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Particle agglomeration refers to formation of assemblages in a
suspension Suspension or suspended may refer to: Science and engineering * Suspension (topology), in mathematics * Suspension (dynamical systems), in mathematics * Suspension of a ring, in mathematics * Suspension (chemistry), small solid particles suspend ...
and represents a mechanism leading to the functional destabilization of
colloid A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
al systems. During this process, particles dispersed in the liquid phase stick to each other, and spontaneously form irregular particle assemblages, flocs, or agglomerates. This phenomenon is also referred to as
coagulation Coagulation, also known as clotting, is the process by which blood changes from a liquid to a gel, forming a blood clot. It potentially results in hemostasis, the cessation of blood loss from a damaged vessel, followed by repair. The mechanism o ...
or
flocculation Flocculation, in the field of chemistry, is a process by which colloidal particles come out of suspension to sediment under the form of floc or flake, either spontaneously or due to the addition of a clarifying agent. The action differs from pr ...
and such a suspension is also called ''unstable''. Particle agglomeration can be induced by adding salts or other chemicals referred to as coagulant or flocculant.M. Elimelech, J. Gregory, X. Jia, R. Williams, ''Particle Deposition and Aggregation: Measurement, Modelling and Simulation'', Butterworth-Heinemann, 1998. Particle agglomeration can be a reversible or irreversible process. Particle agglomerates defined as "hard agglomerates" are more difficult to redisperse to the initial single particles. In the course of agglomeration, the agglomerates will grow in size, and as a consequence they may
settle Settle or SETTLE may refer to: Places * Settle, Kentucky, United States * Settle, North Yorkshire, a town in England ** Settle Rural District, a historical administrative district Music * Settle (band), an indie rock band from Pennsylvania * ''S ...
to the bottom of the container, which is referred to as
sedimentation Sedimentation is the deposition of sediments. It takes place when particles in suspension settle out of the fluid in which they are entrained and come to rest against a barrier. This is due to their motion through the fluid in response to the ...
. Alternatively, a colloidal
gel A gel is a semi-solid that can have properties ranging from soft and weak to hard and tough. Gels are defined as a substantially dilute cross-linked system, which exhibits no flow when in the steady-state, although the liquid phase may still dif ...
may form in concentrated suspensions which changes its rheological properties. The reverse process whereby particle agglomerates are re-dispersed as individual particles, referred to as
peptization Peptization or deflocculation is the process of converting precipitate into colloid by shaking it with a suitable electrolyte called peptizing agent. This is particularly important in colloid chemistry or for precipitation reactions in an aqueous s ...
, hardly occurs spontaneously, but may occur under stirring or
shear Shear may refer to: Textile production *Animal shearing, the collection of wool from various species **Sheep shearing *The removal of nap during wool cloth production Science and technology Engineering *Shear strength (soil), the shear strength ...
. 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 functionally ''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 Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface. Zeta potential is a scientific term for electrokinetic potential in coll ...
. This parameter provides a readily quantifiable measure of interparticle repulsion, which is the key inhibitor of particle aggregation. Similar agglomeration processes occur in other dispersed systems too. In
emulsion An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloids. Althoug ...
s, they may also be coupled to droplet
coalescence Coalescence may refer to: * Coalescence (chemistry), the process by which two or more separate masses of miscible substances seem to "pull" each other together should they make the slightest contact * Coalescence (computer science), the merging of ...
, and not only lead to sedimentation but also to creaming. In
aerosol An aerosol is a suspension (chemistry), suspension of fine solid particles or liquid Drop (liquid), droplets in air or another gas. Aerosols can be natural or Human impact on the environment, anthropogenic. Examples of natural aerosols are fog o ...
s, airborne particles may equally aggregate and form larger clusters (e.g.,
soot Soot ( ) is a mass of impure carbon particles resulting from the incomplete combustion of hydrocarbons. It is more properly restricted to the product of the gas-phase combustion process but is commonly extended to include the residual pyrolysed ...
).


