## Info

Boyd et al.

Boyd et al. unpublished results

Test

Ccr for spring bloom

Ccr for N. Sea bloom

Maximum algal concentration

Ccr in mesocosm

Ccr for Fe fertilization experiment SOIREE

Ccr for Fe fertilization experiment IronEx 2

Ccr to Fe fertilization experiment SERIES

Result

Successfully predict maximum concentration Prediction 10 x high Unclear. Chl higher than expected Successful

Successfully predict non-coagulation Successfully predict timing of export Successfully predict maximum concentration

Comment

Measure a

No actual cell concentration or a measured Conversion of data required Assume a = 1

The critical concentration provides a simple estimate of the maximum concentration that algal population can attain during a bloom situation. It has been remarkably successful when tested against bloom situations (Table 13.2). Its use to predict the effect of ocean fertilization experiments is particularly striking.55 The stickiness parameter a provides an important tuning parameter. Note that Riebesell51'52 would have successfully predicted the maximum bloom concentration in the North Sea with a = 1 rather than the 0.1 he assumed.

### 13.3.1.2 Coagulation in a Stirred Container

One well-studied system is a vessel with an imposed (known) shear rate and an initially uniform (monodisperse) particle population.56,57 In the initial stages of coagulation, interactions among single particles dominate coagulation and, hence, the change in total particle concentration CT. For small changes in particle number in C1, CT decreases by coagulation from collision of monomers:

Time (days)

FIGURE 13.2 Total particle concentration through time for an initially monodisperse system. Solid line: solution calculated numerically using Equation (13.9); dashed line: approximate solution calculated using Equation (13.17). Calculation conditions: y = 10 sec-1; ri = 10 ^m; a = 1. Aggregate sizes in the calculation ranged from i = 1 to 100 monomers. There was little loss of particle mass from the system within the first 0.3 days. The divergence between the approximate and simulated solutions increases with decreasing particle numbers.

Time (days)

FIGURE 13.2 Total particle concentration through time for an initially monodisperse system. Solid line: solution calculated numerically using Equation (13.9); dashed line: approximate solution calculated using Equation (13.17). Calculation conditions: y = 10 sec-1; ri = 10 ^m; a = 1. Aggregate sizes in the calculation ranged from i = 1 to 100 monomers. There was little loss of particle mass from the system within the first 0.3 days. The divergence between the approximate and simulated solutions increases with decreasing particle numbers.

Further simplifying by assuming that Cv,1 is constant, the model predicts that

where C0 is the initial particle concentration. The simplicity of this result has led to its use to determine the value of a as a fitting parameter.46,57,58

A numerical calculation of the coagulation in this system shows how the total particle concentration changes in time (Figure 13.2). The rate of change does diverge with time.

### 13.3.1.3 Steady-State Size Spectra

Hunt8,9 applied the scaling techniques of Friedlander20 to estimate the expected shape of particle size spectra in aquatic systems. He predicted that the spectrum should be proportional to the r-z5, r-4, and r-45 in the size ranges where Brownian motion, shear, and differential sedimentation dominate. This calculation was based on a scaling argument that assumes that particles are continually produced, that coagulation moves mass to ever larger particles until they sediment out, and that only one coagulation mechanism dominates at a given particle size.

Burd and Jackson59 calculated the spectra numerically and compared them to the results from scaling analysis (Table 13.3). Their results showed that the processes

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