Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session L17: Biofluids: Microswimmers and Elasticity |
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Chair: Christophe Eloy, Aix-Marseille University IRPHE Room: 28C |
Monday, November 19, 2012 3:35PM - 3:48PM |
L17.00001: Optimal pumping kinematics of a cilium Christophe Eloy, Eric Lauga In a variety of biological processes, eukaryotic cells use cilia to transport flow. Although the internal molecular structure of cilia has been remarkably conserved throughout evolution, experimental observations report qualitatively diverse kinematics in different species. To address this diversity, we have determined numerically the kinematics of the most efficient cilium. Specifically, we have computed the time-periodic deformation of a wall-bound elastic filament leading to transport of a surrounding fluid at minimum energetic cost. Here, the energetic cost is taken to be the sum of positive works done by the internal torques, such that elastic energy is not conservative. The optimal kinematics are found to strongly depend on the cilium bending rigidity through a single dimensionless number, the Sperm number Sp, and closely resemble the two-stroke ciliary beating pattern observed experimentally. [Preview Abstract] |
Monday, November 19, 2012 3:48PM - 4:01PM |
L17.00002: Sperm Motility in Flow Jeffrey Guasto, Gabriel Juarez, Roman Stocker A wide variety of plants and animals reproduce sexually by releasing motile sperm that seek out a conspecific egg, for example in the reproductive tract for mammals or in the water column for externally fertilizing organisms. Sperm are aided in their quest by chemical cues, but must also contend with hydrodynamic forces, resulting from laminar flows in reproductive tracts or turbulence in aquatic habitats. To understand how velocity gradients affect motility, we subjected swimming sperm to a range of highly-controlled straining flows using a cross-flow microfluidic device. The motion of the cell body and flagellum were captured through high-speed video microscopy. The effects of flow on swimming are twofold. For moderate velocity gradients, flow simply advects and reorients cells, quenching their ability to cross streamlines. For high velocity gradients, fluid stresses hinder the internal bending of the flagellum, directly inhibiting motility. The transition between the two regimes is governed by the Sperm number, which compares the external viscous stresses with the internal elastic stresses. Ultimately, unraveling the role of flow in sperm motility will lead to a better understanding of population dynamics among aquatic organisms and infertility problems in humans. [Preview Abstract] |
Monday, November 19, 2012 4:01PM - 4:14PM |
L17.00003: Helical bodies swim slower... and faster... through a viscoelastic fluid Saverio Spagnolie, Bin Liu, Thomas Powers Microorganisms frequently swim in fluid environments that exhibit both viscous and elastic qualities in response to deformations. In an effort to better understand the fluid-body interactions in such complex systems, we have studied numerically the force-free swimming of a rotating helix in a viscoelastic (Oldroyd-B) fluid. The introduction of viscoelasticity can either enhance or retard the swimming speed depending on the body geometry and the properties of the fluid (through a dimensionless Deborah number). The results are compared to recent experiments on a rotating helix immersed in a Boger fluid. Our findings bridge the gap between studies showing situationally dependent enhancement or retardation of swimming speed, and may help to clarify phenomena observed in systems ranging from spermatozoan swimming to mechanical drilling. [Preview Abstract] |
Monday, November 19, 2012 4:14PM - 4:27PM |
L17.00004: Modeling the swimming of microbes in anisotropic fluids Madison Krieger, Saverio Spagnolie, Thomas Powers Microbes commonly swim in non-Newtonian fluids such as mucus, soil, and tissue. Some of these complex fluids are characterized by long-chain molecules which can align, leading to anisotropy. We study a simple model of swimming in an anisotropic fluid, that of an infinitely long two-dimensional sheet deforming via propagating waves and immersed in a nematic liquid crystal. The liquid crystal is categorized by the dimensionless Ericksen number, which compares viscous and elastic effects. At infinite Ericksen number, where viscous effects dominate over elastic effects and the only time scale is the period of the propagating wave, we calculate the swimming speed and power dissipation as a function of the anisotropic viscosities and the tumbling parameter. We also calculate the swimming speed and power dissipation at finite Ericksen number, where the orientation elasticity introduces an additional time scale, the relaxation time. [Preview Abstract] |
Monday, November 19, 2012 4:27PM - 4:40PM |
