Interaction energy reversible flocculation

When Of a, the potential energy of interaction between an elementary particle and a hoc is equivalent to the potcntiul energy 4(h) between a particle and a fiat plate thus 4(h) used by Huckenstcin and Prieve (1976) still applies. Furthermore, if the conditions necessary for Equation (13) of that paper apply, then (berate constants for reversible flocculation inay be calculated as K/ = 4 / Kf and Kr — Aoaf K where X/ and K, are given by Equation (13). 

FIGURE 10.16. In many colloidal systems, the interaction energy curve will have a small minimum, the secondary minimum, M , that allows the particles to undergo a lose, reversible flocculation. In some systems of relatively large, monodisperse particles, the secondary minimmn may lead to an optical phenomenon called opalescence in which a very regular structure is developed (similar to a crystal structure) that produces beautiful and interesting patterns with incident light. 

Figure 10.3 DLVO theory gives the potential energy as the sum of the electrostatic (repulsive) and the van der Waals (attractive) forces. The equation shown here is for equal-sized spherical particles (H R). If the particles Interact over a (liquid) medium (as opposed to vacuum), the Hamaker constant (A) becomes an effective Hamaker constant. The secondary shallow minimum (of a few kaTj at rather high separations indicates reversible flocculation. The aggregates are rather loose (weak) and are called floes. This secondary minimum has been confirmed experimentally and often can disappear with a small energy input, e.g. gentle stirring...

In the case of biopolymer molecules residing in the space between colloidal particles or droplets, the force associated with the deep energy minimum at contact is often referred to as the depletion force because the intervening biopolymer species are depleted from the narrow gap between the pair of neighbouring particles. This attractive interparticle interaction underlies the phenomenon of reversible depletion flocculation in oil-in-water emulsions (see equation (3.41) in chapter 3). 

From these two successive experiments it can be concluded that (i) flocculation can be induced by macromolecules (ii) this flocculation is a reversible process. The reversibility is due to the low energy of interaction between both components. This last point was obvious from the adsorption isotherm (Figure 2), where significant amounts of free polymer remain in equilibrium with unsaturated surfaces. 

---