Two of the most fundamental properties of any particle, inert or living, are its length and its mass. These two properties determine how a particle interacts with planktonic organisms as food or habitat, how it affects light, and how fast it sinks. Because organisms are discrete entities, particle processes affect them as well as nonliving material.

Life in the ocean coexists with two competing physical processes favoring surface and bottom of the ocean: light from above provides the energy to fuel the system;

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gravity from below collects essential materials encapsulated in particles. Coagulation is the formation of single, larger, particles by the collision and union of two smaller particles; very large particles can be made from smaller particles by multiple collisions. Coagulation makes bigger particles, enhances sinking rates, and accelerates the removal of photosynthate. One result is that coagulation can limit the maximum phytoplankton concentration in the euphotic zone.

Particle size distributions have been measured since the advent of the Coulter Counter in the early 1970s, when Sheldon et al.1 reported on size distributions predominantly from surface waters around the world. They reported values for particles ostensibly between 1 and 1000 ^m, although sampling and instrumental consideration suggest that the range was significantly smaller.2 There were approximately equal amounts of matter in equal logarithmic size intervals,1 a distribution that is characteristic of a particle number size spectrum n ~ r-4, where r is the particle radius and n is defined in Equation (13.1), and has inspired theoretical models of planktonic systems. Platt and Denman3 explained the spectral shape using an ecologically motivated model in which mass cascade energy from one organism to its larger consumer. While the emphasis on organism interactions neglected the interactions of nonliving particles, it stimulated the study of organism size-abundance relationships.4-7 Hunt8,9 was the first to argue that coagulation theory could explain the spectral slope in the ocean.

The use of coagulation theory to explain planktonic processes in the ocean is more recent and was inspired by observations of large aggregates of algae and other material that were named "marine snow."10-13 Among the first observations relating marine snow length and mass were the field and laboratory observations of Alldredge and Gotshalk,14 who fit particle settling rate to power-law relationships of particle length and mass. These observations were later interpreted by Logan and Wilkinson15 as resulting from a fractal relationship between mass and length.

While there has been an extensive history of applying coagulation theory to explain the removal of particulate matter from surface waters, most early work emphasized coagulation as a removal process in lakes and esuaries.16-19 Hunt9 argued that particle size distributions in the ocean were characteristic of coagulation processes, using a dimensional argument that had been made to explain characteristic shapes of atmosphere particle distributions.20 The influential review of McCave21 examined the mechanisms and rates of coagulation in the ocean, but purposely passed over particle interactions in the surface layer because of the belief that biological processes would overwhelm coagulation there.

The early models of planktonic systems22-24 showed that coagulation could occur at rates comparable to those of more biological processes and helped to focus observations on the role of coagulation in marine systems. The physical mechanisms used to describe interactions between inorganic particles in coagulation theory have also been modified to describe the interactions between different types of planktonic organisms, with feeding replacing particle sticking.25-30

This chapter is a survey that highlights some of the evolution and usage of coagulation theory to describe dynamics of planktonic systems. The emphasis is on the physical aspect of coagulation theory, describing collision rates, rather than on the chemical aspect, describing the probability of colliding particles sticking together.

As the theory has evolved, the range of formulations applied to plankton models has increased, with no one formulation becoming standard. The divergence between the evolving sophistication of the models and their usage with observational data is symptomatic of this lack of consensus in models. More attention needs to paid to developing simple diagnostic indices that can be used to interpret field observations.

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