Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session M23: Biofluids: Undulatory Swimming in Newtonian and Non-Newtonian Fluids |
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Chair: Arezoo Ardekani, Purdue University Room: 300 |
Tuesday, November 24, 2015 8:00AM - 8:13AM |
M23.00001: Undulatory swimming in non-Newtonian fluids Arezoo Ardekani, Gaojin Li Microorganisms often swim in complex fluids exhibiting both elasticity and shear-thinning viscosity. The motion of low Reynolds number swimmers in complex fluids is important for better understanding the migration of sperms and formation of bacterial biofilms. In this work, we numerically investigate the effects of non-Newtonian fluid properties, including shear-thinning and elasticity, on the undulatory locomotion. Our results show that elasticity hinders the swimming speed, but a shear-thinning viscosity in the absence of elasticity enhances the speed. The combination of the two effects hinders the swimming speed. The swimming boost in a shear-thinning fluid occurs even for an infinitely long flagellum. The swimming speed has a maximum, whose value depends on the flagellum oscillation amplitude and fluid rheological properties. The power consumption, on the other hand, follows a universal scaling law. [Preview Abstract] |
Tuesday, November 24, 2015 8:13AM - 8:26AM |
M23.00002: Undulatory swimming in shear-thinning fluids: Experiments with Caenorhabditis elegans David Gagnon, Paulo Arratia The swimming behavior of microorganisms can be strongly affected by the rheology of their fluidic environment. In this talk, we experimentally investigate the swimming behavior of the nematode Caenorhabditis elegans ($\approx$1 mm length, 80 $\mathrm{\mu}$m diameter) in shear-thinning fluids using tracking and velocimetry methods. We find substantial differences in the resulting flow fields between the shear-thinning and Newtonian cases, even though the swimming kinematics (e.g. speed and frequency) remain similar. For example, velocimetry data show that shear-thinning viscosity enhances vorticity and increases circulation near the strongest body vortex, located near the head of the nematode. These findings are in good agreement with recent theoretical and numerical results. We then estimate the local viscosity around the swimmer, measure the spatial decay of the flow field, and estimate the mechanical power (i.e. viscous dissipation) due to the worm's motion in shear-thinning fluids. We find that the flow decays more slowly in shear-thinning fluids than in Newtonian fluids, but the resulting mechanical power is approximately the same for swimming in shear-thinning fluids when compared to the Newtonian case. [Preview Abstract] |
Tuesday, November 24, 2015 8:26AM - 8:39AM |
M23.00003: Locomotion in a liquid crystal near a wall Thomas Powers, Madison Krieger, Saverio Spagnolie Recent observations of bacteria swimming in nematic liquid crystal solution motivate the theoretical study of how swimming speed depends on liquid crystal properties. We consider the Taylor sheet near a wall, in which propulsion is achieved by the propagation of traveling waves along the length of the swimmer. Using the lubrication approximation, we determine how swimming speed depends on the Ericksen number, which is the ratio of elastic to viscous stresses. We also study the effect of anchoring strength, at the surface of the swimmer and the surface of the wall. [Preview Abstract] |
Tuesday, November 24, 2015 8:39AM - 8:52AM |
M23.00004: A Simple Method to Measure Nematodes' Propulsive Thrust and the Nematode Ratchet. Haim Bau, Jinzhou Yuan, David Raizen Since the propulsive thrust of micro organisms provides a more sensitive indicator of the animal's health and response to drugs than motility, a simple, high throughput, direct measurement of the thrust is desired. Taking advantage of the nematode \textit{C. elegans} being heavier than water, we devised a simple method to determine the propulsive thrust of the animals by monitoring their velocity when swimming along an inclined plane. We find that the swimming velocity is a linear function of the sin of the inclination angle. This method allows us to determine, among other things, the animas' propulsive thrust as a function of genotype, drugs, and age. Furthermore, taking advantage of the animals' inability to swim over a stiff incline, we constructed a sawteeth ratchet-like track that restricts the animals to swim in a predetermined direction. [Preview Abstract] |
Tuesday, November 24, 2015 8:52AM - 9:05AM |
M23.00005: Flow analysis of C. elegans swimming Thomas Montenegro-Johnson, David Gagnon, Paulo Arratia, Eric Lauga Improved understanding of microscopic swimming has the potential to impact numerous biomedical and industrial processes. A crucial means of analyzing these systems is through experimental observation of flow fields, from which it is important to be able to accurately deduce swimmer physics such as power consumption, drag forces, and efficiency. We examine the swimming of the nematode worm C. elegans, a model system for undulatory micro-propulsion. Using experimental data of swimmer geometry and kinematics, we employ the regularized stokeslet boundary element method to simulate the swimming of this worm outside the regime of slender-body theory. Simulated flow fields are then compared with experimentally extracted values confined to the swimmer beat plane, demonstrating good agreement. We finally address the question of how to estimate three-dimensional flow information from two-dimensional measurements. [Preview Abstract] |
Tuesday, November 24, 2015 9:05AM - 9:18AM |
