2746 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
of the mean radial relative velocity. Case TREF is a super-
position of the effects of gravity and homogenous and iso-
tropic turbulence. The forced background turbulence has
a mean fluid velocity of u 0
f =.Hence without gravity,
particles in an undisturbed fluid far away from the bubble
would perfectly follow the streamlines having on average
no mean radial velocity relative to the bubble. The effects
on the radial relative velocity caused by gravity are over-
shadowed by those of the background turbulence, reducing
the mean radial relative velocity. The same applies to the
area of lower absolute radial relative velocity in the rear of
the bubble. In conjunction with an increase in the particle
and bubble velocity fluctuations for case TREF the parti-
cle-bubble radial relative velocity is more uniform around
the bubble circumference. Overall, this results in a more
uniform distribution of the collision angle for case TREF
compared to case GREF, as shown above. Consequently,
particles have more opportunities to approach and collide
with the bubble.
CONCLUSIONS
Understanding particle-bubble collisions under turbulence
is crucial for discerning the particle-bubble collision sub-
process in flotation, which is key for improving flotation
recovery, performance, and environmental sustainability.
Using DNS enables a detailed analysis of the particle-
bubble collision frequency and its influencing factors in a
realistic and dense three-phase flow. Two highly resolved
simulations were conducted to determine the influence
of turbulence on particle-bubble collisions. The presence
of turbulence significantly increases particle, bubble, and
fluid velocities as well as their fluctuations resulting in a sig-
nificant increase of the particle-bubble collision frequency.
When solely under the influence of gravity, particles and
bubbles tend to move preferentially in the vertical direc-
tion. This leads to a depletion of particles in the bubble
wake and an uneven distribution of the collision angle dis-
tribution with very few collisions on the lower bubble half.
These distributions are significantly more uniform under
the influence of isotropic background turbulence. This, in
turn, leads to an increase in collision frequency as particles
have more opportunities to approach and collide with the
bubble from all sides.
Overall, these results provide promising data for under-
standing the collision process in flotation in more detail,
which will be further build upon using further simulation
and modelling (Tiedemann et al. 2024a, Tiedemann et al.
2024b in preparation).
ACKNOWLEDGMENTS
We thank T.T.K. Chan and D. Krug for very useful dis-
cussions. This project has received funding from the
European Union’s Horizon 2020 Marie Skłodowska-Curie
Actions (MSCA), Innovative Training Networks (ITN),
(a) (b)
Figure 4. 2D PDF of mean particle-bubble radial relative velocity w
r .a) TREF, b) GREF. normalised by u d g
ref b =
of the mean radial relative velocity. Case TREF is a super-
position of the effects of gravity and homogenous and iso-
tropic turbulence. The forced background turbulence has
a mean fluid velocity of u 0
f =.Hence without gravity,
particles in an undisturbed fluid far away from the bubble
would perfectly follow the streamlines having on average
no mean radial velocity relative to the bubble. The effects
on the radial relative velocity caused by gravity are over-
shadowed by those of the background turbulence, reducing
the mean radial relative velocity. The same applies to the
area of lower absolute radial relative velocity in the rear of
the bubble. In conjunction with an increase in the particle
and bubble velocity fluctuations for case TREF the parti-
cle-bubble radial relative velocity is more uniform around
the bubble circumference. Overall, this results in a more
uniform distribution of the collision angle for case TREF
compared to case GREF, as shown above. Consequently,
particles have more opportunities to approach and collide
with the bubble.
CONCLUSIONS
Understanding particle-bubble collisions under turbulence
is crucial for discerning the particle-bubble collision sub-
process in flotation, which is key for improving flotation
recovery, performance, and environmental sustainability.
Using DNS enables a detailed analysis of the particle-
bubble collision frequency and its influencing factors in a
realistic and dense three-phase flow. Two highly resolved
simulations were conducted to determine the influence
of turbulence on particle-bubble collisions. The presence
of turbulence significantly increases particle, bubble, and
fluid velocities as well as their fluctuations resulting in a sig-
nificant increase of the particle-bubble collision frequency.
When solely under the influence of gravity, particles and
bubbles tend to move preferentially in the vertical direc-
tion. This leads to a depletion of particles in the bubble
wake and an uneven distribution of the collision angle dis-
tribution with very few collisions on the lower bubble half.
These distributions are significantly more uniform under
the influence of isotropic background turbulence. This, in
turn, leads to an increase in collision frequency as particles
have more opportunities to approach and collide with the
bubble from all sides.
Overall, these results provide promising data for under-
standing the collision process in flotation in more detail,
which will be further build upon using further simulation
and modelling (Tiedemann et al. 2024a, Tiedemann et al.
2024b in preparation).
ACKNOWLEDGMENTS
We thank T.T.K. Chan and D. Krug for very useful dis-
cussions. This project has received funding from the
European Union’s Horizon 2020 Marie Skłodowska-Curie
Actions (MSCA), Innovative Training Networks (ITN),
(a) (b)
Figure 4. 2D PDF of mean particle-bubble radial relative velocity w
r .a) TREF, b) GREF. normalised by u d g
ref b =
