The passive diffusion of<i>Leptospira interrogans</i>

Koens, Lyndon; Lauga, Eric

doi:10.1088/1478-3975/11/6/066008

Cited by 40 publications

(31 citation statements)

References 40 publications

(115 reference statements)

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“…A similar equivalence may be found for the torque per unit length generated from the surface rotation. For a cylindrical body, the surface velocity, surface traction, and torque per unit length, l(s), resulting from the local rotation Ωt are given by The above torque is identical to that derived from a line of singularities (Koens & Lauga 2014), showing again that the singularity and boundary integral representations capture the same physics in the slender-body limit.…”

Section: Totalmentioning

confidence: 73%

The boundary integral formulation of Stokes flows includes slender-body theory

2018

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The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds number problems analytically and computationally. Alternatively, one can solve the Stokes equations by using an appropriate distribution of flow singularities of the right strength within the boundary, a method particularly useful to describe the dynamics of long slender objects for which the numerical implementation of the BI representation becomes cumbersome. While the BI approach is a mathematical consequence of the Stokes equations, the singularity method involves making judicious guesses that can only be justified a posteriori. In this paper we use matched asymptotic expansions to derive an algebraically accurate slender-body theory directly from the BI representation able to handle arbitrary surface velocities and surface tractions. This expansion procedure leads to sets of uncoupled linear equations and to a single one-dimensional integral equation identical to that derived by Keller & Rubinow (1976) and Johnson (1979) using the singularity method. Hence we show that it is a mathematical consequence of the BI approach that the leading-order flow around a slender body can be represented using a distribution of singularities along its centreline. Furthermore when derived from either the single-layer or double-layer modified BI representation, general slender solutions are only possible in certain types of flow, in accordance with the limitations of these representations. † Email: e.lauga@damtp.cam.ac.uk arXiv:1806.04192v1 [physics.flu-dyn] 11 Jun 2018 † The integration factor is obtained by recognising that ∂sS(s, θ) =t(s) + ∂s[ρ(s)êρ(s, θ)], ∂ θ S(s, θ) = ρ(s)∂ θêρ (s, θ), andt × ∂ θêρ = −êρ and performing a Taylor expansion in .

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Section: Totalmentioning

confidence: 73%

The boundary integral formulation of Stokes flows includes slender-body theory

2018

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“…At χ = χ 0 , the analytical theory breaks down, and higher-order terms should be retained in Eqs.(33)-(35). We did not explore this regime as we do not expect the resistive force theory to be sufficiently accurate at such high values of χ [22][23][24][25].…”

Section: Approximate Solution For Long Helicesmentioning

confidence: 99%

Sedimentation of a rigid helix in viscous media

et al. 2018

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We consider sedimentation of a rigid helical filament in a viscous fluid under gravity. In the Stokes limit, the drag forces and torques on the filament are approximated within the resistiveforce theory. We develop an analytic approximation to the exact equations of motion that works well in the limit of a sufficiently large number of turns in the helix (larger than two, typically). For a wide range of initial conditions, our approximation predicts that the centre of the helix itself follows a helical path with the symmetry axis of the trajectory being parallel to the direction of gravity.The radius and the pitch of the trajectory scale as non-trivial powers of the number of turns in the original helix. For the initial conditions corresponding to an almost horizontal orientation of the helix, we predict trajectories that are either attracted towards the horizontal orientation, in which case the helix sediments in a straight line along the direction of gravity, or trajectories that form a helical-like path with many temporal frequencies involved. Our results provide new insight into the sedimentation of chiral objects and might be used to develop new techniques for their spatial separation. * alexander.morozov@ed.ac.uk 1 arXiv:1811.08491v1 [physics.flu-dyn]

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“…The centerline bending condition here is identical to that required in the framework of SBT. We note that SBT has been used very successfully in applications where this curvature condition has been broken 25 . Therefore slender-ribbon theory could also work when κ or σ are large but the results should be viewed with caution as they are formally outside the expected domain of validity.…”

Section: Middle Regionmentioning

confidence: 99%

Slender-ribbon theory

Koens

Lauga

2016

Physics of Fluids

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Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example when a ribbon has half a twist and is bent into a circle it produces a Möbius strip. Significant effort has gone into determining the structural shapes of ribbons but less is know about their behavior in viscous fluids. In this paper we determine, asymptotically, the leading-order hydrodynamic behavior of a slender ribbon in Stokes flows. The derivation, reminiscent of slender-body theory for filaments, assumes that the length of the ribbon is much larger than its width, which itself is much larger than its thickness. The final result is an integral equation for the force density on a mathematical ruled surface, termed the ribbon plane, located inside the ribbon. A numerical implementation of our derivation shows good agreement with the known hydrodynamics of long flat ellipsoids, and successfully captures the swimming behavior of artificial microscopic swimmers recently explored experimentally. We also study the asymptotic behavior of a ribbon bent into a helix, that of a twisted ellipsoid, and we investigate how accurately the hydrodynamics of a ribbon can be effectively captured by that of a slender filament. Our asymptotic results provide the fundamental framework necessary to predict the behavior of slender ribbons at low Reynolds numbers in a variety of biological and engineering problems.a)

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The passive diffusion ofLeptospira interrogans

Cited by 40 publications

References 40 publications

The boundary integral formulation of Stokes flows includes slender-body theory

The boundary integral formulation of Stokes flows includes slender-body theory

Sedimentation of a rigid helix in viscous media

Slender-ribbon theory

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