## Floc Settling Velocity

Settling velocity measurements of flocs are important for studying the fate of sediments within natural systems and for the evaluation of solids removal from treated effluents and in the estimation of floc wet density. Floc settling velocity has been found to increase with increasing floc size53-57 but not necessarily in accordance with Stokes' law. Floc settling under gravity has been reported to be affected by a wide range of factors including the shape and settling orientation of flocs being measured. The effect of fluid drag force on the settling velocity of a nonspherical particle is larger than that on a spherical particle.58'59 The fastest settling rate is for particles of spherical shape, followed by that of cylindrical, needle-like, and disc-like shape.58 Floc settling velocity may be affected by the settling orientations of the flocs because the drag force depends on the floc area facing the settling direction.53 Fluid flow through the internal structure of flocs may also be important, as this would reduce hydrodynamic resistance and increase settling velocity.15 Zahid and Ganczarczyk54 stated that the computation of settling velocity by Stokes' law from the size and density measurements has to consider the effect of floc permeability. This, however, is in contradiction to the usual way of calculating wet density of flocs from the size-settling velocity measurements. The effect of floc permeability on settling velocity is considered negligible.55'60 To complicate this picture from the floc structure viewpoint, Liss et al.61 showed that the channels that appeared to be open by conventional optical microscopy (COM) and confocal laser scanning microscopy (CLSM) were in many instances filled with extracellular polymeric substance (EPS) fibrils that could be seen only by transmission electron microscopy (TEM).

Floc settling velocity is most commonly determined by measuring the distance traveled by a floc over a known time using multiple exposure photographic and video imaging.34'35'53'57'62'63 These techniques are effective in measuring floc size and settling velocity within the resolution limits of the imaging method used. Klimpel et al.60 used a cinematographic technique to measure larger flocs (>100 ^m), and the multiple exposure technique to measure smaller flocs (< 100 ^m). Droppo et al.57 developed a videographic technique to measure floc settling velocity. This technique involves using a stereoscopic microscope or 1 x tellecentric lens and a video camera to capture images of settling floc in a column filled with a medium similar to the native environment of the samples. A small quantity (~1 ml) of floc samples is introduced at the top of the column. A sufficient travel distance is allowed for flocs to reach terminal velocity. Settling images of flocs are then recorded on a VCR as they pass though the focal plane of the microscope. These images are then analyzed using a computer imaging software for size and settling velocity.

Similar video imaging techniques have been developed to examine floc size-settling velocity relationships in situ in marine and freshwater environments.36'37 All are based on video imaging of settling flocs within a stilled water column. Missing, however' from most studies has been an accurate estimation of floc density. A new instrument called INSSECT (IN situ Size and SEttling Column Tripod) has been designed to measure all the variables that, at present, are thought to influence the flux of fine-grained sediment to the bottom.52 Comprising a rotating sediment trap and settling column, the rotating tripod is equipped with video and still camera systems, current meters, and polyacrylamide gels to capture settling flocs.

There is no simple equation relating the settling velocity of flocs to their size. Stokes' law or modified Stokes' law best describes the settling velocity of particles that approach a perfect sphere. Despite the limitations, estimations of other floc properties (e.g., density) derived from Stokes' law have proven useful in floc research. Stokes' law is defined as follows:

V 18 n where v is the terminal settling velocity, pf the wet density of particle, pw the density of water (assume settling in water), g the gravitational constant, \x the viscosity of water (assume settling in water), and d the diameter of particle.

Li and Ganczarczyk53 used a power function of the form, v = ALn, and a linear function, v = A + BL, to correlate floc settling velocity (v) with its longest dimension as a characteristic size (L), where A, B, and n are the equation coefficients determined experimentally. The power function is considered to be a better way to describe the relationship because the power function predicts that the velocity will be zero when floc size approaches zero while the linear function does not. However, the measured settling velocities can yield coefficients lower than that predicted by Stokes' law (n = 2).54,55,64 The power law coefficients (n) calculated from the power function generally have ranged from 0.55 to 0.88. The number of flocs measured in these studies were as low as 21 and as high as 343. Lee et al.56 managed to measure a total of 1385 flocs for settling velocity and size determinations and reported a power coefficient of 0.7 to 0.8. A modified linear model incorporating the floc settling shape factor was found to improve the correlation coefficient (R2) of the linear relationship.64

In the marine environment, settling velocities of flocs have been inferred from clearance rates in enclosed sedimentation tubes.4,44 Commonly, open-ended tubes are submerged horizontally to permit free flow of particles in suspension and then closed, rotated to 90°, and retrieved. Subsamples are removed from the tube at set intervals during settling and the settling velocity is determined from the change in concentration with time.44 Settling velocities calculated from clearance rates were found to be an order of magnitude less than those determined in situ using camera techniques during the Elbe Estuary intercalibration program.4 However, the ease of use and the direct application of the results for determining vertical sediment flux have made settling columns a common instrument for nearshore studies.

In short, floc settling in any environment is not only highly related to size, but also related to floc shape and density. While Stokes' law gives a reasonable approximation, the relationship between floc size and settling velocity is best described by a power law equation with the value of the exponent close to 1. Recent advances in digital imaging and image analysis and the ability to collect ancillary data have led to better understanding of the size-settling velocity relationship for flocculated suspensions.52

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