Optimal Strokes for Low Reynolds Number Swimmers: An Example

Alouges, François; DeSimone, Antonio; Lefebvre, Aline

doi:10.1007/s00332-007-9013-7

Cited by 138 publications

(201 citation statements)

References 14 publications

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“…Function G 123 (4.3) was introduced by Golestanian & Ajdari (2008) and studied by Alouges et al (2008), Alexander et al (2009) and Golestanian & Ajdari (2009) in the context of a three-sphere micro-robot. We call G ikl a Golestanian function.…”

Section: Self-propulsion Velocitymentioning

confidence: 99%

“…Studies of micro-robots represent a flourishing modern research topic that strives to create a fundamental base for modern applications in medicine and technology, see Purcell (1977), Becker, Koelher & Ryder (2003), Najafi & Golestanian (2004), Dreyfus et al (2005), Chang et al (2007), Earl et al (2007), Alouges, DeSimone & Lefebvre (2008), Golestanian & Ajdari (2008, 2009, Leoni et al (2009), Alexander, Pooley & Yeomans (2009), Gilbert et al (2010) and Lauga (2011). The simplicity of the geometry represents the major advantage in studies of micro-robots (in contrast with the extreme complexity of self-swimming micro-organisms, e.g.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the self-propulsion of an -sphere micro-robot

Vladimirov

2013

J. Fluid Mech.

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The aim of this paper is to describe the self-propulsion of a micro-robot (or microswimmer) consisting of N spheres moving along a fixed line. The spheres are linked to each other by arms with their lengths changing periodically. We use the asymptotic procedure containing the two-timing method and a distinguished limit. We show that self-propulsion velocity appears (in the main approximation) as a linear combination of velocities of all possible triplets of spheres. Velocities and efficiencies of three-, fourand five-sphere swimmers are calculated.

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Section: Self-propulsion Velocitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the self-propulsion of an -sphere micro-robot

Vladimirov

2013

J. Fluid Mech.

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“…In recent papers, many mathematicians have studied the hydro dynamic interactions between close particles immersed in a Stokes uid to simulate the motions of nano scale swimmers robots which is designed from nano-sized medical devices (see [2], [3] and references therein). One of the main di culties is to compute the total forces and torques exerted by the particles.…”

Section: Introductionmentioning

confidence: 99%

“…The surface density of force exerted on the uid at some point x of the surface ∂B i is given by f i (x) = ∇u + ∇u T − pId .n i , (3) where n i denotes the exterior normal on the surface of the particle B i . The total force and total torque exerted by the particle B i on the uid are given by the following formulas,…”

Section: Introductionmentioning

confidence: 99%

Numerical Determination of Truncation Orders in the Correction Method for Stokes Equations

Tran

Nguyen

2018

J. ADV. ENG. COMPUT.

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Abstract. In [15], the authors propose an accurate method, namely the correction method, for computing hydrodynamic interaction between very closed spherical particles in a Stokes uid. The accuracy of this method depends on two truncation parameters for approximating the Neumann to Dirichlet matrix and the velocity correction respectively. In this paper, we establish a numerical determination to estimate these parameters. We perform some numerical experiments to present our method.

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“…A comprehensive study of group micro-organism propulsion has been made by Koch and Subramanian [29] demonstrating that spontaneous motions may occur in systems of organisms induced by the coupling between the stresses generated by bacteria while swimming in fluids and furthermore the rotary motions of the bacteria arising as a result of the associated hydrodynamic disturbances. Further studies include the detailed simulations reported by Alouges et al [30] dwelling on viscous-dominated optimization of micro-organism propulsion, Alouges et al [31] concerning hydrodynamic efficiency of axisymmetric swimming of bacteria and Dal Maso et al…”

Section: Introductionmentioning

confidence: 99%

Bacterial gliding fluid dynamics on a layer of non-Newtonian slime: Perturbation and numerical study

Ali

Asghar

Bég

et al. 2016

Journal of Theoretical Biology

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Abstract:Gliding bacteria are an assorted group of rod-shaped prokaryotes that adhere to and glide on certain layers of ooze slime attached to a substratum. Due to the absence of organelles of motility, such as flagella, the gliding motion is caused by the waves moving down the outer surface of these rodshaped cells. In the present study we employ an undulating surface model to investigate the motility of bacteria on a layer of non-Newtonian slime. The rheological behavior of the slime is characterized by an appropriate constitutive equation, namely the Carreau model. Employing the balances of mass and momentum conservation, the hydrodynamic undulating surface model is transformed into a fourth-order nonlinear differential equation in terms of a stream function under the long wavelength assumption. A perturbation approach is adopted to obtain closed form expressions for stream function, pressure rise per wavelength, forces generated by the organism and power required for propulsion. A numerical technique based on an implicit finite difference scheme is also employed to investigate various features of the model for large values of the rheological parameters of the slime. Verification of the numerical solutions is achieved with a variational finite element method (FEM). The computations demonstrate that the speed of the glider decreases as the rheology of the slime changes from shear-thinning (pseudo-plastic) to shear-thickening (dilatant). Moreover, the viscoelastic nature of the slime tends to increase the swimming speed for the shear-thinning case. The fluid flow in the pumping (generated where the organism is not free to move but instead generates a net fluid flow beneath it) is also investigated in detail. The study is relevant to marine anti-bacterial fouling and medical hygiene biophysics.

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Optimal Strokes for Low Reynolds Number Swimmers: An Example

Cited by 138 publications

References 14 publications

On the self-propulsion of an -sphere micro-robot

On the self-propulsion of an -sphere micro-robot

Numerical Determination of Truncation Orders in the Correction Method for Stokes Equations

Bacterial gliding fluid dynamics on a layer of non-Newtonian slime: Perturbation and numerical study

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