Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session PW: Biofluids XI: Cellular III - Viscoelastic Biofluids |
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Chair: Lisa Fauci, Tulane University Room: 208A-D |
Tuesday, November 24, 2009 11:40AM - 11:53AM |
PW.00001: The dynamics of immersed boundaries in viscoelastic fluids John Chrispell, Ricardo Cortez, Damir Khismatullin, Lisa Fauci Many biological fluids are viscoelastic and require a nonlinear constitutive equation to describe the evolution of the extra-stress tensor. We use an immersed boundary framework to model processes that involve the movement of immersed elastic boundaries interacting with a surrounding viscoelastic fluid. We present recent results on applications including dynamics of a closed membrane moving under surface tension, and phase-locking of swimming sheets. [Preview Abstract] |
Tuesday, November 24, 2009 11:53AM - 12:06PM |
PW.00002: Buckled in translation Anke Lindner, Elie Wandersmann, Nawal Quennouz, Olivia du Roure, Yuan-Nan Young, Michael Shelley An elastic filament can undergo a buckling instability when interacting with a viscous flow. The subsequent deformation of the filament changes its transport properties in the flow. In particular, numerical simulations (Young {\it et al.} Phys. Rev. Lett.,99,058303, 2007) have shown that due to its deformability an elastic filament can move like a random walker in a cellular flow, formed by closed stream lines. We have built an experimental set up using a centimeter scale filament made from a silicon elastomer in a network of counter rotating vortices allowing for a direct study of the coupling of deformation and transport. We quantify the buckling threshold in the complex flow geometry and show that it is in good agreement with analytical and numerical predictions. We directly link the observed buckling to modifications in the transport of the filament and study the probability of the filament to escape from a given vortex as a function of its deformability. We furthermore compare the transport in the vortex array of a rigid and a flexible filament to a small bead and show that not only deformability but also the size of the filament plays a crucial role for its transport behaviour. [Preview Abstract] |
Tuesday, November 24, 2009 12:06PM - 12:19PM |
PW.00003: The Stochastic and Driven Dynamics of Microscopic Elastic Objects Coupled by a Viscous Fluid Matthew Clark, Mark Paul We investigate analytically and numerically the coupled motion of microscopic objects in a viscous fluid. Fluid-coupled structures are encountered across a broad range of fields, including spheres and cantilevers in microscopic instruments and fluid motion sensing in biological systems. Many small scale systems undergo high frequency oscillations with small magnitude resulting in a flow field with significant local inertia contributions that must be described using the unsteady Stokes equation. We study the fluid coupled motion of two infinite cylinders that are each attached to a spring. This geometry is chosen due to its wide use in modeling cantilevers and beams in fluid. We show that the stochastic and driven correlated motion of the two cylinders can be found from a single deterministic calculation -- the response of the cylinders to an impulse in force. The stochastic dynamics are found using the fluctuation-dissipation theorem and the driven dynamics are found using transfer function theory. We derive analytical expressions for the cylinder dynamics that neglects effects of back-action. We compare our analytical expressions with finite element numerical simulations and find our analysis is valid over a range of larger separations. For small separations, with overlapping Stokes layers, we find interesting variations in both the amplitude and phase of the cylinders. [Preview Abstract] |
Tuesday, November 24, 2009 12:19PM - 12:32PM |
PW.00004: Affine transformations capture beak shape variation in Darwin's Finches Michael Brenner, Otger Campas, Riccardo Mallarino, Arhat Abzhanov Evolution by natural selection has resulted in extraordinary morphological complexity of living organisms, whose description has thus far defied any precise mathematical characterization linked to the underlying developmental genetics. Here we demonstrate that the morphological diversity of the beaks of Darwin's finches, the classical example of adaptive morphological radiation, is quantitatively accounted for through the mathematical group of affine transformations. Specifically, we show that all beak shapes of Ground Finches (genus \emph{Geospiza}) are related by scaling transformations (a subgroup of the affine group), and the same scheme occurs for all the beak shapes of Tree and Warbler finches. This analysis shows that the beak shapes within each of these groups differ only by their scales, such as length and depth, each of which is knownto be under genetic control.The complete morphological variability within the beaks of Darwin's finches can be explained by extending the scaling transformations to the entire affine group, by including shear transformations. Altogether our results suggest that the mathematical theory of groups can help decode morphological variability, and points to a potentially hierarchical structure of morphological diversity and the underlying developmental processes. [Preview Abstract] |
Tuesday, November 24, 2009 12:32PM - 12:45PM |
