| 1. |
- 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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| 2. |
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| 3. |
- 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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| 4. |
- Redaelli, T., et al.
(författare)
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Hydrodynamic force on a small squirmer moving with a time-dependent velocity at small Reynolds numbers
- 2023
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Ingår i: Journal of Fluid Mechanics. - 0022-1120. ; 973
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Tidskriftsartikel (refereegranskat)abstract
- We calculate the hydrodynamic force on a small spherical, unsteady squirmer moving with a time-dependent velocity in a fluid at rest, taking into account convective and unsteady fluid inertia effects in perturbation theory. Our results generalise those of Lovalenti & Brady (J. Fluid Mech., vol. 256, 1993, pp. 561-605) from passive to active spherical particles. We find that convective inertia changes the history contribution to the hydrodynamic force, as it does for passive particles. We determine how the hydrodynamic force depends on the swimming gait of the unsteady squirmer. Since swimming breaks the spherical symmetry of the problem, the force is not determined completely by the outer solution of the asymptotic matching problem, as it is for passive spheres. There are additional contributions due to the inhomogeneous solution of the inner problem. We also compute the disturbance flow, illustrating convective and unsteady effects when the particle experiences a sudden start followed by a sudden stop.
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| 5. |
- Redaelli, T., et al.
(författare)
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Unsteady and inertial dynamics of a small active particle in a fluid
- 2022
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Ingår i: Physical Review Fluids. - 2469-990X. ; 7:4
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for nonmotile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows us, for example, to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.
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