Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session MQ: Biolocomotion IX: Micro-Swimming IV |
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Chair: David Saintillan, University of Illinois at Urbana-Champaign Room: Long Beach Convention Center 203B |
Tuesday, November 23, 2010 8:00AM - 8:13AM |
MQ.00001: Low Reynolds number swimming in a stratified fluid Arezoo Ardekani, Roman Stocker Microorganisms live in aquatic environments that are often density-stratified, for example due to temperature or salinity gradients in oceans and lakes. Yet, the effect of stratification on low-Reynolds number swimming has not been investigated, in part because it is generally believed that the length scale of stratification is orders of magnitude larger than microorganisms. We show that this is incorrect and that typical stratifications can affect organisms as small as O(100 $\mu$m). By deriving fundamental singularity solutions (Stokeslet and stresslet) in a stratified fluid$-$ which we call Stratlets$-$ we demonstrate that the characteristic length scale of this problem, $L=\left(\mu \kappa/\gamma g\right)^{1/4}$, is one that combines buoyancy, diffusion and viscosity effects, where $\kappa$ is the diffusivity of the stratifying agent, $\mu$ the dynamic viscosity, $\gamma$ the background density gradient, and $g$ the acceleration of gravity. The importance of stratification for a swimmer of size $a$, relative to diffusion, is measured by the Rayleigh number, $Ra=(a/L)^4$. Stratification dramatically changes the flow generated by a swimmer, creating recirculation cells that diminish in size with increasing $Ra$. Consequently, flow velocity decays with distance from the swimmer considerably faster than in homogeneous fluids. This suggests that stratification acts as a ``silencer'' for hydromechanical signals, for example reducing the perception abilities of microorganisms that rely on mechanosensing to detect prey. [Preview Abstract] |
Tuesday, November 23, 2010 8:13AM - 8:26AM |
MQ.00002: Locomotion by tangential deformation in a polymeric fluid Lailai Zhu, Eric Lauga, Luca Brandt Many biological cells such as bacteria often encounter viscous environments with suspended microstructures or macromolecules. The physics of micro-propulsion in such a non-Newtonian viscoelastic fluid has only recently started to be addressed. Here we present results of three-dimensional numerical simulations for the steady locomotion of a self-propelled body in a model polymeric (Giesekus) fluid at low Reynolds number. The microswimmer is driven by a purely tangential distortion on the outer surface reproduced as non-homogenous boundary condition on a rigid body. The swimming speed and efficiency for different values of the Weissenberg number and the viscosity ratio are reported. The swimming speed is lower in a visco-elastic fluid and is asymptotically recovering for large We approaching values for Newtonian swimmer. Interestingly, the efficiency is seen to significantly increase as the viscosity of the polymeric fluid is increased. Further analysis reveals that polymeric stresses break the Newtonian front-back symmetry in the flow profile around the body. Speed and efficiency for pusher and puller squirmers will be reported together with analysis of the velocity fields. Time-dependent boundary conditions shall also be considered. [Preview Abstract] |
Tuesday, November 23, 2010 8:26AM - 8:39AM |
MQ.00003: Undulatory Swimming in Viscoelastic Fluids at Low Reynolds Number Xiaoning Shen, Paulo Arratia In this talk, we present an experimental investigation on the swimming behavior of the worm nematode \textit{C. elegans} in viscoelastic fluids at low Reynolds number. The \textit{C. elegans}' swimming behavior is characterized by tracking the nematode's body postures and using particle image velocimetry. Results show that the nematode responds to the fluid elastic stresses by adjusting its beating frequency and wave-form. Overall, low levels of elasticity tend to hinder swimming speed by 30{\%} when compared to a Newtonian fluid with similar viscosity. These results, however, are only valid for Wissenberg numbers below unit (\textit{Wi}$<$1) where \textit{Wi} is defined as the product of the fluid relaxation time and the fluid flow shear-rate. [Preview Abstract] |
Tuesday, November 23, 2010 8:39AM - 8:52AM |
