= Solution
<charge stabilization of colloids> supplies repulsion when like-charged surfaces and their <electric double layers> approach. <steric stabilization> uses attached or adsorbed molecular layers whose overlap costs conformational and osmotic <free energy>. Combining both gives <electrosteric stabilization>; a solvated coating must remain attached and well solvated. A viscous medium slows encounters but does not by itself create an equilibrium repulsive barrier.
<DLVO theory> adds screened electrostatic repulsion to <Van der Waals force>. A representative close-gap form is
$$
U(h)\simeq B e^{-\kappa h}-\frac{A_Ha}{12h},
$$
for equal spheres of radius $a$, with <Hamaker constant> $A_H$ and inverse <Debye–Hückel screening length> $\kappa$. The formula is schematic near molecular contact, where hydration, surface roughness and finite <ion> size matter. A repulsive barrier many $k_BT$ high produces kinetic stability even if the primary attractive minimum is deeper than the dispersed state. Entry into that primary minimum generally gives strongly bound aggregation; a shallow secondary minimum can give reversible flocculation.
Adding <electrolyte> increases $\kappa$, shortens the repulsion and can remove the barrier, enabling fast diffusion-limited aggregation. The <critical coagulation concentration> is the approximate salt <concentration> at which this rapid-coagulation regime begins under specified conditions. It is not a universal property of the salt alone. Test the prediction using time-resolved <dynamic light scattering> or turbidity at controlled particle <concentration>, pH and <temperature>; check that added <ions> do not specifically adsorb or change the surface chemistry.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2019/paper-1-colloid-potentials.png]
{title=Original schematic DLVO interaction curves showing a stabilizing barrier, secondary minimum and barrier loss on salt addition}
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