Swimming speeds of filaments in nonlinearly viscoelastic fluids

Fu, Henry; Wolgemuth, Charles W.; Powers, Thomas

doi:10.1063/1.3086320

Cited by 164 publications

(165 citation statements)

References 31 publications

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“…The importance of elastic effects are quantified by the Deborah number De, defined as the ratio of the relaxation time τ of the fluid to the characteristic time scale of the swimmer. For an infinite sheet or filament deformed by low-amplitude traveling waves and suspended in a dilute polymer solution described by the Oldroyd-B model, the swimming speed is always less than the Newtonian speed and decreases with increasing Deborah number (7)(8)(9). These theoretical predictions agree roughly with the measurements of swimming C. elegans (6).…”

supporting

confidence: 80%

Force-free swimming of a model helical flagellum in viscoelastic fluids

Liu

Powers

Breuer

2011

Proc. Natl. Acad. Sci. U.S.A.

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We precisely measure the force-free swimming speed of a rotating helix in viscous and viscoelastic fluids. The fluids are highly viscous to replicate the low Reynolds number environment of microorganisms. The helix, a macroscopic scale model for the bacterial flagellar filament, is rigid and rotated at a constant rate while simultaneously translated along its axis. By adjusting the translation speed to make the net hydrodynamic force vanish, we measure the forcefree swimming speed as a function of helix rotation rate, helix geometry, and fluid properties. We compare our measurements of the force-free swimming speed of a helix in a high-molecular weight silicone oil with predictions for the swimming speed in a Newtonian fluid, calculated using slender-body theories and a boundary-element method. The excellent agreement between theory and experiment in the Newtonian case verifies the high accuracy of our experiments. For the viscoelastic fluid, we use a polymer solution of polyisobutylene dissolved in polybutene. This solution is a Boger fluid, a viscoselastic fluid with a shear-rateindependent viscosity. The elasticity is dominated by a single relaxation time. When the relaxation time is short compared to the rotation period, the viscoelastic swimming speed is close to the viscous swimming speed. As the relaxation time increases, the viscoelastic swimming speed increases relative to the viscous speed, reaching a peak when the relaxation time is comparable to the rotation period. As the relaxation time is further increased, the viscoelastic swimming speed decreases and eventually falls below the viscous swimming speed. motility | propulsion | rheology S mall motile organisms often swim in complex fluids. Mammalian spermatozoa beat their flagella to move through cervical fluid (1). The Lyme disease spirochete Borrelia burgdorferi flexes and rotates its body to move through the extracellular matrix of our skin (2). The nematode Caenorhabditis elegans undulates its body to move through soil saturated with water (3). While there is an extensive framework for understanding the mechanics of swimming of small organisms in purely viscous Newtonian liquids such as water, our understanding of the basic principles of swimming in non-Newtonian fluids is still in its infancy (4). The behavior of complex fluids is varied, and there are many possible nonNewtonian effects a swimmer could encounter, including elastic response of the fluid, shear-dependent viscosity, adhesion to suspended particles or fibers, or the permeability of a porous medium. In this article we focus on swimming in an elastic liquid, and our goal is to determine how the speed of a model bacterial swimmer is changed by elastic effects.It is known that helically shaped bacteria such as Leptospira or B. burgdorferi swim more rapidly in solutions with methylcellulose than in nonviscoelastic solutions of the same viscosity (2, 5). On the other hand, C. elegans, which moves using planar undulations of its body, swims more slowly in a viscoelastic fluid than in a vi...

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supporting

confidence: 80%

Force-free swimming of a model helical flagellum in viscoelastic fluids

Liu

Powers

Breuer

2011

Proc. Natl. Acad. Sci. U.S.A.

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195

167

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“…There, it was shown that, for fixed swimming kinematics, the swimming speed for the swimming sheet systematically decreases compared to the Newtonian case for all Oldroyd-type fluids to leading order in smallamplitude waveforms. Subsequently the same result was obtained for planar undulating filaments [33] and helical waves [34] in Oldroyd-B fluids.…”

Section: Infinite Modelssupporting

confidence: 60%

“…In contrast, prior asymptotic analysis by Fu et al [34] showed that, like the swimming sheet, the leading-order swimming speed (in a small-amplitude perturbation series) of a body propagating helical waves in an Oldroyd-B fluid is always slower than in a non-Newtonian fluid. This discrepancy between the small-amplitude asymptotics and large-amplitude experiments was resolved in numerical work by Spagnolie et al for a helix in an Oldroyd-B fluid [37].…”

