FIGURE 12.8 Relative flocculation time of mud flocs in water column (Equation (12.19)). At large h and u*, residence time is large, c.q. flocculation time is small and we expect Du ^ Dl. At small h and u*, residence time is small, c.q. flocculation time is large and we expect Du « Dl « Dl,e.

FIGURE 12.9 Particle size distribution for initial and equilibrium conditions. (After Kranck and Milligan, J. Geoph. Res., 97(C7), 11373-11382, 1992.)

floc size (i.e., Du > Dl) are expected to occur. This graph suggests that for estuarine conditions, with shear velocities of a few centimeters per second, vertical gradients in floc size only occur for suspended sediment concentrations beyond a few 100 mg/l. Around slack water, suspended sediment concentrations should even be much larger to generate significant vertical gradients in floc size (e.g. Winterwerp9). It is noted that these results are obtained for the parameter settings obtained from laboratory experiments with Ems mud, and therefore cannot be considered to be universally valid. However, this analysis clearly indicates that flocculation processes higher in the water column, as depicted in Figure 12.3, can only occur if the residence time of the flocs in the water column is large enough.

If the flocculation time is much larger than the residence time (i.e. lower left corner of Figure 12.8) vertical gradients in floc size are small: Du « Dl. As Dl is expected to be in equilibrium with the local near-bed hydro-sedimentological conditions (i.e. local G and c), the mean floc size throughout the water column can be estimated from these conditions only.

This analysis was dedicated to one floc size only. However, a limitation in residence times will also have implications for wide floc size distributions, as observed in nature. Figure 12.9 presents the initial floc size distribution, that is, prior to floccula-tion, and the floc size distribution for equilibrium conditions, as measured by Kranck (Kranck and Milligan22). It shows a shift toward larger flocs in the equilibrium situation, as expected. However, if equilibrium conditions are not met, more or less any floc size distribution in between the two curves of Figure 12.9 may occur. Of course, this observation also holds for the median floc size. It is clear that this has major implications on the interpretation of floc size data obtained in the marine environment.

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