Deformation and rupture of lipid vesicles in the strong shear flow generated by ultrasound-driven microbubbles

2008 ◽  
Vol 464 (2095) ◽  
pp. 1781-1800 ◽  
Author(s):  
Philippe Marmottant ◽  
Thierry Biben ◽  
Sascha Hilgenfeldt
Keyword(s):  
Shear Flow ◽  
Acoustic Streaming ◽  
Three Dimensional ◽  
Spherical Shape ◽  
Lipid Vesicles ◽  
Boundary Integral ◽  
Elastic Response ◽  
Lipid Vesicle ◽  
Strong Shear ◽  
Vesicle Rupture

Considering the elastic response of the membrane of a lipid vesicle (artificial cell) in an arbitrary three-dimensional shear flow, we derive analytical predictions of vesicle shape and membrane tension for vesicles close to a spherical shape. Large amplitude deviations from sphericity are described using boundary integral numerical simulations. Two possible modes of vesicle rupture are found and compared favourably with experiments: (i) for large enough shear rates the tension locally exceeds a rupture threshold and a pore opens at the waist of the vesicle and (ii) for large elongations the local tension becomes negative, leading to buckling and tip formation near a pole of the vesicle. We experimentally check these predictions in the case of strong acoustic streaming flow generated near ultrasound-driven microbubbles, such as those used in medical applications.

The dynamics of a vesicle in simple shear flow

2011 ◽  
Vol 674 ◽  
pp. 578-604 ◽  
Author(s):  
HONG ZHAO ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Lipid Membrane ◽  
Shear Plane ◽  
Plane Motion ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Lipid Vesicle ◽  
Simple Shear Flow ◽  
Motion Patterns

We have performed direct numerical simulation (DNS) of a lipid vesicle under Stokes flow conditions in simple shear flow. The lipid membrane is modelled as a two-dimensional incompressible fluid with Helfrich surface energy in response to bending deformation. A high-fidelity spectral boundary integral method is used to solve the flow and membrane interaction system; the spectral resolution and convergence of the numerical scheme are demonstrated. The critical viscosity ratios for the transition from tank-treading (TT) to ‘trembling’ (TR, also called VB, i.e. vacillating-breathing, or swinging) and eventually ‘tumbling’ (TU) motions are calculated by linear stability analysis based on this spectral method, and are in good agreement with perturbation theories. The effective shear rheology of a dilute suspension of these vesicles is also calculated over a wide parameter regime. Finally, our DNS reveals a family of time-periodic and off-the-shear-plane motion patterns where the vesicle's configuration follows orbits that resemble but are fundamentally different from the classical Jeffery orbits of rigid particles due to the vesicle's deformability.

Off-plane motion of a prolate capsule in shear flow

2013 ◽  
Vol 721 ◽  
pp. 180-198 ◽  
Author(s):  
C. Dupont ◽  
A.-V. Salsac ◽  
D. Barthès-Biesel
Keyword(s):  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Shear Plane ◽  
Plane Motion ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Simple Shear Flow ◽  
Flow Vorticity ◽  
Wall Deformation

AbstractThe 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.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

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