Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session BJ: Bio-Fluids: Cell/Vesicle Dynamics II |
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Chair: Juan C. Lasheras, University of California, San Diego Room: 102A |
Sunday, November 23, 2008 10:30AM - 10:43AM |
BJ.00001: Complex Dynamics of Vesicles and Red Blood Cells in Viscous Flows Petia M. Vlahovska, Gerrit Danker, Chaouqi Misbah Closed incompressible membranes exhibit rich behavior in viscous flows. For example, in simple shear flow, vesicles made of lipid bilayers tank-tread, tumble, or breath. Red blood cells also show oscillations in the tank-treading inclination angle. We develop an analytical theory that quantitatively describes this dynamics. Our analysis takes into account that the membrane is deformable, incompressible, and resists bending and shearing. Analytical results for the shape evolution are derived by considering small excess area. In shear flows, the theory predicts that a nearly-spherical closed membrane deforms into a prolate ellipsoid, which tumbles at low shear rates, and exhibits tank-treading accompanied by oscillations in the inclination angle in higher shear rates. The amplitude of the angle oscillations decreases with shear rate. If the viscosity ratio is too high, however, tank-treading never occurs. A comparison to previous work is discussed, namely some approximate models which assume fixed ellipsoidal shape. In quadratic flows, the theory predicts a peculiar coexistence of parachute- and bullet-like vesicle shapes at the flow centerline. Vesicles always migrate towards the flow centerline unlike drops, whose direction of migration depends on the viscosity ratio. [Preview Abstract] |
Sunday, November 23, 2008 10:43AM - 10:56AM |
BJ.00002: Dynamics of Lipid Bilayer Vesicles in Viscous Flows Jonathan Schwalbe, Petia Vlahovska, Michael J. Miksis An analytical theory is developed to describe the dynamics of a closed lipid bilayer membrane (vesicle) in a general linear viscous flow. The dynamics of the membrane is governed by the Stokes equations in the fluid plus the normal and tangential stress condition along the bilayer interface. The effects of the membrane fluidity, incompressibility and resistance to bending are taken into account. The model is a generalization of the work on planar membranes by Seifert and Langer (Europhys. Lett. vol. 23, 71, 1993), which accounted for the variations in lipid density along both leaflets of the bilayer. Considering a nearly spherical vesicle, a perturbation solution is derived. The leading order analysis results in a nonlinear coupled system of equations for the dynamics of the shape and the mean lipid density difference between the inner and outer monolayer. Multiple solution states are found as a function of viscosity ratio and the monolayer slip coefficient. The dynamics and stability of these solutions is discussed. Comparisons are made to previous works based on the minimal curvature model which did not consider variable lipid density. [Preview Abstract] |
Sunday, November 23, 2008 10:56AM - 11:09AM |
BJ.00003: Shape oscillation and transition from tank-treading to tumbling of a nonspherical capsule in shear flow R.M. Kalluri, Prosenjit Bagchi Dynamics of a nonspherical capsule in shear flow is studied using a front-tracking method. The capsule is modeled as a liquid drop enclosed by a thin hyperelastic membrane following (i) the strain-softening neo-Hookean law, and (ii) the strain- hardening Skalak law. The undeformed shape of the capsule is an oblate spheroid with aspect ratio $\alpha$ (ratio of the minor- to-major axis) varying from 1 to 0.6. The viscosity ratio $\lambda$ of the interior to exterior liquid varies from 1 to 20. Unlike for an initially spherical capsule, the Taylor deformation parameter $D$ and the orientation of the nonspherical capsule oscillate in time. We present phase diagrams in terms of dimensionless shear rate (Capillary number, $Ca$), viscosity ratio $\lambda$ and the aspect ratio $\alpha$ to describe regimes of various modes of capsule orientation dynamics. At $\lambda \approx 1$, a swinging mode is observed in which the orientation oscillates about a mean value. At higher $\lambda$, a breathing mode is observed in which the fails to make a complete rotation, and $D$ changes significantly over one cycle. When $\lambda$ is further increased, the full tumbling motion is established. Numerical results are compared with the theory of Keller and Skalak, JFM (1982), vol. 120, and Skotheim and Secomb, PRL (2007), vol. 98. [Preview Abstract] |
Sunday, November 23, 2008 11:09AM - 11:22AM |
BJ.00004: A particle-based model for cell mechanics S. Majid Hosseini, James J. Feng We present a particle-based model for red blood cells (RBCs) using the concept of smoothed particle hydrodynamics. The discrete nature of the model allows us to go beyond the continuum framework to probe changes in mechanical properties of cells as a function of its internal microstructural components. The RBC cytoplasm and the blood plasma are treated as Newtonian liquids, for which the Navier-Stokes equations are discretized by smoothed particles. The cell membrane incorporates two sets of elastic springs, one for stretching and the other for bending. Areal incompressibility is approximated by making the stretching springs follow the Skalak law. To test the mechanical behavior of such a particle-spring ``cell,'' we compute RBC motion and deformation in a capillary. 2D results are in very good agreement with previous numerical and experimental studies. [Preview Abstract] |
Sunday, November 23, 2008 11:22AM - 11:35AM |
BJ.00005: Simulation of cellular interactions in the microcirculation Hong Zhao, Amir H.G. Isfahani, Jonathan B. Freund The flow dynamics of the microcirculation is dominated by multi-body cell interactions. We present a simulation technique based on the Stokes-flow boundary integrations for solving such systems of interacting cells. The cell structures are modeled as elastic membranes with finite bending modulus that enclose a more viscous hemoglobin solution relative to plasma. The surface is mapped from a sphere, upon which variables are discretized through truncated spherical harmonic series. This spectral representation is highly accurate, has uniform error distribution over the cell surface, and facilitates stabilization through dealiasing without affecting the resolved features of the cells with unphysical dissipation. The algorithm evaluates the boundary integrals with an overall computational cost of $O(N \log N)$ by using Ewald sums and subsequently smooth particle-mesh Ewald method. We present the simulation results for the relaxation time scale for deformed cells and the apparent viscosity of blood flow through narrow cylindrical tubes. These results agree well with the published experimental results. [Preview Abstract] |
