Suspension Stability: Why particle size, zeta potential and rheology are important John Duffy, Adrian Hill, Andrew Walton, Fred Mazzeo Malvern Instruments Ltd, Malvern, Worcestershire, UK Suspension Stability Increasing viscosity – Kinetic Stability

Suspensions/Dispersions are encountered in a wide range of Stokes equation can be used to predict settling velocity (V) of a dilute suspension applications with continuous phase viscosity ( η)
Liquid abrasive cleaners, ceramics, medicines, inks… Velocity increases with the square of particle size making this the most critical In most cases it is necessary to keep the suspension stable parameter for the product lifetime To slow down sedimentation rate 2∆ρga 2 In other cases it may be necessary to destabilise the
Increase low shear viscosity V = suspension i.e. water treatment, de-aeration
Decrease particle size 9η Suspension stability can be achieved in a variety of ways
Match density of dispersed and continuous phases DILUTE
Prevent coagulation through inter-particle repulsion (steric or electrostatic stabilisation) For concentrated systems a crowding factor must be introduced, which incorporates the phase 2
Slow down sedimentation by increasing the viscosity of continuous phase – Kinetic stability 2∆ρga 5± 25.0 volume Φ V = 1( −φ)
Make it behave like a solid at rest by creating a network structure – Thermodynamic stability 9η Increasing phase volume decreases sedimentation Which Method?..... It Depends!! rate due to the viscosity increase resulting from CONCENTRATED crowding and the up flow from moving partciles Particle size has a large bearing on stability a 4∆ρg Gravitational Forces since gravitational forces scale with the 4 th If 5mm sedimentation per year was acceptable we would need a viscosity in the Brownian Forces region of 11 Pas for this Silica dispersion power of particle radius kBT If gravitational forces exceed the Brownian forces keeping the particles dispersed Inducing a Network Structure – Thermodynamic Stability then sedimentation will occur For sub micron particles Brownian motion is usually significant to overcome effect When electrostatic forces can be minimized it is possible to produce a secondary of gravity minimum in the potential energy curve For larger particles gravity dominates if there is a significant density difference ( ∆ρ ) If the secondary minimum is deep enough the particles stick together on contact and can form a strong reversible flocculated network Colloidal Stability

To maintain stability through Brownian motion we need to prevent particles sticking together when they collide as this larger aggregate will significantly increase the gravitational forces This can be achieved by increasing the charge associated with the particle i.e. zeta potential, or alternatively by adsorbing species capable of steric stabilisation i.e. deflocculating polymers

REPULSION + + LONG RANGE ELECTROSTATIC Yield Stress Behaviour (DOUBLE LAYER) Decrease Mask / neutralise charge with counter-ions zeta potential The isoelectric point (where the zeta potential is zero) is in the very acidic (pH 1) - - - - ATTRACTION - - region and net charge thus decreases as pH is reduced from 6.2 - + - - + -

- - SHORT RANGE - - - - At lower pH’s particles associate VAN DER WAALS more, causing an increase in pH2.42 Generally a zeta potential of +/- 30mV is considered a suitable threshold viscosity, which is favourable for value for colloidal stability pH3.52 stability Low pH samples show no viscosity Experimental Summary pH3.97 plateau (in shear rate range) 75% w/w Silica dispersion made up in deionised water suggesting solid like behaviour Zeta potential evaluated using a Malvern Zetasizer Nano ZS with autotitrator Measurements repeatable on loaded sample suggesting reversible flocculation due Particle size evaluated using a Malvern Mastersizer 2000 with Hydro S to the presence of a secondary minimum dispersion unit At high pH there is no elastic network Rheological properties measured using a Kinexus Pro and Gemini HR Nano hence no yield stress observed rotational rheometers As pH is lowered stronger interactions occur leading to a more Size and Zeta Measurements robust network and a larger yield stress Initial sample evaluation made at natural pH of dispersion - 6.2 What Yield Stress is Required? Despite having a zeta potential of - 50mV the suspension was found to be For a particle to stay suspended the yield stress must exceed the gravitational unstable. force acting on the particle. This can be estimated from the following equation:

The median particle was determined σ = Y (ρ − ρ )rg …where Y is the critical yield parameter to be 3.7 µm and the largest particle y D C was approximately 20 µm The critical yield parameter has been shown to have a range of values based on The particle density was 2600 kg/m 3 various studies If Y was 0.33 then a yield stress Inputting these values into the following equation for the in excess of 0.05 Pa is required median size gives a value of 45 and for the largest particle to stabilize a 20um particle size a value of 4 x 10 4 Since stress acts over a plane normal to the direction of force then Y = 1.33 is perhaps more accurate mathematically

This means that gravitational forces are dominant for this Extra g forces associated with transportation can increase the effective sample and explains why sedimentation occurs. It also gravitational forces acting on a particle and need to be considered also indicates that another approach is required to induce stability Conclusion REFERENCES Particle size. zeta potential and rheology are important factors governing 1.Barnes, H A (1992), Recent advances in rheology and processing of colloidal systems, The 1992 IChemE Research Event, pp. 24-29, IChemE, Rugby dispersion stability and can be manipulated accordingly to prevent separation 2.Derjaguin, B; Landau, L (1941) Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes , Acta Physico Chemica URSS 14, 633. 3.Hunter, R.J (1988), Zeta Potential in Colloid Science: Principles and Applications , Academic Press, UK. 4.Larson, R.G (1999), The Structure and Rheology of Complex Fluids , Oxford University Press, New York 5.Verwey, E. J. W.; Overbeek, J. Th. G. (1948), Theory of the stability of lyophobic colloids , Amsterdam: Elsevier