Buckling of a pre-compressed or pre-stretched membrane in shear flow

Luo, H. L.; Pozrikidis, C.

doi:10.1016/j.ijsolstr.2007.05.027

Cited by 14 publications

(13 citation statements)

References 9 publications

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“…Since the bending modulus of the membrane has been neglected, the capsule wall should be under tension everywhere; otherwise it may buckle locally in the regions where the elastic tensions are compressive. This phenomenon is well known for thin elastic sheets, see for example Cerda & Mahadevan (2003) and Luo & Pozrikidis (2007). In that case, a full shell model including bending moments and transverse shear forces would be necessary to describe properly the mechanics of the capsule wall.…”

Section: Membrane Mechanicsmentioning

confidence: 97%

Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes

2011

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The large deformations of an initially-ellipsoidal capsule in a simple shear flow are studied by coupling a boundary integral method for the internal and external flows and a finite-element method for the capsule wall motion. Oblate and prolate spheroids are considered (initial aspect ratios: 0.5 and 2) in the case where the internal and external fluids have the same viscosity and the revolution axis of the initial spheroid lies in the shear plane. The influence of the membrane mechanical properties (mechanical law and ratio of shear to area dilatation moduli) on the capsule behaviour is investigated. Two regimes are found depending on the value of a capillary number comparing viscous and elastic forces. At low capillary numbers, the capsule tumbles, behaving mostly like a solid particle. At higher capillary numbers, the capsule has a fluid-like behaviour and oscillates in the shear flow while its membrane continuously rotates around its deformed shape. During the tumbling-to-swinging transition, the capsule transits through an almost circular profile in the shear plane for which a long axis can no longer be defined. The critical transition capillary number is found to depend mainly on the initial shape of the capsule and on its shear modulus, and weakly on the area dilatation modulus. Qualitatively, oblate and prolate capsules are found to behave similarly, particularly at large capillary numbers when the influence of the initial state fades out. However, the capillary number at which the transition occurs is significantly lower for oblate spheroids.

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Section: Membrane Mechanicsmentioning

confidence: 97%

Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes

2011

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“…Since the bending modulus of the membrane has been neglected, the capsule wall buckles locally in the regions where the elastic tensions are compressive (see, for example, Cerda & Mahadevan 2003, Luo & Pozrikidis 2007and Finken & Seifert 2006. In order to study the post-buckling behaviour of the capsule, bending moments and transverse shear forces must be added to (2.9) and a constitutive equation must be postulated to relate bending moments and local deformations.…”

Section: Capsule Membrane Mechanicsmentioning

confidence: 99%

Flow of a spherical capsule in a pore with circular or square cross-section

Salsac

Barthès-Biesel

2011

J. Fluid Mech.

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The motion and deformation of a spherical elastic capsule freely flowing in a pore of comparable dimension is studied. The thin capsule membrane has a neo-Hookean shear softening constitutive law. The three-dimensional fluid–structure interactions are modelled by coupling a boundary integral method (for the internal and external fluid motion) with a finite element method (for the membrane deformation). In a cylindrical tube with a circular cross-section, the confinement effect of the channel walls leads to compression of the capsule in the hoop direction. The membrane then tends to buckle and to fold as observed experimentally. The capsule deformation is three-dimensional but can be fairly well approximated by an axisymmetric model that ignores the folds. In a microfluidic pore with a square cross-section, the capsule deformation is fully three-dimensional. For the same size ratio and flow rate, a capsule is more deformed in a circular than in a square cross-section pore. We provide new graphs of the deformation parameters and capsule velocity as a function of flow strength and size ratio in a square section pore. We show how these graphs can be used to analyse experimental data on the deformation of artificial capsules in such channels.

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“…However, in certain situations it can become the dominating factor. For instance, it defines the wavelength of local wrinkles appearing for capsules especially at low shear rates due to local compressive forces [3,51,[57][58][59][60][61]. Neglecting the bending rigidity in this case reduces not only the numerical stability but also the physical reliance greatly, making realistic simulations practically impossible [3,28,51,59,62].…”

Section: Introductionmentioning

confidence: 99%

On the bending algorithms for soft objects in flows

Guckenberger

Schraml

Chen

et al. 2016

Computer Physics Communications

112

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International audienceOne of the most challenging aspects in the accurate simulation of three-dimensional soft objects such as vesicles or biological cells is the computation of membrane bending forces. The origin of this difficulty stems from the need to numerically evaluate a fourth order derivative on the discretized surface geometry. Here we investigate six different algorithms to compute membrane bending forces, including regularly used methods as well as novel ones. All are based on the same physical model (due to Canham and Helfrich) and start from a surface discretization with flat triangles. At the same time, they differ substantially in their numerical approach. We start by comparing the numerically obtained mean curvature, the Laplace-Beltrami operator of the mean curvature and finally the surface force density to analytical results for the discocyte resting shape of a red blood cell. We find that none of the considered algorithms converges to zero error at all nodes and that for some algorithms the error even diverges. There is furthermore a pronounced influence of the mesh structure: Discretizations with more irregular triangles and node connectivity present serious difficulties for most investigated methods. To assess the behavior of the algorithms in a realistic physical application, we investigate the deformation of an initially spherical capsule in a linear shear flow at small Reynolds numbers. To exclude any influence of the flow solver, two conceptually very different solvers are employed: the Lattice-Boltzmann and the Boundary Integral Method. Despite the largely different quality of the bending algorithms when applied to the static red blood cell, we find that in the actual flow situation most algorithms give consistent results for both hydrodynamic solvers. Even so, a short review of earlier works reveals a wide scattering of reported results for, e.g., the Taylor deformation parameter. Besides the presented application to biofluidic systems, the investigated algorithms are also of high relevance to the computer graphics and numerical mathematics communities

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Buckling of a pre-compressed or pre-stretched membrane in shear flow

Cited by 14 publications

References 9 publications

Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes

Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes

Flow of a spherical capsule in a pore with circular or square cross-section

On the bending algorithms for soft objects in flows

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