| 1. |
- Candelier, F., et al.
(författare)
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Inertial torque on a squirmer
- 2022
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 953
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Tidskriftsartikel (refereegranskat)abstract
- A small spheroid settling in a quiescent fluid experiences an inertial torque that aligns it so that it settles with its broad side first. Here we show that an active particle experiences such a torque too, as it settles in a fluid at rest. For a spherical squirmer, the torque is T '=-9/8m(f)(v(s)((0) )boolean AND v(g)((0))) where v(s)((0) )is the swimming velocity, v(g)((0)) is the settling velocity in the Stokes approximation and mf is the equivalent fluid mass. This torque aligns the swimming direction against gravity: swimming up is stable, swimming down is unstable.
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| 2. |
- Candelier, F., et al.
(författare)
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Role of inertia for the rotation of a nearly spherical particle in a general linear flow
- 2015
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 91:5
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the angular dynamics of a neutrally buoyant, nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, a regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and by assuming that inertial effects are small but finite.
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| 3. |
- Candelier, F., et al.
(författare)
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Second-order inertial forces and torques on a sphere in a viscous steady linear flow
- 2023
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 954
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Tidskriftsartikel (refereegranskat)abstract
- We compute the full set of second-order inertial corrections to the instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in a general steady linear flow. This is achieved by using matched asymptotic expansions and formulating the problem in a coordinate system co-moving with the background flow. Effects of unsteadiness and fluid-velocity gradients are assumed to be small, but to dominate in the far field over those of the velocity difference between the body and fluid, making the results essentially relevant to weakly positively or negatively buoyant particles. The outer solution (which at first order is responsible for the Basset-Boussinesq history force at short time and for shear-induced forces such as the Saffman lift force at long time) is expressed via a flow-dependent tensorial kernel. The second-order inner solution brings a number of different contributions to the force and torque. Some are proportional to the relative translational or angular acceleration between the particle and fluid, while others take the form of products of the rotation/strain rate of the background flow and the relative translational or angular velocity between the particle and fluid. Adding the outer and inner contributions, the known added-mass force or the spin-induced lift force are recovered, and new effects involving the velocity gradients of the background flow are revealed. The resulting force and torque equations provide a rational extension of the classical Basset-Boussinesq-Oseen equation incorporating all first- and second-order fluid inertia effects resulting from both unsteadiness and velocity gradients of the carrying flow.
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| 4. |
- Candelier, F., et al.
(författare)
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Settling of an asymmetric dumbbell in a quiescent fluid
- 2016
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 802, s. 174-185
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Tidskriftsartikel (refereegranskat)abstract
- We compute the hydrodynamic torque on a dumbbell (two spheres linked by a massless rigid rod) settling in a quiescent fluid at small but finite Reynolds number. The spheres have the same mass densities but different sizes. When the sizes are quite different, the dumbbell settles vertically, aligned with the direction of gravity, the largest sphere first. But when the size difference is sufficiently small, then its steady-state angle is determined by a competition between the size difference and the Reynolds number. When the sizes of the spheres are exactly equal, then fluid inertia causes the dumbbell to settle in a horizontal orientation.
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| 5. |
- Candelier, F., et al.
(författare)
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Time-dependent lift and drag on a rigid body in a viscous steady linear flow
- 2019
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 864, s. 554-595
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Tidskriftsartikel (refereegranskat)abstract
- 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 square root of the Reynolds number based on the fluid-velocity gradient is much larger than the Reynolds number based on the slip velocity between the body and the fluid. As a first step towards applications to dilute sheared suspensions and turbulent particle-laden flows, we seek a formulation allowing this force to be determined for an arbitrarily shaped 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.
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| 6. |
- Collins, D., et al.
