Surface Tension and Zeta Potential
Liquid
LV
Air
Cohesion
Solid
SV

SL
The various symbols i refer to
interfacial tensions between liquid
(L), air saturated with vapour (V),
and/or solid (S)
Adhesion
 SV   SL   LV cos 
Young equation (1805)
Work of Adhesion, WA – work required to separate a unit area of a solid-gas
interface.
WA   SL   LV   SV
Dupré equation (1859)
Work of Cohesion, WC - work required to break apart a column of a liquid
having a unit cross-sectional area.
WC  2 LV
LV, at 25 °C
Water 72.8 mJ/m2
Propanol 23.3 mJ/m2
Mercury 485.5 mJ/m2
Work of Adhesion
Work of Cohesion
WA   SV   LV   SL
WC  2 LV
Adhesion between a solid and a liquid, or between two immiscible
liquids.
Cohesion within a liquid.
Combining the Young and Dupré equations, the following
expression is obtained which describes the work required to
remove the bubble from the solid in a liquid environment:
WA   LV( 1  cos  )
When Θ = 0, cosΘ = 1 – perfect "wetting" or total hydrophilicity.
When Θ = 180, cosΘ = -1 – perfect or total hydrophobicity.
deg
deg
Completely hydrophobic solid
Completely hydrophilic solid
When WA = WC , cosΘ = 1 (Θ = 0) – perfect wetting or complete hydrophilicity.
When WA << WC , cosΘ → -1 (Θ = 180) – perfect “dewetting” or complete
hydrophobicity.
The higher the contact angle of water, the more hydrophobic the solid (easier
to float).
• Very few minerals show natural floatability (hydrophobicity)
• Only ONE of those minerals is of any real value – molybdenite
• Some types of coal are hydrophobic and easy to float
• Coal is not a mineral…It is an organic rock (mixture of minerals)
• Diamonds are also hydrophobic – too coarse to float
• Vast majority of minerals are naturally hydrophilic (non-floating)
• So, surface chemical modification is required to float
When a mineral particle is placed in water
1) It may dissolve in water – (e.g., sylvite – KCl or apatite – Ca3(PO4)2 )
- releasing ions into solution
2) It may react with water (hydrolysis) forming functional groups on its
surface (e.g., hematite Fe2O3 forms –OH groups)
3) It ALWAYS becomes electrostatically-charged
- surfaces acquire positive or negative charges
4) It will adsorb almost anything - ions, dissolved organics,
added reagents present in solution
Compact
(Stern) Layer
of Ions
Diffuse Layer of Ions
The ion concentration profile that develops around a charged particle is known as
the Electrical Double Layer (EDL)
Surface Potential
Ψ0 is defined as
Work required to bring a unit charge from  to a charged solid surface
  0 exp(x)
  0 exp(x)
If x = 1/ then /0 = 1/e = 0.3678

is expressed in units of reciprocal distance (e.g., m-1)
So the parameter (1/ ) is referred to as the thickness of the EDL
A particle has a 0 = 40 mV
Calculate the EDL thickness of a particle in 10-3, 10-2 & 10-1 M KCl solution
10-3 M KCl;  = 0.10398 nm-1  1/ = 9.62 nm
10-2 M KCl;  = 0.32881 nm-1  1/ = 3.04 nm
10-1 M KCl;  = 1.03979 nm-1  1/ = 0.96 nm
As electrolyte concentration increases, the thickness of the EDL decreases.
This phenomenon is known as the compression of the EDL.
Compact layer adsorbed
Diffuse layer removed
The shear plane
These phenomena are the foundation
of electrokinetic effects which are used
in measuring the zeta potential (ζ) of
mineral particles.
Zeta potential (ζ) is the electrical potential at the shear plane.
It is not the Surface Potential (0) but rather, the potential at
some distance from the surface.
The shear
plane
The zeta potential is always lower than the surface potential, but it
always has the same sign (either positive or negative)
Unlike Surface Potential, the Zeta Potential strongly depends on
concentration of indifferent ions (such as K and Cl)
Some Practical Examples of Actual Zeta Potential Data
Goethite (FeO(OH))
From Iwasaki et al. 1960.
Zero Point of Charge
6.7 for FeO(OH)
2
4
6
8
10
12
pH
Zero Point of Charge
5.7 for FeO(OH)
Zirconia (ZrO2)
From Cases (1967)
Zero Point of Charge = ZPC or PZC
Or the Iso-Electric Point (IEP)
Zero Point of Charge
Mineral
ZPC (pH units)
Quartz/SiO2
Kaolinite
Illite
TiO2
Apatite
MnO2
~ 2.0
~ 2.5
~ 2.5
3.5
3.8
4.0 -8.7
Flotation Classification of Minerals
Group
Examples
Flotation properties
floats easily with waterA) Inherently hydrophobic
graphite, sulfur, talc, molybdenite,
insoluble oily collectors and
minerals
some coals
frothers
copper, gold, galena, chalcopyrite, floats well with thio-collectors,
B) Sulfides and native metals
sphalerite, pyrite
strongly Eh-pH dependent
floats with thio-collectors after
C) Oxidized minerals of heavy cerussite, anglesite, malachite,
activation (sulfidization), also
metals
smithsonite, chrysocolla
floats with fatty acids
floats very well with either
D) Oxides, silicates and
quartz, hematite, tenorite,
anionic or cationic collectors
aluminosilicates
alumina, cassiterite
depending on pH
E) Sparingly soluble salt-type calcite, dolomite, flurite, apatite,
floats very well with fatty acids
minerals
barite, magnesite, scheelite
and their salts
floats with long-chain primary
F) Soluble salt-type minerals sylvite, halite
amines in saturated brine