Colloids and Colloidal Stability
Colloidal particles or shortly colloids are objects with the dimensions in the range roughly between 100 nanometers to 1 micron. When these particles are dispersed in a liquid medium we get a colloidal suspension. The examples of suspensions from everyday life include milk, paint, blood, etc. One of the key properties of these systems is their stability. Particles can be either stable and well dispersed in the medium or they can stick together to form aggregates. Both processes are important. For example in the paint we want the particles to be stable and not to aggregate and sediment to the bottom of the paint container. On the other hand in the water waste treatment, we want that the fine dirt particles aggregate and sediment in order to separate them from the clean water.
Stability of the suspensions can be measured experimentally by Light Scattering techniques. During the aggregation process the change of the scattering intensity is monitored (Static Light Scattering) and/or the change of the apparent hydrodynamic radius (Dynamic Light Scattering). From this changes the aggregation rate can be calculated and hence the stability ratio [1]. By combining the two techniques into Simultaneous Static and Dynamic Light Scattering (SSDLS) one can measure also the absolute aggregation rate constant [1].

Figure 1. Animation of aggregation of colloidal particles (left) and schematic stability plot of the colloidal suspensions versus the coagulant concentration (right, Source: www.wikipedia.org).
Colloidal suspensions can be also treated theoretically. The classical DLVO theory was developed in 1940s and has successfully explained the stability of the charge particles in the presence of the electrolytes. The basis for this theory is the competition of the attractive van der Waals forces and repulsive electrostatic forces, which compete to either stabilize or de-stabilize the suspension [2, 3]. If the sum of the two contributions is attractive the particles will aggregate, while the repulsive sum leads to the stable suspension.

Figure 2. When the sum of the electrostatic and van der Waals forces is repulsive the suspension is stable (upper figure), whereas the aggregation in the suspension occurs when the sum is attractive (bottom).
The electrostatic part of the DLVO forces is usually treated within the Poisson-Boltzmann theory. The theoretical results agree well with the experimentally measured interactions with AFM [4, 5]. Also the calculated stability ratios are in accordance with the experimental values [6, 7].
References
[1] Holthoff, H. et al. Coagulation rate measurements of colloidal particles by simultaneous static and dynamic light scattering. Langmuir 12, 5541-5549 (1996). doi: 10.1021/la960326e
[2] Israelachvili, J. N. Intermolecular and surface forces: revised third edition. Academic press, 2011.
[3] Russel, W. B.; Saville D. A.; Schowalter, W. R. Colloidal dispersions. Cambridge University Press, 1992.
[4] Popa, Ionel, et al. "Importance of charge regulation in attractive double-layer forces between dissimilar surfaces." Physical review letters 104.22 (2010): 228301. 10.1103/PhysRevLett.104.228301.
[5] Borkovec, Michal, et al. "Investigating Forces between Charged Particles in the Presence of Oppositely Charged Polyelectrolytes with the Multi-Particle Colloidal Probe Technique." Advances in Colloid and Interface Science (2012). 10.1016/j.cis.2012.06.005.
[6] Behrens, Sven Holger, et al. "Charging and aggregation properties of carboxyl latex particles: Experiments versus DLVO theory." Langmuir 16.6 (2000): 2566-2575. 10.1021/la991154z.
[7] Sadeghpour, Amin, Istvan Szilagyi, and Michal Borkovec. "Charging and Aggregation of Positively Charged Colloidal Latex Particles in Presence of Multivalent Polycarboxylate Anions." Zeitschrift fur Physikalische Chemie (2012). 10.1524/zpch.2012.0259.