Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session R21: Focus Session: Biological Hydrodynamics |
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Sponsoring Units: DFD DBP Chair: Ray Goldstein, University of Arizona Room: Baltimore Convention Center 318 |
Wednesday, March 15, 2006 2:30PM - 3:06PM |
R21.00001: Large-scale pattern formation in active particles suspensions: from interacting microtubules to swimming bacteria Invited Speaker: We consider two biological systems of active particles exhibiting large-scale collective behavior: microtubules interacting with molecular motors and hydrodynamically entrained swimming bacteria. Starting from a generic stochastic microscopic model of inelastically colliding polar rods with an anisotropic interaction kernel, we derive set of equations for the local rods concentration and orientation. Above certain critical density of rods the model exhibits orientational instability and onset of large-scale coherence. For the microtubules and molecular motors system we demonstrate that the orientational instability leads to the formation of vortices and asters seen in recent experiments. Similar approach is applied to colonies of swimming bacteria \textit{Bacillus subtilis} confined in thin fluid film. The model is formulated in term of two-dimensional equations for local density and orientation of bacteria coupled to the low Reynolds number Navier-Stokes equation for the fluid flow velocity. The collective swimming of bacteria is represented by additional source term in the Navier-Stokes equation. We demonstrate that this system exhibits formation of dynamic large-scale patterns with the typical scale determined by the density of bacteria. [Preview Abstract] |
Wednesday, March 15, 2006 3:06PM - 3:18PM |
R21.00002: Elastic swimming I: Optimization Eric Lauga, Tony Yu, Anette Hosoi We consider the problem of swimming at low Reynolds number by oscillating an elastic filament in a viscous liquid, as investigated by Wiggins and Goldstein (1998, Phys Rev Lett). In this first part of the study, we characterize the optimal forcing conditions of the swimming strategy and its optimal geometrical characteristics. [Preview Abstract] |
Wednesday, March 15, 2006 3:18PM - 3:30PM |
R21.00003: Elastic swimming II: Experiments Tony Yu, Eric Lauga, Anette Hosoi We consider the problem of swimming at low Reynolds number by oscillating an elastic filament in a viscous liquid, as investigated by Wiggins and Goldstein (1998, Phys Rev Lett). In this second part of the study, we present results of a series of experiments characterizing the performance of the propulsive mechanism. [Preview Abstract] |
Wednesday, March 15, 2006 3:30PM - 3:42PM |
R21.00004: Stress-induced reversal of flagellar propulsion: an ingredient of quorum polarity of {\it Bacillus subtilis} L. Cisneros, C. Dombrowski, R.E. Goldstein, J.O. Kessler Recent experiment have shown large-scale dynamic coherence in suspensions of the bacterium {\it B. subtilis}, characterized by quorum polarity -- the collective parallel swimming of cells. To probe mechanisms leading to quorum polarity, we study the response of individual {\it B. subtilis} cells to steric stress brought on by swimming into a micron-sized spatial constriction. Careful visualization shows that cells can fully reverse their swimming direction at spatial constrictions without turning the cell body. This property, termed ``flippancy," is quantified by measurements of the inward and outward swimming velocities, accelerations and decelerations, and docking times. The asymptotic inward and outward swimming speeds far from the constriction show near perfect correlation, implying that the propelling flagella flip, and that ``forwards" and ``backwards" are dynamically indistinguishable, as with {\it E. coli}. Implications for the collective dynamics are discussed. [Preview Abstract] |
Wednesday, March 15, 2006 3:42PM - 3:54PM |
