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

Type Article
Date 2011-03
Language English
Author(s) Mietta Francesca1, Chassagne Claire1, Verney RomaricORCID2, Winterwerp Johan C.1, 3
Affiliation(s) 1 : Delft Univ Technol, Fac Civil Engn & Geosci, NL-2600 GA Delft, Netherlands.
2 : IFREMER, Lab Dyneco Physed, F-29280 Plouzane, France.
3 : Deltares, NL-2600 MH Delft, Netherlands.
Source Ocean Dynamics (1616-7341) (Springer Heidelberg), 2011-03 , Vol. 61 , N. 2-3 , P. 257-271
DOI 10.1007/s10236-010-0330-2
WOS© Times Cited 27
Keyword(s) Flocculation, Population balance equation, Discretization into classes, Kaolinite, Natural mud, zeta-Potential
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 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.
Full Text
File Pages Size Access
Publisher's official version 15 447 KB Open access
Top of the page