Early stages

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 schemeW. B. Russel, D. A. Saville, W. R. Schowalter,''Colloidal Dispersions'',Cambridge University Press, 1989. : A1 + A1 → A2 In the early stage of the aggregation process, the suspension mainly contains individual particles. The rate of this phenomenon 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'' = ''k''fast/''k'' where ''k''fast 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. 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 the critical coagulation concentration (CCC) ranges for different net charge of the counter
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
. The charge is expressed in units of
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
. 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. Adsorption of oppositely charged species (e.g., protons, specifically adsorbing ions,
surfactant Surfactants are chemical compounds that decrease the surface tension between two liquids, between a gas and a liquid, or interfacial tension between a liquid and a solid. Surfactants may act as detergents, wetting agents, emulsifiers, foaming ...
s, or
polyelectrolyte Polyelectrolytes are polymers whose repeating units bear an electrolyte group. Ion#Anions and cations, Polycations and polyanions are polyelectrolytes. These groups dissociation (chemistry), dissociate in aqueous solutions (water), making the pol ...
s) may destabilize a particle suspension by charge neutralization or stabilize it by buildup of charge, leading to a fast aggregation near the charge neutralization point, and slow aggregation away from it. Quantitative interpretation of colloidal stability was first formulated within the
DLVO theory The DLVO theory (named after Boris Derjaguin and Lev Landau, Evert Verwey and Theodoor Overbeek) explains the aggregation of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium ...
. This theory confirms the existence slow and fast aggregation regimes, even though in the slow regime the dependence on the salt concentration is often predicted to be much stronger than observed experimentally. The Schulze–Hardy rule can be derived from
DLVO theory The DLVO theory (named after Boris Derjaguin and Lev Landau, Evert Verwey and Theodoor Overbeek) explains the aggregation of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium ...
as well. Other mechanisms of colloid stabilization are equally possible, particularly, involving polymers. Adsorbed or grafted polymers may form a protective layer around the particles, induce steric repulsive forces, and lead to steric stabilization at it is the case with
polycarboxylate ether Polycarboxylates are linear polymers with a high molecular mass (Mr ≤ 100 000) and with many carboxylate groups. They are polymers of acrylic acid or copolymers of acrylic acid and maleic acid. The polymer is used as the sodium salt (see: sodium ...
(PCE), the last generation of chemically tailored
superplasticizer Superplasticizers (SPs), also known as high range water reducers, are additives used in making high strength concrete. Plasticizers are chemical compounds that enable the production of concrete with approximately 15% less water content. Superplast ...
specifically designed to increase the workability of
concrete Concrete is a composite material composed of fine and coarse aggregate bonded together with a fluid cement (cement paste) that hardens (cures) over time. Concrete is the second-most-used substance in the world after water, and is the most wi ...
while reducing its water content to improve its properties and durability. When polymers chains adsorb to particles loosely, a polymer chain may bridge two particles, and induce bridging forces. This situation is referred to as bridging
flocculation Flocculation, in the field of chemistry, is a process by which colloidal particles come out of suspension to sediment under the form of floc or flake, either spontaneously or due to the addition of a clarifying agent. The action differs from pr ...
. When particle aggregation is solely driven by diffusion, one refers to ''perikinetic'' aggregation. Aggregation can be enhanced through
shear stress Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ot ...
(e.g., stirring). The latter case is called ''orthokinetic'' aggregation.


Later stages

As the aggregation process continues, larger clusters form. The growth occurs mainly through encounters between different clusters, and therefore one refers to cluster-cluster aggregation process. The resulting clusters are irregular, but statistically self-similar. They are examples of mass
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
s, whereby their mass ''M'' grows with their typical size characterized by the
radius of gyration ''Radius of gyration'' or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentr ...
''R''g as a power-law : M \propto R_g^d where ''d'' is the mass fractal dimension. Depending whether the aggregation is fast or slow, one refers to diffusion limited cluster aggregation (DLCA) or reaction limited cluster aggregation (RLCA). The clusters have different characteristics in each regime. DLCA clusters are loose and ramified (''d'' ≈ 1.8), while the RLCA clusters are more compact (''d'' ≈ 2.1). The cluster size distribution is also different in these two regimes. DLCA clusters are relatively monodisperse, while the size distribution of RLCA clusters is very broad. The larger the cluster size, the faster their settling velocity. Therefore, aggregating particles sediment and this mechanism provides a way for separating them from suspension. At higher particle concentrations, the growing clusters may interlink, and form a particle
gel A gel is a semi-solid that can have properties ranging from soft and weak to hard and tough. Gels are defined as a substantially dilute cross-linked system, which exhibits no flow when in the steady-state, although the liquid phase may still dif ...
. Such a gel is an elastic solid body, but differs from ordinary solids by having a very low
elastic modulus An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is ...
.


