2011
DOI: 10.1137/100808745
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Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall

Abstract: Abstract. The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a boundary has a significant influence on the swimmer's trajectories and poses problems of dynamic stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near a wall, study… Show more

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Cited by 26 publications
(19 citation statements)
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References 70 publications
(88 reference statements)
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“…The induction of the flow, by which we mean the imposition of a controlled background ambient flow, is widely used as a A treadmilling microswimmer near a no-slip wall in simple shear 649 oscillatory periodic motion of the swimmer along the wall, and this behaviour was later shown to be qualitatively the same as that described by analytical solutions that fully describe such a circular treadmiller near the wall without any need for a singularity approximation (Crowdy 2011). Qualitatively similar nonlinear periodic motions have been found in a three-sphere swimmer (Or, Zhang & Murray 2011), a spheroidal squirmer (Ishimoto & Gaffney 2013) and in experiments , which provides evidence that even idealized two-dimensional models can provide useful insights into more complicated three-dimensional dynamics in certain situations, especially when the physical source of the observed dynamics is not clear. More recently, simple two-dimensional swimmer models have been used to study self-diffusiophoretic Janus particles near a wall (Crowdy 2013), swimmer-swimmer interactions in a film (Clarke, Finn & MacDonald 2014) and wall-bounded motion of swimmers incorporating viscoelastic effects (Yazdi, Ardekani & Borham 2014.…”
Section: Introductionmentioning
confidence: 69%
“…The induction of the flow, by which we mean the imposition of a controlled background ambient flow, is widely used as a A treadmilling microswimmer near a no-slip wall in simple shear 649 oscillatory periodic motion of the swimmer along the wall, and this behaviour was later shown to be qualitatively the same as that described by analytical solutions that fully describe such a circular treadmiller near the wall without any need for a singularity approximation (Crowdy 2011). Qualitatively similar nonlinear periodic motions have been found in a three-sphere swimmer (Or, Zhang & Murray 2011), a spheroidal squirmer (Ishimoto & Gaffney 2013) and in experiments , which provides evidence that even idealized two-dimensional models can provide useful insights into more complicated three-dimensional dynamics in certain situations, especially when the physical source of the observed dynamics is not clear. More recently, simple two-dimensional swimmer models have been used to study self-diffusiophoretic Janus particles near a wall (Crowdy 2013), swimmer-swimmer interactions in a film (Clarke, Finn & MacDonald 2014) and wall-bounded motion of swimmers incorporating viscoelastic effects (Yazdi, Ardekani & Borham 2014.…”
Section: Introductionmentioning
confidence: 69%
“…Other examples include the confirmation that detailed flagellar regulation is not required to bring a sperm cell close to a surface [24,25], although a wave form regulation, known as hyperactivation, appears to encourage surface escape [19]. Further studies have also explored the boundary dynamics of idealized swimmers and prospective engineered swimmers [26][27][28], often via the use of dynamical systems ideas [27], and have for instance illustrated that height oscillations above the surface are possible for inertialess swimmers [27], though this has not been predicted by sperm or bacterial modeling to date.…”
Section: Introductionmentioning
confidence: 99%
“…To rationalize this behaviour using simple mathematical models, Crowdy & Or [7] have proposed the study of a simple circular ‘treadmiller’ comprising a cylindrical circular swimmer with an imposed tangential velocity profile; this profile actuates motion in the spirit of an ‘envelope model’ of surface ciliatory motion [14]. Crowdy & Or [7] showed that, in free space, such a swimmer has the singularity distribution comprising a torque-free stresslet and a superposed irrotational quadrupole; as an approximation, they studied the motion of such a singularity combination near a straight no-slip wall and found good qualitative agreement with numerical [12] and laboratory [15] experiments. Davis & Crowdy [4] have since found the general evolution equations for the same swimmer correct to , where ϵ is the swimmer radius.…”
Section: Application: Microswimmers In a Channelmentioning
confidence: 99%