44 research outputs found
Dataset for Settling behaviour of thin curved particles in quiescent fluid and turbulence
No full textThis dataset contains the experimental data and a MATLAB script that enables the reproduction of the figures in: Timothy T.K. Chan, Luis Blay Esteban, Sander G. Huisman, John Shrimpton and Bharathram Ganapathisubramani. Settling behaviour of thin curved particles in quiescent fluid and turbulence. Journal of Fluid Mechanics.
DOI: 10.1017/jfm.2021.520
Data.mat contains three structures: 'Quiescent', 'Turb', and 'PIV'. They represent data of the quiescent cases, the turbulent cases, and PIV respectively. The list below documents the contents of 'Quiescent and 'Turb'. Unless otherwise specified, these fields are present in 'Quiescent' and 'Turb'.
</span
Settling behaviour of thin curved particles in quiescent fluid and turbulence
No full textThe motion of thin curved falling particles is ubiquitous in both nature and industry but is not yet widely examined. Here, we describe an experimental study on the dynamics of thin cylindrical shells resembling broken bottle fragments settling through quiescent fluid and homogeneous anisotropic turbulence. The particles have Archimedes numbers based on the mean descent velocity 0.75×104≲Ar≲2.75×104. Turbulence reaching a Reynolds number of Reλ≈100 is generated in a water tank using random jet arrays mounted in a coplanar configuration. After the flow becomes statistically stationary, a particle is released and its three-dimensional motion is recorded using two orthogonally positioned high-speed cameras. We propose a simple pendulum model that accurately captures the velocity fluctuations of the particles in still fluid and find that differences in the falling style might be explained by a closer alignment between the particle's pitch angle and its velocity vector. By comparing the trajectories under background turbulence with the quiescent fluid cases, we measure a decrease in the mean descent velocity in turbulence for the conditions tested. We also study the secondary motion of the particles and identify descent events that are unique to turbulence such as ‘long gliding’ and ‘rapid rotation’ events. Lastly, we show an increase in the radial dispersion of the particles under background turbulence and correlate the time scale of descent events with the local settling velocity
Towards a physical understanding of bubble–particle collisions in turbulence
No full textThe energy transition to mitigate global warming implies that the demand for minerals is expected to rise significantly. Many common minerals are separated from their ores through froth flotation, in which bubble–particle collisions in turbulence play a central role. This work systematically investigates bubble–particle collisions in statistically stationary homogeneous isotropic turbulence to reveal the underlying collision mechanisms and improve our predictive capabilities of the collision rate.When gravity is negligible, point-bubble and point-particle simulations show that stronger turbulence leads to a net increase in the overall collision rate. The underlying mechanisms, namely spatial segregation and the ‘turnstile mechanisms’, are identified and explored. For the simulated parameters, the collision rate is usually overpredicted by the existing models.Including gravity generally increases the collision rate by reducing segregation and increasing the collision velocity. Surprisingly, the addition of turbulence does not always increase the collision rate. This is due to bubble–particle segregation and nonlinear drag effects on the bubble. This peculiarity, and more generally the collision rate, are not captured well by the existing models. An existing particle–particle collision model is extended to the bubble–particle case. This extended model captures the simulated collision velocity excellently when particle inertia is weak.Finite-size bubbles are subsequently considered, and a model that predicts the collision rate for a wide range of particle inertia is developed. The model predictions agree well with results from simulations of finite-size bubbles and point-particles in turbulence when the flow field near the bubble can be assumed as steady during a collision.Finally, the first step towards the ultimate test of experimentally studying bubble–particle collisions in turbulence is taken. To this end, a versatile 3D-printed droplet generator that produces curable droplets is designed. These cured droplets can then be injected into turbulence facilities to study bubble–particle collisions
The effect of gravity on bubble–particle collisions in turbulence
No full textBubble–particle collisions in turbulence are key to the froth flotation process that is widely employed industrially to separate hydrophobic from hydrophilic materials. In our previous study (Chan et al., 2023 J. Fluid Mech. 959, A6), we elucidated the collision mechanisms and critically reviewed the collision models in the no-gravity limit. In reality, gravity may play a role since, ultimately, separation is achieved through buoyancy-induced rising of the bubbles. This effect has been included in several collision models, which have remained without a proper validation thus far due to a scarcity of available data. We therefore conduct direct numerical simulations of bubbles and particles in homogeneous isotropic turbulence with various Stokes, Froude and Reynolds numbers, and particle density ratios using the point-particle approximation. Generally, turbulence enhances the collision rate compared with the pure relative settling case by increasing the collision velocity. Surprisingly, however, for certain parameters the collision rate is lower with turbulence compared with without, independent of the history force. This is due to turbulence-induced bubble–particle spatial segregation, which is most prevalent at weak relative gravity and decreases as gravitational effects become more dominant, and reduced bubble slip velocity in turbulence. The existing bubble–particle collision models only qualitatively capture the trends in our numerical data. To improve on this, we extend the model by Dodin & Elperin (2002 Phys. Fluids 14, 2921–2924) to the bubble–particle case and found excellent quantitative agreement for small Stokes numbers when the history force is negligible and segregation is accounted for.</p
Bubble-particle collisions in turbulence: insights from point-particle simulations
No full textBubble-particle collisions in turbulence are central to a variety of
processes such as froth flotation. Despite their importance, details of the
