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The Effect of Particle Size and Shape on
Transport Through Confined Channels in
Three-phase Froths
Tarun Bhambhani D. Eng. Sc.
Earth and Environmental Engineering
Solvay – Technology Solutions
Q3 2019 CPaSS IAB
Introduction
Transport
Phenomena in
Complex SystemsIndustrial Relevance
Froth Flotation
Multiphasic
Solid
Dynamic
Tortuous
Geometry
Mobile wallsLiquid Gas Confinement
Channels
Engineering analysis
SizeWettability
(Non-colloidal particles)
Shape
Laminar flow
Large plants: ~250,000 tons/day
Mineral Froth Flotation
3
How does hydrophilic particle aspect ratio affect transport?
www.911metallurgist.com
Hydrophilic
Hydrophobic
• Gas motion
Laplace equation & Darcy’s law for porous media
• Liquid motion:
Foam drainage equation Poiseulle flow
Gravity
Capillary forces
Viscous drag
• Unattached Solids motion
Liquid velocity- advection
Particle settling velocity
Particle dispersion (geometrical)
Modeling the flow of solids in froth
“Apparent fluid density and viscosity depend on solids concentration. At high solids concentrations, or with strongly interacting particles, non-linearities in slurry rheology could complicate the problem- though this is not considered in this work” Neethling et al, 2009
4
CPB= 10~50
Newtonian viscosity
Designed & fabricated froth sampler to
obtain composition as a function of depth
Froth sampling
5
• Volume fractions in flotation are much lower
• Small differences between platy mica and rounded silica
• Bulk rheology measurements alone insufficient to describe transport
behavior for platy mica particles
Bulk rheology measurements- Mica mixtures
𝜂𝑟 = 𝑒
𝐵𝜙
1−𝜙𝜙𝑚𝑎𝑥
6
Hydrophilic Particle transport through froth
Fine mica + fine silica (various ratios):
• Preferential transport of platy mica
particles vs. globular silica particles
Various mica + fine silica (1:1 ratio):
• Platy mica transports slower with
increasing size
Confinement of particles• Confinement parameter l=dp/dc
• Visual observations suggest dc=100-250m
• Particles greater than ~100m should be subject to confinement effects
• High Axial Ratio particles are confined > low Axial Ratio particles
Haffner, B., et al. (2015). JCIS 458: 200-208.
Elucidating results in doped ore flotation
• Recovery of mica always greater
than recovery of silica of
comparable size
• Confinement important when
particle size approaches size of
channels
Effect is concentration dependent
0.1
0.2
0.3
0.4
0.5
0.6
0.1 0.35 0.62 0.87 1.25 1.75
No
rmalized
HP
tra
nsp
ort
in
dex
Confinement parameter l (dp/dc)
25% mica doping
25% silica doping
NHPTImin
Confinement region
Free drainage region
0.1
0.2
0.3
0.4
0.5
0.6
0.1 0.35 0.62 0.87 1.25 1.75
No
rmalized
HP
tra
nsp
ort
in
dex
Confinement parameter l (dp/dc)
50% mica doping
50% silica doping
NHPTImin
Free drainage region
Confinement region
Estimate of
standard error
Estimate of
standard error
Impact of shape on transport
sphericalplates plank fibers
Drag and confinement
effects dominate
Entanglement,
viscosity mediated
effects dominate
Tra
nsport
rate
Shape
Effects are
concentration
dependent
Fg
Fd
Fg
Fd
Fg
Fd
Summary
• Current models still consider interstitial fluid as
Newtonian, and do not account for geometry or
confinement effects
• Novel apparatus for compositional analysis of
froth
Quantify effects of particle size and shape on mass
transport through confined channels
• Bulk rheological measurements using new tools
Viscosity contributes but cannot explain all the transport
rate differences between platy and spherical particles
• Novel experiments
Drag-drainage balanced vs drag-dominated froth
sampling
• In drag dominated regime, mica transports > silica
for all sizes
• Confinement occurs for platy mica > rounded
silica when l>1
11
• Prof. Somasundaran
• Committee Members
• Partha Patra
• Ray Farinato
• D.R. Nagaraj
• Solvay Management, John Schmitt, Nancy Touba, Sarah
Aanonsen, Chermeine Rivera, Frank Bruey
• My family
Acknowledgement
12