PW.00005: An integrated muscle mechanic-fluid dynamic model of lamprey swimming Chia-yu Hsu, Eric Tytell, Lisa Fauci In an effort towards a detailed understanding of the generation and control of vertebrate locomotion, including the role of the CPG and its interactions with reflexive feedback, muscle mechanics, and external fluid dynamics, we study a simple vertebrate, the lamprey. Lamprey body undulations are a result of a wave of neural activation that passes from head to tail, causing a wave of muscle activation. These active forces are mediated by passive structural forces. We present recent results from a model that fully couples a viscous, incompressible fluid with nonlinear muscle mechanics. We measure the dependence of the phase lag between activation wave and mechanical wave as a function of model parameters, such as body stiffness and muscle strength. Simulation results are compared to experiments utilizing both real and synthetic lamprey. [Preview Abstract] |
Tuesday, November 24, 2009 12:45PM - 12:58PM |
PW.00006: Electro-hydrodynamic effects on lipid membranes in giant vesicles Margarita Staykova, Tetsuya Yamamoto, Reinhard Lipowsky, Rumiana Dimova Electric fields are widely applied for cell manipulation in numerous micron-scale systems. Here, we show for the first time that alternating electric fields may cause pronounced flows in the membrane of giant lipid vesicles as well as in the surrounding fluid media.$^{ }$The lipid vesicles are not only biomimetic model for the cell membrane but also have many potential biotechnological applications, e.g. as drug-delivery systems and micro-reactors. The reported effects should be considered in electric micro-manipulation procedures on cells and vesicles. They might be useful for applications in microfluidic technologies, for lipid mixing, trapping and displacement, as will be demonstrated. We also believe that our method for visualization of the lipid flows by fluorescently labeled intra-membrane domains will be helpful for studies on membrane behavior in vesicles subjected to shear or mechanical stresses. [Preview Abstract] |
Tuesday, November 24, 2009 12:58PM - 1:11PM |
PW.00007: Elastohydrodynamics of wet bristles, carpets and brushes Lakshminarayanan Mahadevan, Arvind Gopinath We present an effective field theory for the elastohydrodynamics of ordered brushes and disordered carpets. These soft beds are comprised of elastic filamentous units, interspersed in a fluid and grafted on a substrate. Our formulation leads naturally to a set of constitutive equations coupling bed deformation to fluid flow, accounts for anisotropic properties of the medium, and generalizes poroelasticity to these systems. These effective medium equations are then used to study two canonical problems - the normal settling of a rigid sphere onto a carpet, and the tangential shearing motion of a rigid sphere over the carpet, both problems of much relevance in mechanosensation in biology. [Preview Abstract] |
Tuesday, November 24, 2009 1:11PM - 1:24PM |
PW.00008: Dynamics of polarly driven filaments Michael Shelley, Yuan-Nan Young In this study we investigate the dynamics and transport of bio-polymers such as microtubules or actin filaments when driven by motor proteins. A slender-body hydrodynamic formulation is augmented by a model for the forcing from the motor proteins. Our results show that the spatial gradients in the polar forcing, or the detachment of the filament from the motor proteins, can lead to nontrivial shape dynamics (undulatory traveling waves), and random walk trajectories. The interaction between filament and the simple device geometries is investigated, as is the effect of thermal fluctuations. [Preview Abstract] |
Tuesday, November 24, 2009 1:24PM - 1:37PM |
PW.00009: A fiber-reinforced-fluid model of anisotropic plant root cell growth Oliver E. Jensen, Rosemary J. Dyson We present a theoretical model of a single cell in the expansion zone of the primary root of the plant \textit{Arabidopsis thaliana}. The cell undergoes rapid elongation with approximately constant radius. Growth is driven by high internal turgor pressure causing viscous stretching of the cell wall, with embedded cellulose microfibrils providing the wall with strongly anisotropic properties. We represent the cell as a thin cylindrical fiber-reinforced viscous sheet between rigid end plates. Asymptotic reduction of the governing equations, under simple sets of assumptions about fiber and wall properties, yields variants of the traditional Lockhart equation that relates the axial cell growth rate to the internal pressure. The model provides insights into the geometric and biomechanical parameters underlying bulk quantities such as wall extensibility and shows how either dynamical changes in wall material properties or passive fibre reorientation may suppress cell elongation. [Preview Abstract] |
Tuesday, November 24, 2009 1:37PM - 1:50PM |
PW.00010: Effects of flow on insulin fibril formation at an air/water interface David Posada, Caryn Heldt, Mirco Sorci, Georges Belfort, Amir Hirsa The amyloid fibril formation process, which is implicated in several diseases such as Alzheimer's and Huntington's, is characterized by the conversion of monomers to oligomers and then to fibrils. Besides well-studied factors such as pH, temperature and concentration, the kinetics of this process are significantly influenced by the presence of solid or fluid interfaces and by flow. By studying the nucleation and growth of a model system (insulin fibrils) in a well-defined flow field with an air/water interface, we can identify the flow conditions that impact protein aggregation kinetics both in the bulk solution and at the air/water interface. The present flow system (deep-channel surface viscometer) consists of an annular region bounded by stationary inner and outer cylinders, an air/water interface, and a floor driven at constant rotation. We show the effects of Reynolds number on the kinetics of the fibrillation process both in the bulk solution and at the air/water interface, as well as on the structure of the resultant amyloid aggregates. [Preview Abstract] |
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