Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session A18: Biofluids: General I - Vesicle Modeling and Simulations |
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Chair: Simon Mendez, Centre national de la recherche scientifique (CNRS) Room: 306/307 |
Sunday, November 24, 2013 8:00AM - 8:13AM |
A18.00001: Three-Dimensional Immersed Interface Method Based Vesicle Simulations Prerna Gera, David Salac Solving the Stokes equations for a multi-phase system with an embedded in-extensible interface is crucial for understanding vesicle dynamics. In this talk the Immersed Interface Method is used to solve the Stokes equations across an in-extensible interface. The full jump conditions for a piecewise constant viscosity have been developed and will be presented. An implicit linear system is created to obtain the velocity, pressure and tension fields. Preconditioning strategies needed to ensure convergence of this linear system will be also be presented. Convergence analysis indicates that the accuracy of the method equals the underlying discritization, despite the presence of discontinuous solution fields. [Preview Abstract] |
Sunday, November 24, 2013 8:13AM - 8:26AM |
A18.00002: Numerical simulations of capsules and red blood cells under flow in complex geometries at non-zero Reynolds numbers Simon Mendez, Etienne Gibaud, Julien Siguenza, Franck Nicoud Numerical simulation of flows of vesicles, capsules and cells is a growing field (Misbah 2012). With the objective of understanding the complex fluid-structure interactions involved in such flows, studying microcirculation and suspension rheology or improving drug vectorization, numerous research groups have developed numerical methods to compute the dynamics of deformable objects like capsules and red blood cells, composed by a drop of liquid enclosed by a membrane. However, the most mature methods rely on boundary integrals, the use of which is allowed by the Stokes flow hypothesis: boundary integral method (BIM) is thus an efficient tool to study microfluidics and microcirculation. In some flows, in particular in some medical devices, the Reynolds number may be high, which precludes the use of the BIM. In this talk, we will show how the immersed boundary method can be implemented in an unstructured finite-volume solver to tackle such flows of deformable objects. The method will be detailed and specific attention will be devoted to the validation of the solver, in particular in 2D, where reference results are scarce. Finally, applications of the method to flows of isolated cells will be shown. Reference: Misbah 2012. J. Phys.: Conf. Series 392 (2012) 012005 [Preview Abstract] |
Sunday, November 24, 2013 8:26AM - 8:39AM |
A18.00003: Phase-Field Modeling of Lipid Vesicles With Pores Saman Seifi, David Salac The formation and annihilation of pores in a lipid vesicle membrane is critical to a number of biotechnologies, such as drug delivery. Previous models of vesicle behavior have ignored the influence of topological changes in the vesicle membrane. Here the entire Helfrich model of a vesicle membrane is considered. Topological changes in the vesicle membrane, such as the formation of a pore, are captured through the use of an embedded phase-field model. The numerical method and sample results will be presented. [Preview Abstract] |
Sunday, November 24, 2013 8:39AM - 8:52AM |
A18.00004: Asymmetric Instability, Symmetric Instability, and Pearling of a Vesicle in Extensional Flow Andrew Spann, Vivek Narsimhan, Eric Shaqfeh A vesicle placed in extensional flow can undergo a transition where the vesicle forms a dumbbell shape connected by a thin long neck. We will examine cases where the vesicle shows either symmetric or asymmetric behavior depending on the flow conditions. We present 3D boundary integral simulations for vesicles in planar and uniaxial extensional flows. For high reduced volumes (at least 0.745 for matched inner/outer viscosity vesicles), a stable steady state shape exists for the vesicle at extensional flows of any capillary number, and furthermore this steady state shape approaches an ellipse as capillary number is increased. For lower reduced volume vesicles the equilibrium shape becomes nonconvex and there exists a critical capillary number above which odd perturbations to the vesicle shape drive an asymmetric elongation transition. For vesicles with reduced volume below ~0.6, a symmetric elongation transition exists where the neck thins continuously and the vesicle has no steady shape above a critical capillary number. At sufficiently high capillary number we can see the formation of pearls along the neck of the elongating vesicle. We demonstrate that the rate at which flow is increased can affect the number and position of pearls in this phenomenon. [Preview Abstract] |
Sunday, November 24, 2013 8:52AM - 9:05AM |
