shear plane. For larger deformations, the capsule became asymmetric and presented an S-like shape. When the viscous shear stress increased by three orders of magnitude, the short axis decreased by 70 % whereas the long axis increased by 100 % before any break-up. The inclination angle decreased from 40° to 8°, almost aligned with the flow direction as expected by theory and numerics on capsules and from experiments, theory and numerics on drops and vesicles. Whatever the microcapsule size and the concentration of proteins, the characteristic lengths of the shape, the Taylor parameter and the inclination angle satisfy master curves versus the long axis or the normalized shear stress or the capillary number in agreement with theory for non-negligible membrane viscosity in the regime of moderate deformations. Finally, we observed that very small deviation from sphericity gave rise to swinging motion, i.e. shape oscillations, in the small-deformation regime. In conclusion, this study of tank-treading motion supports the role of membrane viscosity on the dynamics of microcapsules in shear flow by independent methods that compare experimental data both with numerical results in the regime of large deformations and with theory in the regime of moderate deformations.
Stretching of capsules in an elongation flow, a route to constitutive law
- C. de Loubens, J. Deschamps, G. Boedec, M. Leonetti
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- Journal:
- Journal of Fluid Mechanics / Volume 767 / 25 March 2015
- Published online by Cambridge University Press:
- 20 February 2015, R3
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Soft bio-microcapsules are drops bounded by a thin elastic shell made of cross-linked proteins. Their shapes and their dynamics in flow depend on their membrane constitutive law characterized by shearing and area-dilatation resistance. The deformations of such capsules are investigated experimentally in planar elongation flows and compared with numerical simulations for three bidimensional models: Skalak, neo-Hookean and generalized Hooke. An original cross-flow microfluidic set-up allows the visualization of the deformed shape in the two perpendicular main fields of view. Whatever the elongation rate, the three semi-axis lengths of the ellipsoid fitting the experimental shape are measured up to 180 % of stretching of the largest axis. The geometrical analysis in the two views is sufficient to determine the constitutive law and the Poisson ratio of the membrane without a preliminary knowledge of the shear elastic modulus $G_{s}$. We conclude that the membrane of human serum albumin capsules obeys the generalized Hooke law with a Poisson ratio of 0.4. The shear elastic modulus is then determined by the combination of numerical and experimental variations of the Taylor parameter with the capillary number.
Pearling instability of a cylindrical vesicle
- G. Boedec, M. Jaeger, M. Leonetti
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- Journal:
- Journal of Fluid Mechanics / Volume 743 / 25 March 2014
- Published online by Cambridge University Press:
- 04 March 2014, pp. 262-279
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A cylindrical vesicle under tension can undergo a pearling instability, characterized by the growth of a sinusoidal perturbation which evolves towards a collection of quasi-spherical bulbs connected by thin tethers, like pearls on a necklace. This is reminiscent of the well-known Rayleigh–Plateau instability, where surface tension drives the amplification of sinusoidal perturbations of a cylinder of fluid. We calculate the growth rate of perturbations for a cylindrical vesicle under tension, considering the effect of both inner and outer fluids, with different viscosities. We show that this situation differs strongly from the classical Rayleigh–Plateau case in the sense that, first, the tension must be above a critical value for the instability to develop and, second, even in the strong tension limit, the surface preservation constraint imposed by the presence of the membrane leads to a different asymptotic behaviour. The results differ from previous studies on pearling due to the consideration of variations of tension, which are shown to enhance the pearling instability growth rate, and lower the wavenumber of the fastest growing mode.
Settling of a vesicle in the limit of quasispherical shapes
- G. Boedec, M. Jaeger, M. Leonetti
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- Journal:
- Journal of Fluid Mechanics / Volume 690 / 10 January 2012
- Published online by Cambridge University Press:
- 20 December 2011, pp. 227-261
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Vesicles are drops of radius of a few tens of micrometres bounded by an impermeable lipid membrane of approximately 4 nm thickness in a viscous fluid. The salient characteristics of such a deformable object are a membrane rigidity governed by flexion due to curvature energy and a two-dimensional membrane fluidity characterized by a local membrane incompressibility. This provides unique properties with strong constraints on the internal volume and membrane area. Yet, when subjected to external stresses, vesicles exhibit a large deformability. The deformation of a settling vesicle in an infinite flow is studied theoretically, assuming a quasispherical shape and expanding all variables of the problem onto spherical harmonics. The contribution of thermal fluctuations is neglected in this analysis. A system of equations describing the temporal evolution of the shape is derived with this formalism. The final shape and the settling velocity are then determined and depend on two dimensionless parameters: the Bond number and the excess area. This simultaneous study leads to three stationary shapes, an egg-like shape already observed in an analogous experimental configuration in the limit of weak flow magnitude (Chatkaew, Georgelin, Jaeger & Leonetti, Phys. Rev. Lett, 2009, vol. 103(24), 248103), a parachute-like shape and a non-trivial non-axisymmetrical shape. The final shape depends on the initial conditions: prolate or oblate vesicle and orientation compared with gravity. The analytical solution in the small deformation regime is compared with numerical results obtained with a three-dimensional code. A very good agreement between numerical and theoretical results is found.