Lakes particle aggregation

This chapter is written with two objectives (1) to discuss field, laboratory, and modeling results in which the kinetics of particle aggregation and deposition in natural aquatic systems are developed and tested and (2) to indicate approaches for studying the kinetics of such reactions in these and other aquatic systems in practice and in research. The chapter begins with a consideration of the kinetics of particle deposition in groundwater aquifers. This is followed by an assessment of particle aggregation and sedimentation in lakes. A modeling approach for the kinetics of particle-particle interactions in aquatic systems is then presented. 

The term on the left-hand-side of Eq. 6 is the net rate of change in the number concentration of particles of size k in the epilimnion. The first two terms on the right-hand side are Smoluchowski s (1917) expressions for the kinetics of particle aggregation. The third term is the rate of loss of particles of size k from the epilimnion to the bottom waters by sedimentation. The fourth term W, includes all particle inputs to the lake save for those in riverine inflows, and also particle destruction processes in the epilimnion. The final two terms on the right-hand side describe rates of particle inputs and discharge by river flows. 

Particle aggregation in Lake Zurich is considered here to have an attachment probability of 0.1 (Table 5). When both coagulation and sedimentation are occurring [i.e., if rx(/, 0.1 and pp — 1.05 gem 3], smaller particles are... 

With hydraulic residence times ranging from months to years, lakes are efficient settling basins for particles. Lacustrine sediments are sinks for nutrients and for pollutants such as heavy metals and synthetic organic compounds that associate with settling particles. Natural aggregation (coagulation) increases particle sizes and thus particle settling velocities (Eq. 7.1) and accelerates particle removal to the bottom sediments and decreases particle concentrations in the water column. 

Model simulations of particle volume concentrations in the summer as functions of the particle production flux in the epilimnion of Lake Zurich, adapted from Weilenmann, O Melia and Stumm (1989). Predictions are made for the epilimnion (A) and the hypolimnion (B). Simulations are made for input particle size distributions ranging from 0.3 to 30 pm described by a power law with an exponent of p. For p = 3, the particle size distribution of inputs peaks at the largest size, i.e., 30 pm. For p = 4, an equal mass or volume input of particles is in every logaritmic size interval. Two particle or aggregate densities (pp) are considered, and a colloidal stability factor (a) of 0.1 us used. The broken line in (A) denotes predicted particle concentrations in the epilimnion when particles are removed from the lake only in the river outflow. Shaded areas show input fluxes based on the collections of total suspendet solids in sediment traps and the composition of the collected solids. 

A model for the kinetics of aggregation and sedimentation in lakes has been presented elsewhere (O Melia, 1980) a short summary is given here. The approach begins with a particle balance for the epilimnion of a lake ... 

Here nh np and nk are the number concentrations of particles of sizes i, j, and k in the epilimnion and nfc in is the number concentration of fc-size particles in river inflows. The term X(i,j)s incorporates most of the effects of physical processes on the rate at which particles of size i and j come into close proximity. The subscript S is used to indicate that Smoluchowski s approach (1917) to the kinetics of particle transport has been adopted. Smoluchowski did not consider hydro-dynamic retardation in his early analysis, and it has not been included here in Mi,j)s. A more rigorous approach is possible (Valiolis and List, 1984a, b). The term a(i J)s incorporates chemical factors that retard the kinetics of aggregation between particles of size i and j and also those aspects of the kinetics of particle transport that are not included in Smoluchowski s analysis. The Stokes settling velocity of a particle of size k is denoted as vk the mean depth of the epilimnion is zc qin and qoul refer to river flows into and out of the lake expressed as volume of water per unit of lake surface area and time (the sum of such inflows or outflows is also termed the areal hydraulic loading of the lake). The symbol W refers to all processes of production or destruction of particles in the epilimnion it can include a variety of chemical and biological processes. 

Measurements are performed to determine experimental values of the attachment coefficient, a(iJ)S(exp. These experiments involve aggregation studies using natural particles and samples of lake water in laboratory studies where interparticle contacts are produced predominantly by fluid shear. Details are given by Ali (1985) and Weilenmann (1986). Illustrative results for five lakes are given in Table 5, together with information about the concentrations of dissolved organic carbon (DOC) and Ca2 + in these lakes. 

The model for aggregation and sedimentation in lakes (Eq. 6) has a conceptual basis and is consistent with some field observations. It is used here to make predictions about the kinetics and effects of coagulation and sedimentation in Lake Zurich. The responses of a lake to coagulation and sedimentation can be represented as mass flux distributions (O Melia and Bowman, 1984). Simulations of mass fluxes by river flow, net production in the epilimnion, coagulation, and sedimentation for Lake Zurich are presented in Figure 6. The particle mass flux distributions, AJ/(A log dp), are plotted as functions of particle size (log scale) for mass fluxes by these processes in the epilimnion. A positive sign indicates a flux of mass into a given size class. 

Additional results of model simulations of the effects of coagulation and sedimentation in Lake Zurich are presented in Figure 7, adapted from Weilenmann et al. (1989). Total particle volume concentrations in the epilimnion and hypolimnion are plotted as functions of the net particle production flux in the epilimnion. Observed particle volume concentrations are 5 10 cm3 m-3 in the epilimnion and 1 cm3 m 3 in the hypolimnion. Model simulations indicate i hat these concent rations can result from a net particle production flux of S 10 cm3 m 2 day and a particle or aggregate density ranging from 1.05 to... 

The interaction in a two-body collision in a dilute suspension has been expanded to provide a useful and quantitative understanding of the aggregation and sedimentation of particulate matter in a lake. In this view, Brownian diffusion, fluid shear, and differential sedimentation provide contact opportunities that can change sedimentation processes in a lake, particularly when solution conditions are such that the particles attach readily as they do in Lake Zurich [high cc(i,j)exp]. Coagulation provides a conceptual framework that connects model predictions with field observations of particle concentrations and size distributions in lake waters and sediment traps, laboratory determinations of attachment probabilities, and measurements of the composition and fluxes of sedimenting materials (Weilenmann et al., 1989). 

There are other ways of defining the partition coefficient, e.g., not as amount in solution divided by total amount in suspension, but as concentration in water relative to concentration on suspended matter. Here, Kd is set to 0.1 as a default value, which means that 10% of X is in solution and 90% is particulate. In practice, it is evident that the Kd-value is not a constant, but a variable, which depends on, e.g., (1) the given substance X, (2) lake water pH (and all cluster parameters linked to pH, such as hardness, conductivity, alkalinity, etc.), which influences the equilibrium between X and the particulate phase and the aggregation processes of the carrier particles, (3) the presence of colored substances (humus), which often have a strong affinity to many types of suspended substances (like metals, organic toxins, radioisotopes, etc.), and (4) the character of the particulate phase (if this is clays, humic matter, Fe-oxides/hydroxides, etc.). So, in more extensive ecosystem models, one would need comprehensive submodels to predict the partition coefficient. 

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