MQ.00004: Stokesian locomotion in elastic fluids: Experiments Roberto Zenit, Eric Lauga In many instances of biological relevance, self-propelled cells have to swim through non-Newtonian fluids. In order to provide fundamental understanding on the effect of such non-Newtonian stresses on locomotion, we have studied the motion an oscillating magnetic swimmer immersed in both Newtonian and non-Newtonian liquids at small Reynolds numbers. The swimmer is made with a small rare earth (Neodymium-Iron-Boron) magnetic rod (3 mm) to which a flexible tail was glued. This array was immersed in cylindrical container (50 mm diameter) in which the test fluid was contained. A nearly uniform oscillating magnetic field was created with a Helmholtz coil (R=200mm) and a AC power supply. For the Newtonian case, a 30,000 cSt silicon oil was used. In the non-Newtonian case, a fluid with nearly constant viscosity and large first normal stress difference (highly elastic) was used; this fluid was made with Corn syrup with a small amount of polyacrylamide. The swimming speed was measured, for different amplitudes and frequencies, using a digital image analysis. The objective of the present investigation is to determine whether the elastic effects of the fluid improve or not the swimming performance. Some preliminary results will be presented and discussed. [Preview Abstract] |
Tuesday, November 23, 2010 8:52AM - 9:05AM |
MQ.00005: Finite-length swimmer in a nonlinearly viscoelastic fluid Henry Fu Many swimming microorganisms naturally encounter non-Newtonian, viscoelastic fluids, including mucus in airways, the stomach, and the reproductive tract. Most of the analytical work on swimming in such complex media has involved swimmers of infinite length, in both two-dimensional and three-dimensional geometries. I present an analytic calculation of a finite-length three-dimensional swimmer, the Golestanian 3-sphere swimmer, in the limit of small sphere radius relative to sphere separation and small displacement relative to sphere radius. I discuss the effect of nonlinear viscoelasticity on the swimming speeed and on the internal forces exerted by the spheres on one another. Finite-length corrections occur at second order in displacements, the same order as the Newtonian swimming speed and the viscoelastic corrections observed for infinite swimmers. For this finite-length swimmer, viscoelastic corrections to the swimming speed rely on spatial asymmetry in the swimming stroke amplitude. [Preview Abstract] |
Tuesday, November 23, 2010 9:05AM - 9:18AM |
MQ.00006: Marine ostracod swimming behavior in the benthic boundary layer under different field flow conditions Kelly Sutherland, John Dabiri, Mimi Koehl Marine organisms swimming in water near the substratum are subjected to boundary layer flow, which is characterized by steep velocity gradients and turbulence. How do small swimming organisms navigate flows at this interface to forage and interact with mates? We recorded in the field the swimming behavior of marine ostracods near complex living substrata exposed to different ambient water flow conditions. Ostracod trajectories and background water flow were recorded simultaneously using a Self-Contained Underwater Velocimetry Apparatus (SCUVA). Particle image velocimetry enabled us to map the instantaneous water velocity fields in which the ostracods were swimming. In slow flows (U$_{rms} \quad \sim $0.3 cm s$^{-1})$, ostracod swimming tracks were more tortuous, and encounters with bottom-dwelling organisms and with other ostracods were more frequent than in higher velocity wave-driven flows (U$_{rms} \quad \sim $2.8 cm s$^{-1})$, indicating that foraging and mating activities may be curtailed when ambient water flow is too rapid or variable. [Preview Abstract] |
Tuesday, November 23, 2010 9:18AM - 9:31AM |
MQ.00007: Escaping From Predation At Low Reynolds Number: A Compensatory Mechanism Brad Gemmell, Jian Sheng, Ed Buskey Small planktonic organisms such as copepods are often the first foods for many species of fish and thus, subject to high predation rates. They have developed strong escape responses to attacks from visual predators and this behavior is found even in the youngest development stage. Because of their small size (approx. 100 $\mu$m), these juvenile copepods must contend with greater viscous forces than their predators during encounters. In this study, we investigate the role of viscosity on escape swimming performance of young copepods within the context of the environmental temperatures (10C-30C) these animals experience along the Texas coast. 3-Dimensional high speed (3000 frames per second) digital holographic techniques were used to elucidate kinematics and kinetics of swimming. Here we show that although escape velocity and acceleration are reduced as a function of both increasing viscosity and decreasing temperature, total escape distance is conserved. Interestingly, we observed no difference in the number swimming strokes per escape. Instead, the animals exhibit a compensatory mechanism based on increasing power stroke duration to recovery stroke duration to counter act the increasing viscosity at lower temperature. Flow analysis shows this results in the conservation of energy expenditure, and consequently escape distance. [Preview Abstract] |
