Motion of a Particle Bubble Aggregate in a Rectangular Cavity

Authors:

Wang, G. - Presenter, University of Newcastle

Zhou, S. - Presenter

Evans, G. M. - Presenter, The University of Newcastle

Jameson, G. - Presenter

Joshi, J. B. - Presenter, Homi Bhabha National Institute

Motion of a
particle bubble aggregate in a rectangular cavity

line-height:normal">

line-height:normal">Flotation
is an important particle separation technique using bubbles attach hydrophobic
particles. For
recent years, efforts have been devoted to increase flotation recovery rate of
coarse particles (Jameson, 2010) due to substantial benefits in coarse particle
flotation. According to Bond law of grinding, energy needed to grind mineral
particles of certain size is related to final size of the particle. Grinding,
however, is a highly energy-intensive process. Substantial benefit of coarse
particle recovery is that less energy is required in grinding operations, which
has immense economic benefits. By applying flotation to large particles
separation, less electricity is needed and the amount of greenhouse gas
emission to generate the required electricity is reduced. Moreover, less
grinding operation means less grinding maintenance cost, such as grinding ball
replacement. Nevertheless, it is hard for bubbles to collect coarse mineral
particles with large gravity. Besides, coarse particle bubble aggregates are
usually very unstable and sensitive to fluid hydrodynamics. For this reason,
the high vulnerability of aggregates means that particle bubble detachment is
the major limiting factor in coarse particle flotation.

justify;text-justify:inter-ideograph;line-height:normal">A
force balance approach is usually used to analyse particle bubble detachment
process. Considering equilibrium of all the forces acting on a bubble-particle
aggregate, the maximum floatable particle size can be obtained. Gaudin (1957)
showed the maximum floatable size of minerals in quiescent liquid can be 10
times larger than the maximum particles size of actual flotation process. Such
anomaly exists because in a flotation cell, particle bubble aggregates are
subjected to other disruptive forces due to turbulent fluid motion. In contrast
to the static case (stagnant fluid around the bubble-particle aggregate), turbulent
fluid force is considered to act on the attached particle in actual floatation
cell where a turbulent flow condition persists. To describe such
detaching/disruptive forces, Schulze (1982) hypothesized interactions of
rotating turbulent flow structures (eddies) with the bubble-particle aggregate in
a way that the particle-bubble aggregate was trapped in a rotating eddy and centrifugal
force originated from the rotating flow structures detached particle from
bubble. This theory is based on the assumption that particle bubble aggregate
trapped in the eddy of the same scale will rotate along the eddy to the extent
where centrifugal force exceeds adhesive force. A simpler expression for the
centrifugal force can be obtained assuming isotropic turbulence following
Kolmogorov?s theory:

justify;text-justify:inter-ideograph;line-height:normal">Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (1)

justify;text-justify:inter-ideograph;line-height:normal">where
position:relative;top:5.5pt'> font-family:"Times New Roman","serif";color:black'>Â is the turbulent
acceleration generated by the eddies and can be determined by the root mean
square of the fluctuating velocitiesover the
rotating length scale position:relative;top:5.5pt'> font-family:"Times New Roman","serif";color:black'>Â as follows:

line-height:normal"> color:black'>Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (2)

justify;text-justify:inter-ideograph;line-height:normal">Schulze
(1982) assumed that particles moved with the same velocity as the eddy, and the
radius of rotation can be represented by bubble diameter, d_B.
Then, centrifugal acceleration position:relative;top:5.5pt'> font-family:"Times New Roman","serif";color:black'>, can be rearranged as

line-height:normal"> color:black'>Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (3)

justify;text-justify:inter-ideograph;line-height:normal">Notwithstanding,
lots of work have been done to get a clear understanding of coarse particle
flotation, it is still not clear the interactions between hydrodynamics and
particle bubble aggregates. To minimise turbulence influence on particle
detachment whilst ensuring high flotation recovery, it is essential to
understand how turbulence (eddy in more real sense) act on the particle
attached to a bubble. It is still mysterious in the way this detachment process
occurs, but still proactive effort is needed to experimentally presenting particle
detachment process. Given the situation that role of hydrodynamics on particle
detachment is still not fully explored, the objective of this work is focused
on clarifying detachment process, especially on eddy?s influence on particle
bubble aggregate stability.