Rolling motion of a sphere on a plane boundary in oscillatory flow

Martin, C. Samuel; Padmanabhan, M.; Ponce‐Campos, C. David

doi:10.1017/s0022112076000839

Cited by 8 publications

(8 citation statements)

References 19 publications

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“…Particle motion in oscillating flows has generated a significant amount of research activity. In sinusoidal background flow, it has been shown that the free particle motion in the stationary regime is represented by a sinusoidal wave as assumed above (Chao 1968;Hinze 1975;Martin, Padmanabhan & Ponce-Campos 1976;Coimbra & Rangel 2001). The harmonic motion of a sphere in a quiescent fluid has also been investigated (Stokes 1850;Landau & Lifshitz 1959;Odar & Hamilton 1964) and since the motion of the sphere in this case is prescribed, these studies represent a starting point for studies of suspended particles that are free to move in oscillatory flow.…”

Section: Introductionmentioning

confidence: 93%

An experimental study on stationary history effects in high-frequency Stokes flows

et al. 2004

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We report results of a series of detailed experiments designed to unveil the dynamics of a particle of radius $a$ moving in high-frequency, low-Reynolds-number oscillatory flow. The fundamental parameters in the problem are the Strouhal ($\hbox{\it Sl}$) and the particle Reynolds numbers ($\hbox{\it Re}_p$), as well as the fluid-to-particle density ratio $\alpha$. The experiments were designed to cover a range of $\hbox{\it Sl} \hbox{\it Re}_p$ from 0.015 to 5 while keeping $\hbox{\it Re}_p < 0.5$ and $\hbox{\it Sl} > 1$. The primary objective of the experiments is to investigate stationary history effects associated with the Basset drag, which are maximized when the viscous time scale $a^2/\nu$ is of the same order of the flow time scale $9/\Omega$, where $9$ is a geometrical factor for the sphere, $\nu$ is the kinematic viscosity and $\Omega$ is the angular frequency of the background flow. The theoretically determined behaviour of stationary history effects is confirmed unequivocally by the experiments, which also validate the fractional derivative behaviour (of order $1/2$) of the history drag for the range of parameters under study.

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Section: Introductionmentioning

confidence: 93%

An experimental study on stationary history effects in high-frequency Stokes flows

et al. 2004

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“…However, Eq. ( 27) cannot hold when considering strongly nonlinear drag or turbulent flows (see, e.g., [28]). Nevertheless, a linear dependence of A * r on A * was previously observed in experiments [8,18].…”

Section: B Quantitative Description Of the Particle Trajectoriesmentioning

confidence: 99%

“…We here refrain from a further in-depth, quantitative analysis on the effect of particle rotation on the spacing of the gap. A good starting point for future studies would be to isolate the effect of rotation on the particle dynamics and steady streaming by examining a system with a single rotating sphere in an oscillating flow, similar to, e.g., [28].…”

Section: E Effect Of Particle Rotationmentioning

confidence: 99%

Numerical study of a pair of spheres in an oscillating box filled with viscous fluid

et al. 2022

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“…( 27) cannot hold when considering strongly nonlinear drag or turbulent flows, see e.g. [27]. Nevertheless, a linear dependence of A * r on A * was previously observed in experiments [8,18].…”

Section: B Quantitative Description Of the Particle Trajectoriesmentioning

confidence: 94%

Section: E Effect Of Particle Rotationmentioning

confidence: 99%

A numerical study of a pair of spheres in an oscillating box filled with viscous fluid

Overveld¹,

Shajahan²,

Breugem³

et al. 2021

Preprint

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When two spherical particles submerged in a viscous fluid are subjected to an oscillatory flow, they align themselves perpendicular to the direction of the flow leaving a small gap between them. The formation of this compact structure is attributed to a non-zero residual flow known as steady streaming. We have performed direct numerical simulations of a fully-resolved, oscillating flow in which the pair of particles is modeled using an immersed boundary method. Our simulations show that the particles oscillate both parallel and perpendicular to the oscillating flow in elongated figure 8 trajectories. In absence of bottom friction, the mean gap between the particles depends only on the normalized Stokes boundary layer thickness δ * , and on the normalized, streamwise excursion length of the particles relative to the fluid A * r (equivalent to the Keulegan-Carpenter number). For A * r 1, viscous effects dominate and the mean particle separation only depends on δ * . For larger A * r -values, advection becomes important and the gap widens. Overall, the normalized mean gap between the particles scales as L * ≈ 3.0δ * 1.5 + 0.03A * r 3 , which also agrees well with previous experimental results. The two regimes are also observed in the magnitude of the oscillations of the gap perpendicular to the flow, which increases in the viscous regime and decreases in the advective regime. When bottom friction is considered, particle rotation increases and the gap widens. Our results stress the importance of simulating the particle motion with all its degrees of freedom to accurately model the system and reproduce experimental results. The new insights of the particle pairs provide an important step towards understanding denser and more complex systems.

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Rolling motion of a sphere on a plane boundary in oscillatory flow

Cited by 8 publications

References 19 publications

An experimental study on stationary history effects in high-frequency Stokes flows

An experimental study on stationary history effects in high-frequency Stokes flows

Numerical study of a pair of spheres in an oscillating box filled with viscous fluid

A numerical study of a pair of spheres in an oscillating box filled with viscous fluid

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