Section: B Large-amplitude Deformationsmentioning

confidence: 58%

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Theory of Locomotion Through Complex Fluids

Elfring

Lauga

2014

Complex Fluids in Biological Systems

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Microorganisms such as bacteria often swim in fluid environments that cannot be classified as Newtonian. Many biological fluids contain polymers or other heterogeneities which may yield complex rheology. For a given set of boundary conditions on a moving organism, flows can be substantially different in complex fluids, while non-Newtonian stresses can alter the gait of the microorganisms themselves. Heterogeneities in the fluid may also be characterized by length scales on the order of the organism itself leading to additional dynamic complexity. In this chapter we present a theoretical overview of small-scale locomotion in complex fluids with a focus on recent efforts quantifying the impact of non-Newtonian rheology on swimming microorganisms.

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“…One exception is the literature on swimmers wherein models have been developed for a single organism or a few organisms that propel themselves in viscous [48][49][50][51][52][53][54][55][56][57][58] and non-Newtonian fluids [57,[59][60][61][62][63][64][65][66][67]. In particular, swarming hydrodynamic theories have been derived wherein swimmer densities with or without fluid flows are described as continuous fields [4,19,68,69].…”

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confidence: 99%

Swarming in viscous fluids: Three-dimensional patterns in swimmer- and force-induced flows

2016

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We derive a three-dimensional theory of self-propelled particle swarming in a viscous fluid environment. Our model predicts emergent collective behavior that depends critically on fluid opacity, mechanism of self-propulsion, and type of particle-particle interaction. In "clear fluids" swimmers have full knowledge of their surroundings and can adjust their velocities with respect to the lab frame, while in "opaque fluids" they control their velocities only in relation to the local fluid flow. We also show that "social" interactions that affect only a particle's propensity to swim towards or away from neighbors induces a flow field that is qualitatively different from the long-ranged flow fields generated by direct "physical" interactions. The latter can be short-ranged but lead to much longer-ranged fluid-mediated hydrodynamic forces, effectively amplifying the range over which particles interact. These different fluid flows conspire to profoundly affect swarm morphology, kinetically stabilizing or destabilizing swarm configurations that would arise in the absence of fluid. Depending upon the overall interaction potential, the mechanism of swimming ( e.g., pushers or pullers), and the degree of fluid opaqueness, we discover a number of new collective three-dimensional patterns including flocks with prolate or oblate shapes, recirculating pelotonlike structures, and jetlike fluid flows that entrain particles mediating their escape from the center of mill-like structures. Our results reveal how the interplay among general physical elements influence fluid-mediated interactions and the self-organization, mobility, and stability of new three-dimensional swarms and suggest how they might be used to kinetically control their collective behavior. DOI: 10.1103/PhysRevE.93.043112 The collective behavior of self-propelled agents in natural and artificial systems has been extensively studied . Many of the lessons learned from experimental and theoretical work conducted on organisms as diverse as bacteria, ants, locusts, and birds [23][24][25][26][27][28][29][30][31][32][33][34][35][36] have been successfully applied to engineered robotic systems to help frame decentralized control strategies through ad hoc algorithms [37][38][39][40][41][42][43][44]. In most mathematical "swarming" models, particles are assumed to be self-driven by internal mechanisms that impart a characteristic speed. A pairwise short-ranged repulsion and a long-ranged decaying attraction are typically employed as the most realistic choices when modeling aggregating particles [9,11,45]. The interplay between self-propulsion, particle interactions, initial conditions, and number of particles is key in determining the large scale patterns that dynamically arise. In two dimensions, rotating mills and translating flocks are often observed, the latter configuration also arising in three dimensions [9,10,17,19,46,47]. It is possible to classify swarm morphology in terms of interaction strength and length scales, as shown for particles coupled via conserved f...

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Swimming speeds of filaments in nonlinearly viscoelastic fluids

Cited by 164 publications

References 31 publications

Force-free swimming of a model helical flagellum in viscoelastic fluids

Force-free swimming of a model helical flagellum in viscoelastic fluids

Theory of Locomotion Through Complex Fluids

Swarming in viscous fluids: Three-dimensional patterns in swimmer- and force-induced flows

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