Homoaggregation versus heteroaggregation

When aggregation occurs in a suspension composed of similar monodisperse colloidal particles, the process is called ''homoaggregation'' (or ''homocoagulation''). When aggregation occurs in a suspension composed of dissimilar colloidal particles, one refers to ''heteroaggregation'' (or ''heterocoagulation''). The simplest heteroaggregation process occurs when two types of monodisperse colloidal particles are mixed. In the early stages, three types of doublets may form : A + A → A2 : B + B → B2 : A + B → AB While the first two processes correspond to homoaggregation in pure suspensions containing particles A or B, the last reaction represents the actual heteroaggregation process. Each of these reactions is characterized by the respective aggregation coefficients ''k''AA, ''k''BB, and ''k''AB. For example, when particles A and B bear positive and negative charge, respectively, the homoaggregation rates may be slow, while the heteroaggregation rate is fast. In contrast to homoaggregation, the heteroaggregation rate accelerates with decreasing salt concentration. Clusters formed at later stages of such heteroaggregation processes are even more ramified that those obtained during DLCA (''d'' ≈ 1.4). An important special case of a heteroaggregation process is the deposition of particles on a substrate. Early stages of the process correspond to the attachment of individual particles to the substrate, which can be pictures as another, much larger particle. Later stages may reflect blocking of the substrate through repulsive interactions between the particles, while attractive interactions may lead to multilayer growth, and is also referred to as ripening. These phenomena are relevant in membrane or filter
fouling Fouling is the accumulation of unwanted material on solid surfaces. The fouling materials can consist of either living organisms (biofouling) or a non-living substance (inorganic or organic). Fouling is usually distinguished from other surf ...
.


Experimental techniques

Numerous experimental techniques have been developed to study particle aggregation. Most frequently used are time-resolved optical techniques that are based on
transmittance Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is t ...
or scattering of light. Light transmission. The variation of transmitted light through an aggregating suspension can be studied with a regular spectrophotometer in the visible region. As aggregation proceeds, the medium becomes more turbid, and its
absorbance Absorbance is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample (excluding the effects on cell walls)". Alternatively, for samples which scatter light, absorbance may be defined as "the negative lo ...
increases. The increase of the absorbance can be related to the aggregation rate constant ''k'' and the stability ratio can be estimated from such measurements. The advantage of this technique is its simplicity. Light scattering. These techniques are based on probing the scattered light from an aggregating suspension in a time-resolved fashion.
Static light scattering Static light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight ''Mw'' of a macromolecule like a polymer or a protein in solution. Measurement of the scattering ...
yields the change in the scattering intensity, while
dynamic light scattering Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using ...
the variation in the apparent hydrodynamic radius. At early-stages of aggregation, the variation of each of these quantities is directly proportional to the aggregation rate constant ''k''. At later stages, one can obtain information on the clusters formed (e.g., fractal dimension). Light scattering works well for a wide range of particle sizes. Multiple scattering effects may have to be considered, since scattering becomes increasingly important for larger particles or larger aggregates. Such effects can be neglected in weakly turbid suspensions. Aggregation processes in strongly scattering systems have been studied with
transmittance Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is t ...
, backscattering techniques or diffusing-wave spectroscopy. Single particle counting. This technique offers excellent resolution, whereby clusters made out of tenths of particles can be resolved individually. The aggregating suspension is forced through a narrow capillary
particle counter A particle counter is used for monitoring and diagnosing particle contamination within specific clean media, including air, water and chemicals. Particle counters are used in a variety of applications in support of clean manufacturing practices, ...
and the size of each aggregate is being analyzed by light scattering. From the scattering intensity, one can deduce the size of each aggregate, and construct a detailed aggregate size distribution. If the suspensions contain high amounts of salt, one could equally use a
Coulter counter A Coulter counter is an apparatus for counting and sizing particles suspended in electrolytes. The Coulter counter is the commercial term for the technique known as resistive pulse sensing or electrical zone sensing, the apparatus is based on ...
. As time proceeds, the size distribution shifts towards larger aggregates, and from this variation aggregation and breakup rates involving different clusters can be deduced. The disadvantage of the technique is that the aggregates are forced through a narrow capillary under high shear, and the aggregates may disrupt under these conditions. Indirect techniques. As many properties of colloidal suspensions depend on the state of aggregation of the suspended particles, various indirect techniques have been used to monitor particle aggregation too. While it can be difficult to obtain quantitative information on aggregation rates or cluster properties from such experiments, they can be most valuable for practical applications. Among these techniques
settling Settling is the process by which particulates move towards the bottom of a liquid and form a sediment. Particles that experience a force, either due to gravity or due to centrifugal motion will tend to move in a uniform manner in the direction e ...
tests are most relevant. When one inspects a series of test tubes with suspensions prepared at different concentration of the flocculant, stable suspensions often remain dispersed, while the unstable ones settle. Automated instruments based on light scattering/transmittance to monitor suspension settling have been developed, and they can be used to probe particle aggregation. One must realize, however, that these techniques may not always reflect the actual aggregation state of a suspension correctly. For example, larger primary particles may settle even in the absence of aggregation, or aggregates that have formed a colloidal gel will remain in suspension. Other indirect techniques capable to monitor the state of aggregation include, for example,
filtration Filtration is a physical separation process that separates solid matter and fluid from a mixture using a ''filter medium'' that has a complex structure through which only the fluid can pass. Solid particles that cannot pass through the filter ...
,
rheology Rheology (; ) is the study of the flow of matter, primarily in a fluid ( liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an appl ...
, absorption of ultrasonic waves, or
dielectric properties In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
.