A18.00005: Lateral migration of a 3D elastic capsule in a Poiseuille flow Boyoung Kim, Hyung Jin Sung The lateral migration of a 3D elastic capsule undergoing large deformation in a 3D Poiseuille flow was explored at moderate Reynolds number (10$\le $Re$\le $100) as a function of the initial lateral position (y$_{0})$, Reynolds number (Re), aspect ratio ($\varepsilon )$, viscosity ratio ($\lambda )$, membrane stretching coefficient ($\varphi )$ and bending coefficient ($\gamma )$. Several numerical methods were used to simulate the problem: the immersed boundary method for fluid-structure interaction, the penalty method for volume conservation in the capsule and the front-tracking method for distinguishing the fluid in capsule from the fluid outside capsule. Three different types of capsule motions were observed: tank-treading (TT) motion, tumbling (TU) motion and swinging (SW) motion according to variations of $\varepsilon $ and Re. The initial behavior of the elastic capsule was influenced by the initial lateral position (y$_{0})$, but the equilibrium position and the dynamic motion of the capsule were not affected by such variations. The capsule had a strong tendency toward TU motion at higher values of Re, $\varphi $ and $\gamma $, whereas the capsule underwent TT or SW motion as the values of $\varepsilon $ and $\lambda $ increased. [Preview Abstract] |
Sunday, November 24, 2013 9:05AM - 9:18AM |
A18.00006: The Electrohydrodynamics of Lipid Bilayer Vesicles in AC and DC Fields Lane McConnell, Petia Vlahovska, Michael Miksis Vesicles, which are closed, fluid-filled lipid bilayers, provide an ideal model to study cellular electro and hydrodynamics. Recent experiments and small deformation analysis of vesicles exposed to an electric field have revealed several interesting phenomena, including transitions from oblate to prolate ellipsoidal shapes and poration of the vesicle membrane. Here we use the boundary integral method to numerically investigate the dynamic behavior of a vesicle in various electric field types, including a DC field, an AC field, and a combination of the two. The vesicle membrane is modeled as an infinitely thin, capacitive, area-incompressible interface, with the surrounding fluids presumed to act as leaky dielectrics which allow for charge advection. Vesicle dynamics are determined by balancing the viscous, elastic, and electric stresses on the membrane. We present a comparison of the full nonlinear numerical results with small deformation theory and recent experimental data, then analyze our results in the relevant parameter space and discuss the role of symmetry in the problem. [Preview Abstract] |
Sunday, November 24, 2013 9:18AM - 9:31AM |
A18.00007: Equilibrium electrodeformation of a vesicle in an ac electric field Yuan-Nan Young, Herve Nganguia Under an ac electric field the equilibrium shape of a vesicle (closed liposome) depends on various physical parameters, such as the electric field frequency, mismatch in fluid conductivities and permittivities. In this work we use a spheroidal model to investigate these dependences. We derive the transmembrane potential for a leaky dielectric spheroidal shell and compute the equilibrium spheroidal shape. When compared with experiments and previous small-deformation analysis, we found that the spheroidal model agrees better with the experiments. In particular the spheroidal model allows for asymptotic analysis on the cross-over frequency between prolate and oblate vesicles, and the comparison with experiments near the cross-over shows that the spheroidal model captures the prolate-oblate transition better than the small-deformation theory. [Preview Abstract] |
Sunday, November 24, 2013 9:31AM - 9:44AM |
A18.00008: Electrohydrodynamics of Three-Dimensional Vesicles Ebrahim Kolahdouz, David Salac A new numerical method is presented to model the dynamic behavior of three-dimensional vesicles in the Stokes regime and in the presence of electric fields. The interface is described using the Jet Level Set method of Nave et. al, while a multi-step projection method is used to simultaneously enforce fluid and interface conditions. The electric field is obtained through a second-order Immersed Interface Method, for which the necessary jump conditions have been developed. The fluid equations are solved for using a Continuum Surface Force method. The formulation and a parallel implementation will be presented, in addition to sample results. [Preview Abstract] |
Sunday, November 24, 2013 9:44AM - 9:57AM |
A18.00009: Deformation of biomimetic membranes under electroporation using DC electric pulses Paul Salipante, Petia Vlahovska Electrohydrodynamics of vesicles (closed bilayer membranes) made of lipids or polymers are investigated under strong DC pulses. When a uniform electric field is applied across a membrane, free charges accumulate on both sides of the membrane and the membrane acts as a capacitor. While the membrane is charging, the vesicle deforms into either an oblate or prolate ellipsoid depending on the bulk fluids conductivities. However, once the membrane is fully charged the vesicle adopts a prolate shape. In strong DC pulses, typically used in cell electroporation, the electric stress can induce pores in both lipid and polymer membranes. The instability short-circuits the membrane capacitor, leading to non-ellipsoidal shape and vesicle collapse. The evolution of vesicle shape and the effect of poration is experimentally studied for DC pulses of different strength and duration. Vesicle shape is related to the critical threshold for membrane poration. Membrane composition is varied to observe the effect of membrane viscosity, membrane capacitance, and poration threshold. The transient response of the vesicle, in particular vesicle collapse, is shown to be sensitive to membrane viscosity. [Preview Abstract] |
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