M23.00006: Maneuverability and chemotaxis of \textit{Caenorhabditis elegans} in three-dimensional environments Jerzy Blawzdziewicz, Alejandro Bilbao, Amar Patel, Siva Vanapalli Locomotion of the nematode {\it C.\ elegans} in water and complex fluids has recently been investigated to gain insight into neuromuscular control of locomotion and to shed light on nematode evolutionary adaptation to environments with varying mechanical properties. Previous studies focused mainly on locomotion efficiency and on adaptation of the nematode gait to the surrounding medium. Much less attention has been devoted to nematode maneuverability, in spite of its crucial role in the survival of the animal. Recently [Phys.\ Fluids 25, 081902 (2013)] we have provided a quantitative analysis of turning maneuvers of crawling and swimming nematodes on flat surfaces and in 2D fluid layers. Based on this work, we follow with the first full 3D description of how {\it C.\ elegans} moves in complex 3D environments. We show that by superposing body twist and 2D undulations, a burrowing or swimming nematode can rotate the undulation plane and change the direction of motion within that plane by varying undulation-wave parameters. A combination of these corkscrew maneuvers and 2D turns allows the nematode to explore 3D space. We conclude by analyzing 3D chemotaxis of nematodes burrowing in gel and swimming in water, which demonstrates an important application of our maneuverability model. [Preview Abstract] |
Tuesday, November 24, 2015 9:18AM - 9:31AM |
M23.00007: Amplitude transitions of swimmers and flexors in viscoelastic fluids Robert Guy, Becca Thomases In both theoretical and experimental studies of the effect of fluid elasticity on micro-organism swimming, very different behavior has been observed for small and large amplitude strokes. We present simulations of an undulatory swimmer in an Oldroyd-B fluid and show that the resulting viscoelastic stresses are a nonlinear function of the amplitude. Specifically, there appears to be an amplitude dependent transition that is key to obtaining a speed-up over the Newtonian swimming speed. To understand the physical mechanism of the transition, we examine the stresses in a time-symmetric oscillatory bending beam, or flexor. We compare the flow in a neighborhood of the flexor tips with a large-amplitude oscillatory extensional flow, and we see similar amplitude dependent transitions. We relate these transitions to observed speed-ups in viscoelastic swimmers. [Preview Abstract] |
Tuesday, November 24, 2015 9:31AM - 9:44AM |
M23.00008: Flexibility, stroke, and dimensionless parameters: the importance of telling the whole story for swimming micro-organisms in complex fluids Becca Thomases, Robert Guy The question of how fluid elasticity affects the swimming performance of micro-organisms is complicated and has been the subject of many recent experimental and theoretical studies. The Deborah number, $De = \lambda \omega$, is typically used to characterize the strength of the fluid elasticity in these studies, and for swimmers is expressed as the product of the elastic relaxation time and the frequency of the swimmer stroke. In simulations of undulatory flexible swimmers in an Oldroyd-B-type fluid, we find that varying the frequency of the stroke and varying the relaxation time separately results in a significantly different dependence of swimming speed for the same $De.$ Thus the elastic effects on swimming cannot be characterized by a single dimensionless number. The Weissenberg number, defined as the product of elastic relaxation time and characteristic strain rate ($Wi=\lambda\dot{\gamma}$), is another dimensionless parameter useful for describing complex fluids. For a fixed swimmer frequency, varying the relaxation time will also vary the Weissenberg number. We conjecture that the different behavior is a consequence of a Weissenberg-number transition in the fluid, which additionally depends on the amplitude of the swimmer stroke. [Preview Abstract] |
Tuesday, November 24, 2015 9:44AM - 9:57AM |
M23.00009: Swimming sheet in a Newtonian fluid confined by a Brinkman medium Seyed Amir Mirbagheri, Henry Fu Many microorganisms swim through complex materials such as viscoelastic mucus in their natural habitats. As microorganisms move through complex materials, they may induce spatial heterogeneity in the medium, which can affect swimming properties. For example, the rotating flagella of bacteria may deplete polymer concentration near the flagella, while H pylori can turn nearby mucin gel into sol by elevating the pH. Here we examine a simple model of swimming in such scenarios, by investigating Taylor's two-dimensional swimming sheet swimming in a layer of Newtonian fluid. The Newtonian fluid is bounded above by a Brinkman medium, which represents the complex material that has been locally depleted or dissolved near the swimmer. We analytically derive the velocity for a small amplitude wave of an infinite sheet using a perturbation series to second order in the wave amplitude. For a fixed swimmer geometry, we explore the dependence of the velocity on the thickness of the Newtonian fluid and the permeability and porosity of the Brinkman medium. [Preview Abstract] |
Tuesday, November 24, 2015 9:57AM - 10:10AM |
M23.00010: Swimming Speeds of Filaments in Viscous Fluids with Resistance Nguyenho Ho, Sarah Olson Spermatozoa and bacteria can utilize lateral and spiral bending waves to propagate in a fluid. Often, they encounter different fluid environments filled with mucus, cells, hormones, and other large proteins. These extra materials act as friction, possibly preventing or enhancing forward progression of swimmers. To understand these effects, we employ Taylor's techniques to calculate the asymptotic swimming speeds of a cylinder of infinite extent in a viscous fluid with resistance known as a Brinkman fluid. We find that, up to the second order expansion, the swimming speeds are enhanced as resistance increases. The Stokes limit can also be also recovered from this result as resistance goes to zero. In addition, we show numerical results for a Lagrangian algorithm of a rod waving in a porous medium and compare numerical results to asymptotic swimming speeds. [Preview Abstract] |
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