6. Colloidal instability, flocculation and rheology of dispersions

Instability in colloidal dispersions

• Sedimentation 

• Creaming

• Flocculation (aggregation)

• Ostwald ripening

What is sedimentation and creaming?

Sedimentation: Particle density is higher than the density of continuous phase → particles sink 

Creaming: Particle density is lower than the density of continuous phase → particles rise to surface

Flocculation/aggregation

a process where a solute (particles) comes out of solution in the form of floccules due to insufficient repulsion between particles 

Ostwald ripening

Large particles grow at the expense of smaller ones. Depends on how soluble dispersed phase is in continuous phase, size and laplace pressure

Smaller droplets → higher laplace pressure → higher driving force 

At which concentration is Stokes law a good estimation of real sedimentation?

Low concentration (φ<5%): v_sed = v_Stokes

For dispersion by particles is 25%

High concentration: (φ>5%): v_sed< v_Stokes

Sedimentation rates are lower than Stoke’s law predict  

Hindered sedimentation/creaming

The sedimentation or creaming rate decreases with increasing concentration of the dispersed phase.

When we have more 40% sedimentation doesn’t occur since there is no space, the particles are too crowded 

There are three mechanisms for flocculation:

• Brownian motions

The particles get close to each other through random movement 

• Shear induced flocculation

Some particles experience higher or lower shear stress depending on their surface

• Gravitity induced flocculation

Comparison between Brownian and shear flocculation rate

Brownian:

• Decreases with increased size

• Decreases with increased viscosity

Shear:

• Increases with increased size

• Increases with increased shear rate

N = number concentration of particles, k_B = Boltzmann constant, T = absolute temp., η =

dynamic viscosity, w = stability factor, φ = volume fraction of particles, γ = shear rate

Stability factor w

w=1 →  each collision leads to aggregation (high possibility of flocculation) 

w=10⁶ → one collision in a million leads to aggregation

Comparison between shear and brownian flocculation

d_o=0.1 μm

Small particles flocculate quickly due to Browian but then it is too big and slow down 

Brownian: Initially rapid, but then slowly

Shear: In the beginning, it is slow, but then rapidly increases 

d_o=3 μm

Shear: Rapid growth of particle size. Large and likely to meet than small particles in shear-like movement. 

Browian: Slow. Larger particles have a slower diffusion so it takes them longer to randomly meet 

Fractal aggregates (flocs)

Aggregates that occupy a larger volume than the individual particles are called fractal aggregates or flocs

Repulsive interactions and aggregate structure

Repulsion dominates → dense flocs

Attractive interactions and aggregate structure

Attraction dominates → less dense flocs

Larger fractal flocks

Larger structure but lower density → more rapid sedimentation

Smaller fractal flocks

Higher density

Ostwald ripening and laplace pressure

Ostwald ripening riven by the Laplace pressure

• Molecules from smaller particles dissolve and diffuse to larger particles

• Occurrence and rate also depend on the solubility disperse phase molecules in the continuous phase

– Low solubility slows it down or inhibits it

• Also referred to as ”disproportionation” in foams

We have pressure and high surface tension. We need solubility

If this has low solubility in the continuous phase, process slowed down 

Dispersion rheology

Higher viscosity is the result of particles disturbing the applied flow field and particles ”bumping into each other”.

In pure liquids: viscosity is the result of friction between molecules.

Relative viscosity relation to volume fraction

Higher volume fraction —> higher relative viscosity

How does aggregation/flocculation affect viscosity?

• Dispersed particles in continuous phase

• Flocculation occurs → Viscosity decreases

How does breaking up aggregates affect viscosity?

More particles flowing around bumping into each other → Viscosity increases