Mechanisms And Models Of Colloidal Aggregation And Scavenging

Scavenging of pollutants and trace metals depends upon the size spectrum of the particulate material. Large particles (e.g., greater than 50 ^.m), although relatively scarce, dominate the vertical flux because of their mass and large sinking velocity. On the other hand, colloidal particles dominate the particle number concentration and adsorption kinetics. Particle aggregation and disaggregation provide physical mechanisms linking these two particle sizes — this is demonstrated in the Brownian Pumping model92-96 where trace metals are absorbed onto colloidal particles, which subsequently aggregate thereby incorporating the trace metals into larger particles. Scavenging and transport of materials, therefore, depend upon both the kinetics of aggregation and adsorption, resulting in aparticle concentration dependence of kinetic constants of metal transfer to particles with broken exponents.92,94,95

Two types of mechanism contribute to the formation of aggregates: particle collision and adhesion. The classical theory of particle collisions is well developed, at least for particles of a simple shape.35,57,97,98 The physical processes that bring particles together (Brownian motion, shear, differential sedimentation) are well described and hydrodynamic forces that can alter collision efficiencies can be taken into account.57,97 Simple models assume that a single physical collision process operates in a given particle size range, but observations and more sophisticated models suggest that this is not the case.99-101 However, on the whole, size distributions calculated from aggregation models agree favorably with observed particle size distributions.102

The probability that two particles will adhere once they have collided is less well understood. Traditionally, the DLVO (Derjaguin, Landau, Verwey, and Overbeek) theory has been used where the electrostatic and van der Waals forces between the two particles (and their environment) are evaluated to determine if the overall force is attractive or repulsive.103 A coupling of statistical-based particle aggregation models with DLVO theory gives a good representation of the formation of aggregates comprised of inorganic particles.103,104 However, it has recently become apparent that such a model cannot fully describe colloidal interactions between abiotic and biotic colloids in aquatic systems.105 This is particularly important since biologically produced transparent exopolymer particles (TEP) are thought to form the matrix around which larger aggregates form.43,45,71 Indeed, steric forces may determine exopolymer interactions in seawater.106 In addition, hydrophobic interactions and Brownian movement forces may also be important in particle adhesion involving bacterial exopolymers.107

New experiments and models are needed to improve our understanding of exopolymer interactions, and hence our ability to predict the stickiness of aquatic particles under various environmental conditions.

In many aggregation models, particularly those used to model aggregation between a broad range of heterogeneous particles, adhesion is usually described using a single, constant stickiness coefficient, a. When a = 1, all collisions result in attachment. This produces aggregates that have open, highly porous structures because small particles will have a low probability of diffusing to the central regions of a larger aggregate before colliding with, and adhering to, some part of it. Small values of the stickiness coefficient result in more compact, less porous aggregates. Because of these structural differences, the value of the stickiness coefficient should affect the sinking velocity of the particle since this depends on the particle's excess density, and hence porosity. Indeed, Engel108 has shown that increased TEP concentrations enhance the stickiness coefficient during a diatom bloom. In addition, Engel and Schartau91 have shown that particles with higher specific TEP content have lower settling velocities and a less pronounced variation of settling velocity with particle size. This indicates that the presence of biologically produced polymers can affect the fundamental structure and physical properties of large-scale macroparticles, specifically their porosity or fractal dimension and settling velocity.

Stickiness (a) is a function of many factors including pH, ionic strength, etc. Using a combination of models and observational data, Mari and Burd41 estimated the stickiness between TEP particles as being 0.6, and that between TEP and non-TEP particles as being lower at 0.3. Using radio-labeled colloidal organic matter, which was passed through silica columns, Quigley et al.55 determined a slightly higher stickiness factor of 0.88 for the polysaccharide enriched fraction (containing mostly fibrils) vs. 0.7 for the bulk fraction. These estimates indicate that TEP concentration is important for determining the structure of aquatic particles; however, they are rarely included explicitly in models.

Simulations of particle aggregation in aquatic systems have usually been restricted to considering aggregates composed of homogeneous primary particles, usually spheres. In these simulations, all aggregates are assumed to have the same fractal dimension regardless of their size. Aggregation dynamics proceeds by the standard Smoluchowsi model.97 These models have successfully incorporated particle sizes ranging from 1 nm to 1 ^m and have been used to examine the scavenging of thorium from surface oceanic waters.96 These models indicate the importance of particle size in determining the adsorption rate of trace metals.

In reality, environmental aggregates are highly heterogeneous.1,11 The structure and physical properties of aggregates formed from monomers of different sizes differ from those formed from monomers of a single size.109 More sophisticated models that can include different particle types (e.g., phytoplankton and fecal pellets) have been developed110,111 and indicate the importance of particle aggregation for understanding the vertical flux of material from the ocean surface.

A different modeling approach has used combinations of small spherical particles and polymer chains—bridging flocculation,112-114 shown in Figure 9.5. The structure of polymer chains varies with environmental conditions such as pH, and both aggregation kinetics and aggregate structure depend upon the concentration and conformation

FIGURE 9.5 The effect of the relative concentration of chains and particles on aggregate structure: (a) 20 chains, (c) 40 chains. Aggregates have a structure similar to that arising from cluster-cluster aggregation when the relative concentration of chains is low. For high chain concentration, the aggregate has a network structure. (Taken from ref. [113].)

of these chains. Constant, prescribed stickiness coefficients were used, though different values were chosen for chain-chain interactions, particle-particle interactions, and chain-particle interactions. The resulting simulations indicate that polymer chain fractal dimension and the relative concentration of particles and chains are important in determining the rate of aggregate formation. Interestingly, this work also indicates that bridging flocculation can be described using simple scaling laws.

Looking into the future, full molecular dynamics simulations of large polysac-charides in aqueous environments may soon be feasible. This is a computationally difficult problem because polysaccharides contain a large number of flexible and polar hydroxyl (neutral sugars) and carboxyl or sulfate (acidic sugars) groups. These can form hydrogen bonds not only between molecules but also between groups in the same molecule. Improved models of the force fields for carbohydrates115,116 bring closer the possibility of molecular dynamics models of acid polysaccharides.

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