Modeling mud flocculation using variable collision and breakup efficiencies

Solution of the Winterwerp (1998) floc growth and breakup equation yields time dependent median floc size as an outcome of collision driven floc growth and shear induced floc breakage. The formulation is quite nice in that it is an ODE that yields fast solution for median floc size and can be incorporated into sediment transport models. The Winterwerp (1998) floc size equation was used to model floc growth and breakup data from laboratory experiments conducted under both constant and variable turbulent shear rate (Keyvani 2013). The data showed that floc growth rate starts out very high and then reduces with size to asymptotically approach an equilibrium size. In modeling the data, the Winterwerp (1998) model and the Son and Hsu (2008) variant were found to be able to capture the initial fast growth phase and the equilibrium state, but were not able to well capture the slow growing phase. This resulted in flocs reaching the equilibrium state in the models much faster than the experimental data. The objective of this work was to improve the ability of the general Winterwerp (1998) formulation to better capture the slow growth phase and more accurately predict the time to equilibrium. To do this, a full parameter sensitivity analysis was conducted using the Winterwerp (1998) model. Several modifications were tested, including the variable fractal dimension and yield strength extensions of Son and Hsu (2008, 2009). The best match with the in-house data, and data from the literature, was achieved using floc collision and breakup efficiency coefficients that decrease with floc size. The net result of the decrease in both of these coefficients is that floc growth slows without modification to the equilibrium size. Inclusion of these new functions allows for substantial improvement in modeling the growth phase of flocs in both steady and variable turbulence conditions. The improvement is particularly noticeable when modeling continual growth in a decaying turbulence field similar to what might be experienced in a river mouth jet. Inclusion of the functions does, however, result in problems with capturing rapid floc breakage due to a stepwise increase in turbulent shear. References Keyvani, A. (2013). Flocculation processes in river mouth fluvial to marine transitions. Ph.D. dissertation, University of Houston. Son, M. & Hsu, T.J. (2008). Flocculation model of cohesive sediment using variable fractal dimension. Environmental Fluid Mechanics, 8(1), 55-71. Son, M. & Hsu, T.J. (2009). The effect of variable yield strength and variable fractal dimension on flocculation of cohesive sediment. Water Research, 43(14), 3582 - 3592. Winterwerp, J. C. (1998). A simple model for turbulence induced flocculation of cohesive sediment. Journal of Hydraulic Research, 36(3), 309-326.