Towards a Physical Understanding of Bubble--Particle Collisions in Turbulence
Tsz Kin Timothy Chan is a PhD student in the department Physics of Fluids. (Co)Promotors are dr. D.J. Krug and prof.dr. D. Lohse from the faculty of Science & Technology.
The transition towards renewable energy 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 studies bubble–particle collisions in statistically stationary homogeneous isotropic turbulence to reveal the underlying collision mechanisms and improve our predictive capabilities of the collision rate.
We first simulate bubbles and particles in homogeneous isotropic turbulence without gravity using the point-particle approach. The results show that increasing the strength of turbulence leads to a net increase in the overall collision rate. This is not clear a priori since we identify collision mechanisms that are unique to bubble–particle systems, namely spatial segregation and the local and nonlocal ‘turnstile mechanisms’, which demonstrate that bubble–particle relative behaviour is different from that of particle–particle systems. For the simulated parameters, the collision rate is generally overpredicted by the existing models.
We then expand our parameter space and include gravity in our point-particle and point-bubble simulations, such that bubbles now float and particles settle. Generally, gravity increases the collision rate by reducing segregation and increasing the collision velocity. We surprisingly find that the inverse is not universally true: adding 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 when turbulence plays a noticeable role, are not well captured by the existing models. We therefore extend the model by Dodin & Elperin (Phys. Fluids, vol. 14, no. 8, 2002, pp.2921–2924) to the bubble–particle case. The extended model captures the measured collision velocity excellently when particle inertia is weak.
Afterwards, we go beyond the point-bubble approach by considering finite-size bubbles in turbulence and present a model that predicts the collision rate based on the bubble, particle, and background flow properties. This model is applicable for particles with a wide range of inertia in contrast to Kostoglou et al. (Adv. Colloid Interface Sci., vol. 284, 2020, p.102270). Central to our model are the frozen turbulence approximation, which assumes that the flow field near the bubble is steady during the collision time scale; and the probability density function of the bubble slip speed, which we model using independent and normally distributed slip velocity components. We additionally simulate finite-size bubbles and point-particles in homogeneous isotropic turbulence to show that our model predictions agree well with the simulation results when the frozen turbulence approximation is valid.
Finally, we take the first step towards the ultimate test of experimentally studying bubble–particle collisions in turbulence. To this end, we develop a 3D-printed droplet generator that produces curable droplets. This droplet generator operates based on the Rayleigh–Plateau instability, which allows the production of droplets with various sizes using the same fluidic chip. To demonstrate its versatility, we generate single- and double-emulsion droplets containing epoxy resin, a hardener, and melamine. These droplets are subsequently solidified into particles and capsules, respectively, which can in turn be injected into turbulence facilities to study bubble–particle collisions.