Tuesday, November 23, 2010 9:31AM - 9:44AM |
MQ.00008: A High-Speed Tomographic PIV System for Measuring Plankton-Generated Flow D.W. Murphy, D.R. Webster, J. Yen Plankton such as copepods, fish larvae, and mysids occupy a fluid environment in which neither inertia nor viscosity dominates. At this intermediate Reynolds number (range of 1 to 1000), locomotion, hydrodynamic signal detection, and foraging of these organisms are influenced by both viscous and inertial effects. The millimeter length and millisecond time scales at which these animals operate present significant difficulties to obtaining flow measurements using traditional planar PIV systems, which additionally cannot quantify the three-dimensional nature of the flow. We describe the design and application of a novel PIV system comprising four high-speed cameras (2190 fps), two near IR lasers (808 nm), and the associated optics used to illuminate and interrogate a volume of approximately 1 cubic centimeter. Illumination in the near IR wavelengths does not affect copepod behavior. Fine-scale three-dimensional fluid velocity measurements around free-swimming animals provide insight into their locomotion-induced flow. Further, calculation of the complete strain rate tensor and vorticity vector allows estimation of the flow disturbance and mechanosensory reaction levels. The system also facilitates studies of organism response to environmental cues such as laboratory-generated turbulence. [Preview Abstract] |
Tuesday, November 23, 2010 9:44AM - 9:57AM |
MQ.00009: Bacteria swimming in a wall-bounded shear flow studied with microfluidic-DHM H. Agarwal, M. Barry, R. Stocker, J. Sheng Observations of bacterial motility in a wall-bounded shear flow are crucial to understand cell attachment at the onset of biofilm formation. We combined microfluidics and holography to measure 3-D trajectories of \textit{Escherichia coli }in shear flows, for shear rates up to 200/s. Acquisition of $>$3,000 trajectories over short times (5 min) enabled the robust quantification of swimming velocities and dispersion coefficients. We find that near-wall hydrodynamic interactions, including swimming in circles and the reduction in tumbling frequency, reduce the wall-normal dispersion of bacteria, favoring surface attachment. Preliminary results on the effect of shear will also be discussed. [Preview Abstract] |
Tuesday, November 23, 2010 9:57AM - 10:10AM |
MQ.00010: Autonomous motion of semipermeable colloidal particles via chemical reactions: self-osmophoresis Misael Diaz, Ubaldo Cordova-Figueroa While a large body of work exists on the design of catalytically-driven colloidal particles, little work exists on particles with the ability to permeate fluid through its surface that may be used for applications in lab-on-a-chip systems and drug delivery. We propose a model for the catalytically-driven motion of a semipermeable particle (e.g., non-motile microorganisms and vesicles) surrounded by reactant solutes in a Newtonian fluid. It is assumed that a first-order consumption reaction of surrounding reactants---which could be enzymatic or catalytic---occurs on half of the outer surface of the membrane. In equilibrium, the osmotic pressure inside the particle balances that of outside. The reaction creates an imbalance in osmotic pressure, causing outer fluid facing the catalytic side to permeate inside the particle as inner fluid permeates through the passive side. This fluid motion satisfies mass conservation inside the particle, causing particle motion towards regions of low reactant concentration by a mechanism known as osmophoresis. Preliminary results show that the particle velocity--defined as a P\'eclet number--is a function of the permeability of the membrane, a ``characteristic'' osmotic velocity, and the Damk\"ohler number--which is a measure of relative impacts of the diffusion and chemical reaction. The permeating fluid retards particle motion by dragging the solute against the induced osmotic imbalance. [Preview Abstract] |
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