collision process have not received much attention yet. This is compounded by
the sometimes counter-intuitive behaviour of bubbles and particles in
turbulence, as exemplified by the fact that they segregate in space. Although
bubble-particle relative behaviour is fundamentally different from that of
identical particles, the existing theoretical models are nearly all extensions
of theories for particle-particle collisions in turbulence. The adequacy of
these theories has yet to be assessed as appropriate data remain scarce to
date. In this investigation, we study the geometric collision rate by means of
direct numerical simulations of bubble-particle collisions in homogeneous
isotropic turbulence using the point-particle approach over a range of the
relevant parameters, including the Stokes and Reynolds numbers. We analyse the
spatial distribution of bubble and particles, and quantify to what extent their
segregation reduces the collision rate. This effect is countered by increased
approach velocities for bubble-particle compared to monodisperse pairs, which
we relate to the difference in how bubbles and particles respond to fluid
accelerations. We found that in the investigated parameter range, these
collision statistics are not altered significantly by the inclusion of a lift
force or different drag parametrisations, or when assuming infinite particle
density. Furthermore, we critically examine existing models and discuss
inconsistencies therein that contribute to the discrepancy.Comment: 29 pages, 18 figures to be published in Journal of Fluid Mechanic
Dynamics of heavy and buoyant underwater pendulums
No full textThe humble pendulum is often invoked as the archetype of a simple, gravity driven, oscillator. Under ideal circumstances, the oscillation frequency of the pendulum is independent of its mass and swing amplitude. However, in most real-world situations, the dynamics of pendulums is not quite so simple, particularly with additional interactions between the pendulum and a surrounding fluid. Here we extend the realm of pendulum studies to include large amplitude oscillations of heavy and buoyant pendulums in a fluid. We performed experiments with massive and hollow cylindrical pendulums in water, and constructed a simple model that takes the buoyancy, added mass, fluid (nonlinear) drag and bearing friction into account. To first order, the model predicts the oscillation frequencies, peak decelerations and damping rate well. An interesting effect of the nonlinear drag captured well by the model is that, for heavy pendulums, the damping time shows a non-monotonic dependence on pendulum mass, reaching a minimum when the pendulum mass density is nearly twice that of the fluid. Small deviations from the model’s predictions are seen, particularly in the second and subsequent maxima of oscillations. Using time-resolved particle image velocimetry (TR-PIV), we reveal that these deviations likely arise due to the disturbed flow created by the pendulum at earlier times. The mean wake velocity obtained from PIV is used to model an extra drag term due to incoming wake flow. The revised model significantly improves the predictions for the second and subsequent oscillations
Underfunding of Defined Benefit Pension Plans and Benefit Guarantee Insurance - An Overview of Theory and Empirics
No full textWe review the theoretical literature on defined benefit (DB) pension plans, particularly focusing on the issue of plan underfunding and benefit guarantee insurance schemes. The literature shows that underfunding can, under reasonable assumptions, be an equilibrium outcome even in the absence of benefit insurance. The introduction of benefit guarantee funds was a reaction to the problem of underfunding, and we summarize the ensuing standard problems of moral hazard and adverse selection. We briefly discuss the small empirical research on the subject and propose directions for future research.defined benefit pension plans, underfunding, pension benefit guarantee
A Critique of Computable General Equilibrium Models for Trade Policy Analysis
No full textThe paper will deal in turn with three sets of modelling issues: the question of 'data'; the 'micro' problem of specifying market behaviour, and the. 'macro' issue of 'closing' the models in aggregate. I will conclude with some suggestions for future research. The basic theme of the paper is this: CGE modelling is essentially a conservative or 'neoclassical' scientific endeavour, and exhibits the strengths and weaknesses of neoclassicism. And as for the recent injection of apparently nonneoclassical imperfect competition or industrial organization (IO) concepts into CGE, though, as an 10 specialist myself I certainly welcome this in principle, I have doubts about the usefulness of the practice.International Relations/Trade,
Deficiencies of bubble–particle collision models in light of point-particle simulations in homogeneous isotropic turbulence
No full textA predictive model for bubble–particle collisions in turbulence
No full textThe modelling of bubble–particle collisions is crucial to improving the efficiency of industrial processes such as froth flotation. Although such systems usually have turbulent flows and the bubbles are typically much larger than the particles, there currently exist no predictive models for this case which consistently include finite-size effects in the interaction with the bubbles as well as inertial effects for the particles simultaneously. As a first step, Jiang and Krug [2025] proposed a frozen turbulence approach which captures the collision rate between finite-size bubbles and inertial particles in homogeneous isotropic turbulence using the bubble slip velocity probability density function measured from simulations as an input. In this study, we further develop this approach into a model where the bubble–particle collision rate can be predicted a priori based on the bubble, particle, and turbulence properties. By comparing the predicted collision rate with simulations of bubbles with Stokes numbers of 2.8 and 6.3, and particles with Stokes numbers ranging from 0.01 to 2 in turbulence with a Taylor Reynolds number of 64, good agreement is found between model and simulations for Froude number Fr ≤ 0.25. Beyond this range of bubble Stokes number, we propose a criterion for using our model and discuss the model’s validity. Evaluating our model at typical flotation parameters indicates that particle inertia and settling effects are usually important. Generally, smaller bubbles, larger particles, and stronger turbulence increase the overall collision rate
