On the behavior of mud floc size distribution: model calibration and model behavior

Abstract

In this paper, we study a population balance equation (PBE) where flocs are distributed into classes according to their mass. Each class i contains i primary particles with mass m p and size L p . All differently sized flocs can aggregate, binary breakup into two equally sized flocs is used, and the floc's fractal dimension is d 0 = 2, independently of their size. The collision efficiency is kept constant, and the collision frequency derived by Saffman and Turner (J Fluid Mech 1:16-30, 1956) is used. For the breakup rate, the formulation by Winterwerp (J Hydraul Eng Res 36(3):309-326, 1998), which accounts for the porosity of flocs, is used. We show that the mean floc size computed with the Responsible Editor: Susana B. Vinzon PBE varies with the shear rate as the Kolmogorov microscale, as observed both in laboratory and in situ. Moreover, the equilibrium mean floc size varies linearly with a global parameter P which is proportional to the ratio between the rates of aggregation and breakup. The ratio between the parameters of aggregation and breakup can therefore be estimated analytically from the observed equilibrium floc size. The parameter for aggregation can be calibrated from the temporal evolution of the mean floc size. We calibrate the PBE model using mixing jar flocculation experiments, see Mietta et al. (J Colloid Interface Sci 336(1):134-141, 2009a, Ocean Dyn 59:751-763, 2009b) for details. We show that this model can reproduce the experimental data fairly accurately. The collision efficiency α and the ratio between parameters for aggregation and breakup α and E are shown to decrease linearly with increasing absolute value of the ζ -potential, both for mud and kaolinite suspensions. Suspensions at high pH and different dissolved salt type and concentration have been used. We show that the temporal evolution of the floc size distribution computed with this PBE is very similar to that computed with the PBE developed by Verney et al. (Cont Shelf Res, 2010) where classes are distributed following a geometrical series and mass conservation is statistically ensured. The same terms for aggregation and breakup are used in the two PBEs. Moreover, we argue, using both PBEs, that bimodal distributions become monomodal in a closed system with homogeneous sediment, even when a variable shear rate is applied.

Hydro-meteorological influences and multimodal suspended particle size distributions in the Belgian nearshore area (southern North Sea)

“…Chang et al (2007) mention that only the fraction <8 μm (analysed after pre-treatment in the laboratory) is present in flocs. This, together with the fact that the median grain size of the SPM from the study area is about 2 μm (Fettweis 2008), confirms that our flocculi (15 μm) consist of clusters of clay minerals rather than silt-sized particles, which are hardly broken down to primary particles (clay minerals), even under high shear (Mietta 2010). The data show that primary particles of possibly different composition (calcareous particles, clay minerals) and flocculi occur as building blocks of the flocs.…”

“…This behaviour is well described in the literature (e.g. Manning et al 2006;Mikkelsen et al 2007;Mietta et al 2010;Verney et al 2011) and is typically associated with tidal forcing. PSDs during storm conditions or other high-energy conditions (maximum flood currents during spring tide) are different and show unimodal or multimodal distributions.…”

“…With increasing turbulent shear, breakage of flocs generates smaller particles/flocs but resuspension of bigger deposited minerals can generate larger particles and flocs in suspension. SPM is therefore likely to have a multimodal particle size distribution Mietta et al 2010;Lee et al 2011;Verney et al 2011), which reflects the fast temporal changes in floc sizes due to variation in turbulent shear as well as the overlapping distributions of flocs and mineral grains in mixed sediment environments under strongly varying shear stresses.…”

Guidance on Setup, Calibration, and Validation of Hydrodynamic, Wave, and Sediment Models for Shelf Seas and Estuaries

“…In these cases, water sampling can destroy the delicate structures, and changes in temperature/salinity can enhance or reduce occulation potential. Both factors can lead to errors, and thus, these kinds of data must be treated with caution in the context of model calibration [87].…”

Effect of Organic Matter on the Flocculation of Colloidal Montmorillonite: A Modeling Approach

“…Flocculation can be modeled as the net sum of aggregation and breakup processes using the population balance equation (PBE) (Mietta et al, 2011;Verney et al, 2011). The PBE, based on the Smoluchowski coagulation equation (Thomas, Judd, and Fawcett, 1999), handles the floc-size spectrum using a series of discrete size bins and describes the temporal evolution of the floc population in each bin.…”