Relevance

Particle aggregation is a widespread phenomenon, which spontaneously occurs in nature but is also widely explored in manufacturing. Some examples include. Formation of river delta. When river water carrying suspended sediment particles reaches salty water, particle aggregation may be one of the factors responsible for river delta formation. Charged particles are stable in river's fresh water containing low levels of salt, but they become unstable in sea water containing high levels of salt. In the latter medium, the particles aggregate, the larger aggregates sediment, and thus create the river delta.
Papermaking Papermaking is the manufacture of paper and cardboard, which are used widely for printing, writing, and packaging, among many other purposes. Today almost all paper is made using industrial machinery, while handmade paper survives as a speciali ...
. Retention aids are added to the pulp to accelerate paper formation. These aids are coagulating aids, which accelerate the aggregation between the cellulose fibers and filler particles. Frequently, cationic polyelectrolytes are being used for that purpose.
Water treatment Water treatment is any process that improves the Water quality, quality of water to make it appropriate for a specific end-use. The end use may be drinking water, drinking, industrial water supply, irrigation, river flow maintenance, water recrea ...
. Treatment of municipal waste water normally includes a phase where fine solid particles are removed. This separation is achieved by addition of a flocculating or coagulating agent, which induce the aggregation of the suspended solids. The aggregates are normally separated by sedimentation, leading to sewage sludge. Commonly used flocculating agents in water treatment include multivalent metal ions (e.g., Fe3+ or Al3+),
polyelectrolyte Polyelectrolytes are polymers whose repeating units bear an electrolyte group. Ion#Anions and cations, Polycations and polyanions are polyelectrolytes. These groups dissociation (chemistry), dissociate in aqueous solutions (water), making the pol ...
s, or both. Cheese making. The key step in cheese production is the separation of the milk into solid curds and liquid whey. This separation is achieved by inducing the aggregation processes between casein micelles by acidifying the milk or adding rennet. The acidification neutralizes the carboxylate groups on the micelles and induces the aggregation.


See also

*
Aerosol An aerosol is a suspension (chemistry), suspension of fine solid particles or liquid Drop (liquid), droplets in air or another gas. Aerosols can be natural or Human impact on the environment, anthropogenic. Examples of natural aerosols are fog o ...
*
Colloid A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
*
Clarifying agent Clarifying agents are used to remove suspended solids from liquids by inducing flocculation, causing the solids to form larger aggregates that can be easily removed after they either float to the surface or sink to the bottom of the containment vess ...
*
Double layer forces Double layer forces occur between charged objects across liquids, typically water. This force acts over distances that are comparable to the Debye length, which is on the order of one to a few tenths of nanometers. The strength of these forces incr ...
*
DLVO theory The DLVO theory (named after Boris Derjaguin and Lev Landau, Evert Verwey and Theodoor Overbeek) explains the aggregation of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium ...
(stability of colloids) * Electrical double layer *
Emulsion An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloids. Althoug ...
*
Flocculation Flocculation, in the field of chemistry, is a process by which colloidal particles come out of suspension to sediment under the form of floc or flake, either spontaneously or due to the addition of a clarifying agent. The action differs from pr ...
*
Gel A gel is a semi-solid that can have properties ranging from soft and weak to hard and tough. Gels are defined as a substantially dilute cross-linked system, which exhibits no flow when in the steady-state, although the liquid phase may still dif ...
*
Nanoparticle A nanoparticle or ultrafine particle is usually defined as a particle of matter that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 1 ...
*
Particle deposition Particle deposition is the spontaneous attachment of particles to surfaces. The particles in question are normally colloidal particles, while the surfaces involved may be planar, curved, or may represent particles much larger in size than the depos ...
*
Peptization Peptization or deflocculation is the process of converting precipitate into colloid by shaking it with a suitable electrolyte called peptizing agent. This is particularly important in colloid chemistry or for precipitation reactions in an aqueous s ...
*
Reaction rate The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit ...
*
Settling Settling is the process by which particulates move towards the bottom of a liquid and form a sediment. Particles that experience a force, either due to gravity or due to centrifugal motion will tend to move in a uniform manner in the direction e ...
*
Smoluchowski coagulation equation In statistical physics, the Smoluchowski coagulation equation is a population balance equation introduced by Marian Smoluchowski in a seminal 1916 publication, describing the time evolution of the number density of particles as they coagulate (in ...
* Sol-gel * Surface charge * Suspension (chemistry)


References


External links


in Microgravity
{{DEFAULTSORT:Particle Aggregation Chemistry Materials science Colloidal chemistry