R21.00005: Effects of nonlinear membrane elasticity on capsule recovery Andres Gonzalez-Mancera, Charles Eggleton The recovery of a capsule from an initially deformed shape is considered. The problem is solved numerically for a capsule made of an incompressible liquid surrounded by a thin elastic membrane using the Boundary Integral Method. Elastic membranes with different constitutive models providing a wide range of behaviors at large deformations (strain-hardening, strain- softening and linear elastic) were considered. The results suggest that the recovery process is dominated by the isotropic dilatation modulus. The recovery process from small deformations was seen to be nearly independent of the membrane constitutive model. Recovery from large deformations was highly dependent on the constitutive model and the initial geometry of the capsule. Analysis of the recovery from large deformations demonstrated that the process is modulated by the tangential component of the elastic traction, $\backslash$F$_t$, acting on the membrane. This component of the traction was seen to either favor or oppose the recovery depending on the constitutive equation used to model the elastic membrane. The differences in the recovery process can be used to identify the best model for a particular capsule based on features observed during the recovery process. [Preview Abstract] |
Wednesday, March 15, 2006 3:54PM - 4:06PM |
R21.00006: Balancing energy input and viscous dissipation in the Zooming BioNematic J.O. Kessler, R.E. Goldstein, R. Cortez Beyond a concentration threshold, populations of the swimming bacteria {\it Bacillus subtilis} form a phase (the Zooming BioNematic=ZBN) comprising intermittent domains of co-aligned cells all swimming in the same direction. Collectively generated hydrodynamic forces between bacteria, the cells' ability to flip flagella, thereby changing swimming polarity, and their tendency to swim upstream into a collectively generated current are fundamental interactions leading to the ZBN. But how does the ZBN generate dynamic patterns, similar to ones at $Re\gg1$? The energy put into the fluid by the swimming organisms overwhelms viscous damping, as demonstrated by a new dimensionless ratio $Bs$, analogous to $Re$ but replacing the numerator by a measure of bacterial energy input. The magnitude of $Bs$ is estimated via the Navier-Stokes equations, considering individual bacteria at moderate concentration, and entire domains at high. $Bs$ is proportional to the bacterial concentration, and in both of those regimes, $Bs\gg 1$. Remarkably, unlike the Reynolds number, $Bs$ is independent of viscosity. [Preview Abstract] |
Wednesday, March 15, 2006 4:06PM - 4:18PM |
R21.00007: Multicellularity and the Functional Interdependence of Motility and Molecular Transport C. Solari, S. Ganguly, J.O. Kessler, R. Michod, R.E. Goldstein Benefits, costs and requirements accompany the transition from motile totipotent unicellular organisms to multicellular organisms having cells specialized into reproductive (germ) and vegetative (sterile soma) functions such as motility. In flagellated colonial organisms such as the volvocalean green algae, organized beating by the somatic cells' flagella yields propulsion important in phototaxis and chemotaxis. It has not been generally appreciated that for the larger colonies, flagellar stirring of boundary layers and remote transport are fundamental for maintaining a sufficient rate of metabolite turnover, one not attainable by diffusive transport alone. We describe experiments that quantify the role of advective dynamics in enhancing productivity in germ-soma differentiated colonies. First, experiments with suspended deflagellated colonies of {\it Volvox carteri} show that forced advection improves productivity. Second, Particle Imaging Velocimetry of fluid motion around colonies reveals flow fields with very large characteristic velocities $U$ extending to length scales comparable to the colony radius $R$. For a typical metabolite diffusion constant $D$, the Peclet number $Pe=2UR/D \gg 1$, indicative of the dominance of advection over diffusion, with striking augmentation at the cell division stage. [Preview Abstract] |
Wednesday, March 15, 2006 4:18PM - 4:30PM |
R21.00008: Flagella-Driven Flows Circumvent Diffusive Bottlenecks that Inhibit Metabolite Exchange Martin Short, Cristian Solari, Sujoy Ganguly, John Kessler, Raymond Goldstein, Thomas Powers The evolution of single cells to large and multicellular organisms requires matching the organisms' needs to the rate of exchange of metabolites with the environment. This logistic problem can be a severe constraint on development. For organisms with a body plan that approximates a spherical shell, such as colonies of the volvocine green algae, the required current of metabolites grows quadratically with colony radius whereas the rate at which diffusion can exchange metabolites grows only linearly with radius. Hence, there is a bottleneck radius beyond which the diffusive current cannot keep up with metabolic demands. Using {\it Volvox carteri} as a model organism, we examine experimentally and theoretically the role that advection of fluid by surface-mounted flagella plays in enhancing nutrient uptake. We show that fluid flow driven by the coordinated beating of flagella produces a convective boundary layer in the concentration of a diffusing solute which in turn renders the metabolite exchange rate quadratic in the colony radius. This enhanced transport circumvents the diffusive bottleneck, allowing increase in size and thus evolutionary transitions to multicellularity in the Volvocales. [Preview Abstract] |
