The Effect of Gravity on Bubble-Particle Collisions in Turbulent Flows

Conceitos essenciais

Gravity plays a significant role in bubble-particle collisions in turbulent flows, affecting the collision rate, spatial distribution, and collision velocity. Turbulence can both enhance and reduce the collision rate compared to the pure relative settling case, depending on the Stokes and Froude numbers.

Resumo

The study investigates the effect of gravity on bubble-particle collisions in homogeneous isotropic turbulence (HIT) through direct numerical simulations. The key findings are:

At weak gravity (low Froude number), turbulence mechanisms dominate the collision process, with bubbles and particles forming their own clusters and segregating. This reduces the collision rate compared to the no-gravity case.

As gravity becomes stronger (higher Froude number), it plays an increasingly important role. Gravity reduces the spatial segregation between bubbles and particles and increases the collision velocity, leading to a higher collision rate.

Surprisingly, for certain Stokes and Froude number combinations, the collision rate can be lower with turbulence compared to the pure relative settling case. This is due to two effects:
a. Turbulence-induced spatial segregation, which is most prevalent at weak relative gravity and decreases as gravitational effects become more dominant.
b. Reduced bubble slip velocity in turbulence due to enhanced nonlinear drag from horizontal slip velocity components.

Existing bubble-particle collision models only qualitatively capture the trends observed in the numerical data. An extended model based on Dodin & Elperin (2002) shows excellent quantitative agreement for small Stokes numbers when accounting for the effect of spatial segregation.

Estatísticas

The mean vertical fluid velocity at bubble and particle positions is lower than the terminal velocities, indicating a reduction in the bubble slip velocity in turbulence.
The norm of the rotation rate at bubble and particle positions decreases with increasing gravity, suggesting a change in the clustering location and/or reduced clustering.

Citações

"Surprisingly, however, we observe that for certain parameters the collision rate is lower with turbulence compared to without."
"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."

Principais Insights Extraídos De

The effect of gravity on bubble-particle collisions in turbulence

by Timothy T. K... às arxiv.org 10-03-2024

https://arxiv.org/pdf/2410.01557.pdf

Perguntas Mais Profundas

How would the results change if the bubble and particle sizes were different, leading to different Stokes numbers?

If the bubble and particle sizes were different, resulting in varying Stokes numbers, the dynamics of bubble-particle collisions in turbulence would be significantly affected. The Stokes number (St) is a dimensionless quantity that characterizes the response of a particle to the surrounding fluid flow, defined as the ratio of the particle's inertial forces to the viscous forces acting on it. A higher Stokes number indicates that the particle is less influenced by the fluid's motion, while a lower Stokes number suggests a stronger coupling with the fluid.
In scenarios where bubbles and particles have different sizes, the collision mechanisms would vary based on their respective Stokes numbers. For small Stokes numbers (St < 1), the collision rate is primarily influenced by local fluid shear and the local turnstile effect, where bubbles and particles experience opposite slip velocities due to their density differences. As the Stokes number increases, the collision dynamics shift towards non-local effects, where the history of the particle's path becomes more significant. This could lead to a reduced collision rate due to spatial segregation, as larger particles may preferentially sample different regions of the turbulent flow compared to smaller bubbles.
Moreover, the collision kernel would likely exhibit a more complex dependence on the Froude number (Fr) and Reynolds number (Reλ), as the interplay between buoyancy and turbulence becomes more pronounced. The segregation effects would also be more intricate, potentially leading to enhanced clustering of either bubbles or particles depending on their relative sizes and densities. Overall, varying bubble and particle sizes would necessitate a reevaluation of existing collision models to account for these differences in Stokes numbers and their impact on collision rates and efficiencies.

What are the implications of the reduced bubble slip velocity in turbulence on the overall efficiency of the froth flotation process?

The reduced bubble slip velocity in turbulence has significant implications for the efficiency of the froth flotation process, which relies on the effective collision and attachment of hydrophobic particles to rising bubbles. In the context of bubble-particle collisions, the slip velocity is the difference between the bubble's rising velocity and the fluid's velocity. When turbulence is present, the slip velocity can be diminished due to enhanced nonlinear drag forces acting on the bubbles, primarily caused by the horizontal slip velocities induced by turbulent eddies.
A lower bubble slip velocity results in a decreased relative velocity between bubbles and particles, which can lead to a reduction in the collision rate. This is particularly critical in the froth flotation process, where the efficiency of particle separation is contingent upon the frequency of successful bubble-particle collisions. If the collision rate decreases, fewer particles will attach to the bubbles, leading to lower recovery rates of the desired hydrophobic materials.
Additionally, the study indicates that at higher Froude numbers (Fr), the collision kernel can dip below the relative settling case in still fluid, suggesting that turbulence can counterintuitively reduce the collision rate. This reduction in collision efficiency due to turbulence and reduced slip velocity could necessitate adjustments in operational parameters, such as bubble size, flow rates, and chemical additives, to optimize the froth flotation process and enhance the recovery of valuable materials.

How might the findings from this study on bubble-particle collisions in turbulence with gravity be applicable to other multiphase flow systems, such as sediment transport or cloud microphysics?

The findings from this study on bubble-particle collisions in turbulence with gravity have broad applicability to other multiphase flow systems, including sediment transport and cloud microphysics. In sediment transport, the dynamics of particles settling through a fluid are influenced by similar forces, including gravity, buoyancy, and turbulence. Understanding how these forces affect particle collisions and segregation can provide insights into sedimentation rates, the formation of sediment layers, and the overall transport of sediments in natural water bodies.
In cloud microphysics, the interactions between cloud droplets and aerosols are critical for understanding cloud formation, precipitation processes, and the development of weather systems. The principles governing bubble-particle collisions in turbulence can be extended to droplet-aerosol interactions, where the size and density differences between droplets and aerosols lead to varying Stokes numbers. The study's insights into how turbulence affects collision rates and spatial distribution can inform models of cloud dynamics, helping to predict cloud behavior and precipitation patterns more accurately.
Overall, the study's findings highlight the importance of considering the effects of turbulence and gravity in multiphase flow systems, providing a framework for understanding complex interactions that govern the behavior of particles in various environmental and industrial processes.