(författare)
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Lord Kelvin's isotropic helicoid
- 2021
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Ingår i: Physical Review Fluids. - 2469-990X. ; 6:7
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Tidskriftsartikel (refereegranskat)abstract
- Nearly 150 years ago, Lord Kelvin proposed the isotropic helicoid, a particle with isotropic yet chiral interactions with a fluid so that translation couples to rotation. An implementation of his design fabricated with a three-dimensional printer is found experimentally to have no detectable translation-rotation coupling, although the particle point-group symmetry allows this coupling. We explain these results by demonstrating that in Stokes flow, the chiral coupling of such isotropic helicoids made out of nonchiral vanes is due only to hydrodynamic interactions between these vanes. Therefore it is small. In summary, Kelvin's predicted isotropic helicoid exists, but only as a weak breaking of a symmetry of noninteracting vanes in Stokes flow.
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| 7. |
- Einarsson, Jonas, et al.
(författare)
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Rotation of a spheroid in a simple shear at small Reynolds number
- 2015
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Ingår i: Physics of Fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 27:6
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Tidskriftsartikel (refereegranskat)abstract
- 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 and log-rolling is unstable. For oblate spheroids, by contrast, log-rolling is stable and tumbling is unstable provided that the particle is not too disk-like (moderate asphericity). For very flat oblate spheroids, both log-rolling and tumbling are stable, separated by an unstable limit cycle.
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| 8. |
- Mehaddi, R., et al.
(författare)
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Inertial drag on a sphere settling in a stratified fluid
- 2018
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 855, s. 1074-1087
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Tidskriftsartikel (refereegranskat)abstract
- We compute the drag force on a sphere settling slowly in a quiescent, linearly stratified fluid. Stratification can significantly enhance the drag experienced by the settling particle. The magnitude of this effect depends on whether fluid-density transport around the settling particle is due to diffusion, to advection by the disturbance flow caused by the particle or due to both. It therefore matters how efficiently the fluid disturbance is convected away from the particle by fluid-inertial terms. When these terms dominate, the Oseen drag force must be recovered. We compute by perturbation theory how the Oseen drag is modified by diffusion and stratification. Our results are in good agreement with recent direct numerical simulation studies of the problem.
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| 9. |
- Meibohm, J., et al.
(författare)
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Angular velocity of a sphere in a simple shear at small Reynolds number
- 2016
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Ingår i: Physical Review Fluids. - : university of teheran. - 2469-990X. ; 1:8
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the angular velocity of a small neutrally buoyant spheroid log rolling in a simple shear. When the effect of fluid inertia is negligible the angular velocity. equals half the fluid vorticity. We compute by singular perturbation theory how weak fluid inertia reduces the angular velocity in an unbounded shear, and how this reduction depends upon the shape of the spheroid (on its aspect ratio). In addition we determine the angular velocity by direct numerical simulations. The results are in excellent agreement with the theory at small but not too small values of the shear Reynolds number Res, for all aspect ratios considered. For the special case of a sphere we find omega/s = -1/2 + 0.0540 Re-s(3/2) where s is the shear rate. The O( Re-s(3/2)) correction differs from that derived by Lin et al. who obtained a numerical coefficient roughly three times larger.
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| 10. |
- Meibohm, Jan, et al.
(författare)
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Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number
- 2016
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Ingår i: Physical Review Fluids. - 2469-990X. ; 1:8
-
Tidskriftsartikel (refereegranskat)abstract
- We analyse the angular velocity of a small neutrally buoyant spheroid log rolling in a simple shear. When the effect of fluid inertia is negligible the angular velocity ω equals half the fluid vorticity. We compute by singular perturbation theory how weak fluid inertia reduces the angular velocity in an unbounded shear, and how this reduction depends upon the shape of the spheroid (on its aspect ratio). In addition we determine the angular velocity by direct numerical simulations. The results are in excellent agreement with the theory at small but not too small values of the shear Reynolds number, for all aspect ratios considered. For the special case of a sphere we find ω/s=−1/2+0.0540 Re_s^3/2 where s is the shear rate, and Re_s is the shear Reynolds number. This result differs from that derived by Lin et al. [J. Fluid Mech. 44 (1970) 1] who obtained a numerical coefficient roughly three times larger.
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