Role of inertia for the rotation of a nearly spherical particle in a general linear flow

Candelier, Fabien; Einarsson, Jonas; Lundell, Fredrik; Mehlig, B.; Angilella, Jean-Régis

doi:10.1103/physreve.91.053023

Cited by 21 publications

(25 citation statements)

References 12 publications

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“…22 The results of this calculation agree to order ϵ with the results presented above. Further, we have checked that the particle-inertia correction in Eq.…”

Section: B Linear Stability Analysis At Infinitesimal Re Ssupporting

confidence: 80%

Rotation of a spheroid in a simple shear at small Reynolds number

et al. 2015

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We derive an effective equation of motion for the orientational dynamics of a neutrally buoyant spheroid suspended in a simple shear flow, valid for arbitrary particle aspect ratios and to linear order in the shear Reynolds number. We show how inertial effects lift the degeneracy of the Jeffery orbits and determine the stabilities of the log-rolling and tumbling orbits at infinitesimal shear Reynolds numbers. For prolate spheroids we find stable tumbling in the shear plane, log-rolling is unstable. For oblate particles, by contrast, log-rolling is stable and tumbling is unstable provided that the aspect ratio is larger than a critical value. When the aspect ratio is smaller than this value tumbling turns stable, and an unstable limit cycle is born.

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“…22 The results of this calculation agree to order ϵ with the results presented above. Further, we have checked that the particle-inertia correction in Eq.…”

Section: B Linear Stability Analysis At Infinitesimal Re Ssupporting

confidence: 80%

Rotation of a spheroid in a simple shear at small Reynolds number

et al. 2015

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“…Influence of the body inertia in the case where the particle stands close to a wall also induces dramatic changes because, combined with the wall-particle hydrodynamic interaction, it induces a drift of the particle towards the wall (Gavze & Shapiro 1998). Small-but-finite fluid inertia effects are known to affect the hydrodynamic torque and angular motion in such a way that the marginal stability of the Jeffery orbits of spheroidal particles is broken (Subramanian & Koch 2005;Einarsson et al 2015a;Candelier et al 2015;Rosen et al 2015;Dabade et al 2016); these conclusions were recently extended to an arbitrary linear flow field (Marath & Subramanian 2018). Unsteady fluid inertia effects have also been shown to make a significant contribution to the body-shape dependence of the stability exponents of the Jeffery orbits (Einarsson et al 2015b).…”

Section: Influence Of Small Inertia Effects On the Sedimentation Of Nmentioning

confidence: 99%

Time-dependent lift and drag on a rigid body in a viscous steady linear flow

2019

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We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the variation of the undisturbed flow at the body scale is much larger than the slip velocity between the body and the fluid. Motivated by applications to turbulent particleladen flows, we seek a formulation allowing this force to be determined for an arbitrarilyshaped body moving in a general linear flow. We express the equations governing the flow disturbance in a non-orthogonal coordinate system moving with the undisturbed flow and solve the problem using matched asymptotic expansions. The use of the co-moving coordinates enables the leading-order inertial corrections to the force to be obtained at any time in an arbitrary linear flow field. We then specialize this approach to compute the time-dependent force components for a sphere moving in three canonical flows: solid body rotation, planar elongation, and uniform shear. We discuss the behaviour and physical origin of the different force components in the short-time and quasi-steady limits. Last, we illustrate the influence of time-dependent and quasi-steady inertial effects by examining the sedimentation of prolate and oblate spheroids in a pure shear flow. arXiv:1806.05734v1 [physics.flu-dyn]

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“…Ding and Aidun [23] showed through direct numerical simulations that the period of a prolate spheroid diverges for higher Reynolds numbers as the particle remains motionless when it is nearly aligned with the flow direction. Recently, Einarsson et al [24][25][26][27][28][29] have shown theoretically that in the limit of weak flow and particle inertia, the degeneracy of Jeffery orbits is indeed lifted. The first effects due to weak inertia cause a prolate spheroid in simple shear to drift to a stable tumbling limit cycle, whatever the initial condition [24].…”

Section: Introductionmentioning

confidence: 99%

Jeffery orbits in shear-thinning fluids

Abtahi

Elfring

2019

Physics of Fluids

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We investigate the dynamics of a prolate spheroid in a shear flow of a shear-thinning Carreau fluid. The motion of a prolate particle is developed analytically for asymptotically weak shear thinning and then integrated numerically. We find that shear-thinning rheology does not lift the degeneracy of Jeffery orbits observed in Newtonian fluids but the instantaneous rate of rotation and trajectories of the orbits are modified. Qualitatively, shear thinning has a similar effect to elongating the particle in a Newtonian fluid. The period of rotation increases as the particle slows down more when aligned with the flow due to a reduction of shear stresses. Unlike Jeffery orbits in Newtonian fluids, in shear-thinning fluids the period of orbits depends on the specific trajectory (or initial orientation of the particle). * gelfring@mech.ubc.ca arXiv:1908.08687v2 [physics.flu-dyn]

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Role of inertia for the rotation of a nearly spherical particle in a general linear flow

Cited by 21 publications

References 12 publications

Rotation of a spheroid in a simple shear at small Reynolds number

Rotation of a spheroid in a simple shear at small Reynolds number

Time-dependent lift and drag on a rigid body in a viscous steady linear flow

Jeffery orbits in shear-thinning fluids

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