Wednesday, March 15, 2006 4:30PM - 4:42PM |
R21.00009: Measurement of Flow Patterns and Dispersion in the Human Airways Frank E. Fresconi, Ajay K. Prasad A detailed knowledge of the flow and dispersion within the human respiratory tract is desirable for numerous reasons. Both risk assessments of exposure to toxic particles in the environment and the design of medical delivery systems targeting both lung-specific conditions (asthma, cystic fibrosis, and chronic obstructive pulmonary disease (COPD)) and system-wide ailments (diabetes, cancer, hormone replacement) would profit from such an understanding. The present work features experimental efforts aimed at elucidating the fluid mechanics of the lung. Particle image velocimetry (PIV) and laser induced fluorescence (LIF) measurements of oscillatory flows were undertaken in anatomically accurate models (single and multi-generational) of the conductive region of the lung. PIV results captured primary and secondary velocity fields. LIF was used to determine the amount of convective dispersion across an individual generation of the lung. [Preview Abstract] |
Wednesday, March 15, 2006 4:42PM - 4:54PM |
R21.00010: On small insect flight -- a two-dimensional study Paulo Ferreira de Sousa Small insect flight is characterized by very small Reynolds numbers and relatively simple wing motions. In this study, a two-dimensional approximation of small insect flight is calculated with a newly developed high-order immersed boundary incompressible Navier-Stokes flow solver. The simulated motion of the model wing is a simplification of the flight of Drosophila melanogaster, and was done in line with previous experimental and numerical simulations available in the literature. Calculations were carried out until a time-periodic steady-state was achieved. Changes in lift generation and vortex dynamics are studied for Reynolds numbers spanning two orders of magnitude, in order to accurately find the critical Re number above which flapping flight is possible. Above the critical Reynolds number, vortices are alternately shed during translation. Below the critical Reynolds number, vortices are formed but not shed during translation, creating two attached and almost identical vortices. This transition is significant because, below it, an important mechanism of lift generation no longer applies, effectively indicating a lower bound for insect flight to occur. [Preview Abstract] |
Wednesday, March 15, 2006 4:54PM - 5:06PM |
R21.00011: Wake characteristics of a model ornithopter Alfredo Juarez, Jacob Harlow, James Allen, Paulo Ferreira de Sousa This paper details unsteady wake measurements from a model Ornithopther flying in a wind tunnel at representative flight conditions. Testing over a range of Strouhal number, 0.1-0.3, shows that the unsteady wake is composed of coherent vortical structures that resemble vortex rings. A single ring is formed in the wake of each wing during one wing beat. Momentum balance from velocity field measurements are reconciled with unsteady lift and drag measurements from a drag balance. [Preview Abstract] |
Wednesday, March 15, 2006 5:06PM - 5:18PM |
R21.00012: Vertical hovering of a symmetric flapping model Makoto Iima, Tatsuo Yanagita We study the motion of a model equipped with flapping wings under the influence of gravity (external force). This model moves in a two-dimensional fluid according to the hydrodynamic force generated by vortices separated from its wings. As a result of the interaction between the vortices and the wings, the model moves steadily in a direction against the gravity. Moreover, hovering, i.e., a steady flight staying in a particular position, can be achieved here by the effective use of vortex structures enhancing the hydrodynamic force that supports the model against gravity. The system exhibits a transition from the state with hovering to a state where hovering is impossible, as the model parameters are changed. [Preview Abstract] |
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