## Floc Density And Porosity

Floc density and porosity are two important floc characteristics in evaluating floc behavior. Along with floc size and shape, floc density plays a strong role in influencing settling velocity with concomitant transport and industrial efficiency implications. As the porosity of a floc has consistently been shown to be negatively correlated to density,7 it too is an important parameter for floc behavioral assessment. Density is usually derived from the settling velocity-size measurements using Stokes' law or modified Stokes' law.34,35,53-57,60,65 The validity of this approach has been questioned because it usually assumes spherical flocs and the settling velocity and size relationship do not follow Stokes' law. Zahid and Ganczarczyk54 stated that there were a number of uncertainties involved in the density calculation from Stokes' law, therefore the approach was regarded only as an approximation. Lee et al.56 also supported this approach since it provides at least qualitatively valid density estimation.

The following equation is often used to calculate floc porosity from density:53

Ps - Pw where ps and pf are the dried floc density (1.34 to 1.69 g/cm3) and wet floc density, respectively, and Pw is the liquid density.

Andreadakis66 made use of interference microscopy for floc density determination and used the above equation to calculate floc porosity. Density determinations for aggregates are usually based upon observations of terminal velocity, although a method based upon a series of sucrose solutions of incremented densities has been presented by Lagvankar and Gemmell.67 Ozturgut and Lavelle59 employed a linear-density stratified column which allows flocs to settle to their isopycnic levels to measure low density but settleable wastewater effluent flocs. Dammel and Schroeder68 used a similar density gradient centrifugation technique, which allows the flocs to settle in a fluid of continuous increasing density until the flocs become stationary, to measure the density of activated sludge flocs. This technique, however, does not measure floc size concurrently with its density, thus, a size and density relationship might not be established easily. In addition, the ionic strength of the suspension medium and the nature of the medium itself have to be compatible and nontoxic with the biological flocs.

A variety of floc density models have been proposed. Magara et al.34 proposed the following floc effective density (pe) model based on Stokes' law, pe = pf - pw = 0.003698 ■ nwvd-2 (1.3)

where pf and pw are the floc density and liquid density, respectively (g/cm3), /w is the liquid viscosity (g/cm3 sec-1), v is the floc settling velocity (cm/s) and d is the floc ESD (cm). Tambo and Watanabe35 suggest a model based on Stokes' law for effective floc density and size:

assuming a drag coefficient of 45/Re and a floc sphericity of 0.8. Andreadakis66 suggested that the floc density (pf) is a function of its size (d), pf = 1 + 0.30 d-a82 (1.5)

assuming a dried sludge density of 1.34 g/cm3. Glasgow and Hsu65 developed an empirical equation for kaolin-polymer aggregate to relate its density (p) to diameter (d) and pH, p = 1.05 ■ d°.0038ph+°.00716) (1.6)

assuming a sphericity of 1.0.

Zahid and Ganczarczyk54 plotted effective density as a function of average diameter on a logarithmic scale and developed the following equation for the floc effective density and the average diameter (D),

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