The viscosity of flocculated systems

The depth of the secondary minimum formed due to the addition of the repulsive and attractive forces will vary from a few kT units—which means no flocculation because Brownian motion will keep the particles apart—to 10 - 20 kT. Forces in this latter range mean that typical flows can break-up any floes present, although they will reform under more quiescent conditions. The size and architecture of the floes formed play a major role in determining the rheology and physical stability of the suspension. 

Shearing hard enough will result in the floes being reduced to the primary particles, but shearing at a low shear rate results in the partial breakdown or reformation of floes. The form of the floe depends on the interaction force and to some extent on the flow history attending the floe formation. Depending on its 

We will spend a little time considering the nature of floes. A floe is a collection of particles where the spatial arrangement often follows some simple law. It might be that the average particle concentration is the same throughout the floe, but usually the concentration decreases from the centre towards the outside. This is due to the way that the floes are formed. 

The simplest way of describing such a floe is to use fractals. In our case this simply means that the concentration falls off according to a power law with distance from the floe s centre. Then we can write down the following. 

From the mathematical relationship above we can redefine the phase volume as the effective phase volume, assuming for the sake of simplicity that the phase volume is now that defined by the enclosing spheres of the floes of radius Ro. Then it is easy to show that 

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