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