L17.00005: Direct micro-mechanical measurements of the material properties and motility of \textit{C. elegans} Matilda Backholm, William S. Ryu, Kari Dalnoki-Veress The model organism {\it C. elegans}, a millimeter-sized nematode, provides an excellent biophysical system for both static and dynamic mechanical studies. The undulatory motion exhibited by the worm as it swims or crawls through a medium is ubiquitous in nature at scales from microns to meters, and has been the focus of intense research. However, for a successful description of this form of locomotion, a better knowledge of the material properties as well as the worm's output forces is needed. Here we present a new experimental assay, with which the material properties and dynamics of {\it C. elegans} can be directly probed. In this technique, we use the deflection of a very flexible micropipette to measure the flexural rigidity of {\it C. elegans} at all stages of its life cycle, as well as along the body of the adult worm. By modelling the worm as a viscoelastic material, we have achieved new insights into its mechanical properties. Furthermore, the forces involved during the undulatory motion of {\it C. elegans} have been studied. It is the hope that the direct experimental characterization of this model organism will provide guidance for theoretical treatments of undulatory locomotion in general. [Preview Abstract] |
Monday, November 19, 2012 4:40PM - 4:53PM |
L17.00006: Effect of rotational diffusion on the collective behavior of swimming microorganisms in viscoelastic fluids Yaser Bozorgi, Patrick Underhill Hydrodynamic interactions of swimming microorganisms can lead to coordinated behaviors of large groups. The impact of viscoelasticity on the collective behavior of active particles driven by hydrodynamic interactions has been quantified with the inclusion of rotational diffusion. Oldroyd-B, Maxwell, and generalized linear viscoelastic modeled are considered as the constitutive equation of the suspending fluid, inspired by some biological fluids. A mean field assumption is used to model the suspension dynamics near an isotropic state. The onset of instability has been quantified by a linear stability analysis in terms of wavenumber, diffusivities, and constitutive equation parameters. Some key results are in contrast to suspensions in Newtonian fluids. The maximal growth rate can occur at a particular wavelength, and diffusion can act to make the system more unstable. Viscoelasticity can also affect the long time dynamics of the continuum equations. [Preview Abstract] |
Monday, November 19, 2012 4:53PM - 5:06PM |
L17.00007: Propulsion with a Reciprocal Stroke Enabled by Nonlinear Rheology Paulo Arratia, Xiaoning Shen, Nathan Keim In a fluid that is entirely viscous, a reciprocal swimming stroke results in no net displacement. However, complex fluids such as mucus or dense suspensions exhibit nonlinear rheology even at low Reynolds number. This nonlinear fluid response can lead to time-reversal symmetry breaking which can enable a reciprocal swimmer to move. Here we demonstrate this principle with a reciprocally-actuated artificial propeller in two viscoelastic fluids: a polymeric fluid with elasticity but negligible shear thinning, and a wormlike micellar fluid that exhibits shear thinning and shear-bands. Propulsion is absent in Newtonian fluid, and is strongest in the shear-thinning micellar fluid. We report on the role of elasticity (Deborah number) in setting the speed of propulsion, and of body shape and boundary conditions in setting its direction. This work is supported by the Army Research Office through award W911NF-11-1-0488. [Preview Abstract] |
Monday, November 19, 2012 5:06PM - 5:19PM |
L17.00008: Simulations of micro-swimmer scattering by soft elastic filaments Rodrigo Ledesma-Aguilar, Julia M. Yeomans The locomotion of microorganisms in the presence of elastic filaments, such as hairs and flagella, is very common in biological systems. We perform a theoretical study, using a simple point-force hydrodynamic model, to analyse the scattering of a dipolar swimmer and semiflexible filaments. Our swimmers consist of active dumbbells that undergo a non-reciprocal swimming stroke leading to locomotion. Fluid-mediated interactions with the elastic chains are modelled using Oseen-level hydrodynamics. We explore the effect of the elasticity of the filaments on the swimmer velocity and orientation. [Preview Abstract] |
Monday, November 19, 2012 5:19PM - 5:32PM |
L17.00009: Dynamics of Purcell's three-link microswimmer with a passive elastic tail Emiliya Passov, Yizhar Or One of the few possible mechanisms for self-propulsion at low Reynolds number is undulations of an elastic tail, as proposed in the classical work of [Purcell, 1977]. This effect is studied here by investigating a variant of Purcell's three link swimmer model where the front joint angle is periodically actuated while the rear joint is driven by a passive torsional spring. The dynamic equations of motion are formulated and explicit expressions for the leading-order solution are derived by using perturbation expansion. The dependence of the motion on the actuation amplitude and frequency is analyzed, and leading-order expressions are formulated for the travel-per-stroke, mechanical work per travel distance, and average Lighthill's efficiency. Finally, optimization with respect to the actuation frequency and the swimmer's geometry is conducted. [Preview Abstract] |
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