Particle aggregation

Particle agglomeration refers to formation of assemblages in a suspension and represents a mechanism leading to destabilization of colloidal systems. During this process, particles dispersed in the liquid phase stick to each other, and spontaneously form irregular particle clusters, flocs, or aggregates. This phenomenon is also referred to as coagulation or flocculation and such a suspension is also called unstable. Particle aggregation can be induced by adding salts or another chemical referred to as coagulant or flocculant. Some people refer specifically to flocculation when aggregation is induced by addition of polymers or polyelectrolytes, while coagulation is used in a broader sense. Particle agglomeration refers to formation of assemblages in a suspension and represents a mechanism leading to destabilization of colloidal systems. During this process, particles dispersed in the liquid phase stick to each other, and spontaneously form irregular particle clusters, flocs, or aggregates. This phenomenon is also referred to as coagulation or flocculation and such a suspension is also called unstable. Particle aggregation can be induced by adding salts or another chemical referred to as coagulant or flocculant. Some people refer specifically to flocculation when aggregation is induced by addition of polymers or polyelectrolytes, while coagulation is used in a broader sense. Particle aggregation is normally an irreversible process. Once particle aggregates have formed, they will not easily disrupt. In the course of aggregation, the aggregates will grow in size, and as a consequence they may settle to the bottom of the container, which is referred to as sedimentation. Alternatively, a colloidal gel may form in concentrated suspensions which changes its rheological properties. The reverse process whereby particle aggregates are disrupted and dispersed as individual particles, referred to as peptization, hardly occurs spontaneously, but may occur under stirring or shear. Colloidal particles may also remain dispersed in liquids for long periods of time (days to years). This phenomenon is referred to as colloidal stability and such a suspension is said to be stable. Stable suspensions are often obtained at low salt concentrations or by addition of chemicals referred to as stabilizers or stabilizing agents. The stability of particles, colloidal or otherwise, is most commonly evaluated in terms of zeta potential. This parameter provides a readily quantifiable measure of interparticle replusion, which is the key inhibitor of particle aggregation. Similar aggregation processes occur in other dispersed systems too. In emulsions, they may also be coupled to droplet coalescence, and not only lead to sedimentation but also to creaming. In aerosols, airborne particles may equally aggregate and form larger clusters (e.g., soot). A well dispersed colloidal suspension consists of individual, separated particles and is stabilized by repulsive inter-particle forces. When the repulsive forces weaken or become attractive through the addition of a coagulant, particles start to aggregate. Initially, particle doublets A2 will form from singlets A1 according to the scheme In the early stage of the aggregation process, the suspension mainly contains particle monomers and some dimers. The rate of this reaction is characterized by the aggregation rate coefficient k. Since doublet formation is a second order rate process, the units of this coefficients are m3s−1 since particle concentrations are expressed as particle number per unit volume (m−3). Since absolute aggregation rates are difficult to measure, one often refers to the dimensionless stability ratio W = kfast/k where kfast is the aggregation rate coefficient in the fast regime, and k the coefficient at the conditions of interest. The stability ratio is close to unity in the fast regime, increases in the slow regime, and becomes very large when the suspension is stable. When the interaction potential between the particles is purely attractive, the aggregation process is solely limited by mutual diffusion (or Brownian motion) of the particles, one refers to fast, rapid or diffusion limited aggregation (DLA). When the interaction potential shows an intermediate barrier, the aggregation is slowed down by the fact that numerous attempts will be necessary to overcome this barrier, and one refers to slow or reaction limited aggregation (RLA). The aggregation can be tuned from fast to slow by varying the concentration of salt, pH, or an other additive. Since the transition from fast to slow aggregation occurs in a narrow concentration range, and one refers to this range as the critical coagulation concentration (CCC). Often, colloidal particles are suspended in water. In this case, they accumulate a surface charge and an electrical double layer forms around each particle. The overlap between the diffuse layers of two approaching particles results in a repulsive double layer interaction potential, which leads to particle stabilization. When salt is added to the suspension, the electrical double layer repulsion is screened, and van der Waals attraction become dominant and induce fast aggregation. The figure on the right shows the typical dependence of the stability ratio W versus the electrolyte concentration, whereby the regimes of slow and fast aggregation are indicated. The table below summarizes CCC ranges for different net charge of the counter ion.The charge is expressed in units of elementary charge. This dependence reflects the Schulze-Hardy rule, which states that the CCC varies as the inverse sixth power of the counter ion charge. The CCC also depends on the type of ion somewhat, even if they carry the same charge. This dependence may reflect different particle properties or different ion affinities to the particle surface. Since particles are frequently negatively charged, multivalent metal cations thus represent highly effective coagulants.