The power law in particle size analysis for aquacultural facilities

Fine particles tend to accumulate in recirculating aquacultural facilities, which can lead to serious fish health problems. The literature indicated that in many particle systems, the particle size distribution may be accurately represented by a two-parameter, hyperbolic power-law function, dN/dl=Al^−β.

The purpose of this paper is to investigate whether this observation holds for aquacultural facilities. Particle size distribution data from four research establishments were examined, using 14 data sets, comprising 11 aquacultural systems, and covering three species of salmonids and one of striped bass. In the data examined, the exponent, β, varied from 2.9 to 4.6, with one sample reaching as high as 6.3. Correlation coefficients varied from 0.998 to 0.975. Larger exponents, indicating a greater number of fine particles, appear to dominate recirculating aquaculture systems.

The results strongly suggest that a hyperbolic distribution is valid for aquaculture systems. The usefulness in this technique is that once a worker has established the exponent from the distribution of particle sizes at any given point in his facility, an estimate of particulate contributions by size to the total particle number, surface area and volume/mass concentration can be obtained.