Settling velocity and effective density analysis for aquaculture floc particles: An approach through bivariate parametric copula

The study of flocs' characteristics in aquaculture tanks remains challenging due to their complex composition. Nevertheless, the application of experimental methods, such as particle tracking velocimetry (PTV), has made it possible to measure particle diameters and settling velocities. With the experimental data, bivariate distribution functions through copula modelling were employed to provide a more accurate estimation of the effective density of flocs through the empirical model proposed by Lau and Krishnappan. It was observed that the primary particle density constituting the flocs varied between 1051 kg/m³ and 1426 kg/m³. Moreover, when considering a variable primary particle density, effective floc density values ranging from 980 kg/m³ to 1500 kg/m³ were obtained for floc diameters ranging from 0.068 mm to 1.9 mm, respectively. This variation confirms that the b and c parameters of the Lau-Krishnappan model change for each floc diameter range following the quantiles associated with the conditional probability of diameter and settling velocity. Thus, employing copula approximation, a more accurate fit of the Lau-Krishnappan model was achieved, considering a wide range of particle diameters at the tails. This approach offers better estimates of floc effective density and settling velocity, essential for enhancing the selection and design of aquaculture tanks and settlers to ensure efficient solids removal.