Sunday, November 23, 2008 11:35AM - 11:48AM |
BJ.00006: Vesicle dynamics in external flows Konstantin Turitsyn, Sergei Vergeles, Vladimir Lebedev A vesicle can exhibit a variety of different dynamical behaviors when placed in an external flow. At least three qualitative different motions have been observed in recent experiments: tumbling, tank-treading, trembling. We present a theoretical investigation of this effect, resulting in a phase-diagram which predicts the type of the vesicle motion. For planar external flows, the character of the vesicle dynamics is determined by two dimensionless parameters, which are formed out of viscosities of inner and outer fluids, external velocity gradient matrix and vesicle excess area. Transitions between different types of motions are analyzed separately. The tank-treading to tumbling transition is described by a saddle-node bifurcation whereas the tank-treading to trembling transition occurs via a Hopf bifurcation. In the vicinity of the transition lines the vesicle experiences critical slowing down, which can be described universal scaling exponents. [Preview Abstract] |
Sunday, November 23, 2008 11:48AM - 12:01PM |
BJ.00007: Lateral migration of vesicles with viscosity contrast in simple shear and Poiseuille flows Gwennou Coupier, Natacha Callens, Badr Kaoui, Christophe Minetti, Frank Dubois, Chaouqi Misbah, Thomas Podgorski The ability of soft objects (such as vesicles, drops or blood cells) to adapt their shapes under non-equilibrium conditions allows them to migrate transversally to the flow in a confined situation, even in the Stokes limit. We present an overview of our recent experiments on phospholipidic vesicles placed in two simple flows : simple shear between two sliding walls and Poiseuille flow in a channel. Some of these experiments were run under microgravity conditions in order to get rid of the screening of the lift forces by the vesicle's weight. Quantitative migration laws are exhibited and discussed. In particular, they depend strongly and non monotonously on the reduced volume (or excess area) of vesicles and the viscosity contrast between internal and external fluids. [Preview Abstract] |
Sunday, November 23, 2008 12:01PM - 12:14PM |
BJ.00008: Lattice Boltzmann simulation of the behavior of spherical and nonspherical particles in a square pipe flow Takaji Inamuro, Hirofumi Hayashi, Masahiro Koshiyama The lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to the simulations of solid-fluid mixture flows including spherical and nonspherical particles in a square pipe. A spherical solid particle is modeled by a droplet with strong interfacial tension and large viscosity, and consequently there is no need to track the moving solid-liquid boundary explicitly. Nonspherical (discoid and biconcave discoid) solid particles are made by applying artificial forces to the spherical droplet. It is found that spherical particles move around stable positions between the wall and the center of the pipe. On the other hand, a biconcave discoid particle moves along a helical path around the center of the pipe with periodic oscillations in its orientation. The radius of the helical path and the polar angle of the orientation increase as the hollow of the concave becomes larger. [Preview Abstract] |
Sunday, November 23, 2008 12:14PM - 12:27PM |
BJ.00009: Modeling cell migration in tapered microchannels Keng-Hwee Chiam, Fong Yew Leong Cellular deformation in confined environment has attracted much attention in the past decade, primarily in the hopes that this can lead to efficient tools for cancer diagnostics in time to come. To further our understanding of cell deformability and motility, cells can be made to flow through micro-fluidic channels. These micro-fluidic devices offer the means of quantifying cell motility characteristics in-vitro through velocity measurements and cell morphology observations. In this study, we are interested in computational modelling of cell migration phenomena in micro-fluidic channels. More specifically, the immersed boundary method is implemented to track the moving cellular interface coupled with the fluid background. It is shown that the migration velocity of the cell is dramatically reduced at the inlet of the micro-channel: a phenomenon also observed experimentally. Furthermore, it is shown that the mechanical properties of the nucleus are important factors affecting cell motility and deformation in a constriction. Comparison is made between two different cases of whole cell in micro-channel flow and isolated nucleus in micro-pipette aspiration. [Preview Abstract] |
Sunday, November 23, 2008 12:27PM - 12:40PM |
BJ.00010: Deformation and transport of an elastic fiber in a cellular flow Elie Wandersman, Olivia du Roure, Anke Lindner, Marc Fermigier Flexible fibers can undergo a buckling instability when they are in interaction with a viscous flow. It has been predicted numerically that the deformation of an elastic fiber can affect both the macroscopic rheology and the transport of the individual fiber through a cellular flow [1]. However, direct experimental observations of the coupling between fiber conformation and flow behavior are still missing. We study experimentally the deformation and the transport of an individual elastic fiber (Length $L \sim 1$ cm, radius $r \sim 100 \mu$m, Young's modulus $Y \sim 0.1$ MPa) in a cellular flow formed by a lattice of hyperbolic stagnation points. In the vicinity of a stagnation point, the fiber buckles if the viscous forces acting on the fiber overcome the elastic forces. We focus on: \begin{itemize} \item the onset of the buckling instability of the fiber, varying the elastic properties of the fiber, the shear rate and the ratio fiber length to the cell size. \item The dynamical properties of the fiber, and more precisely, the modification of the transport of the fiber in the lattice due to its deformation in the flow. \end{itemize} [1] Young et. al. \textit{Phys. Rev. Lett.} \textbf{99} 058303 (2007) [Preview Abstract] |
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