Fig. 10. Relation between $ (100-R_{r})/R_{r} $ and expression pressure.

Fig. 11. Relation between $ w_{\infty}/w_{d} $ and reciprocal expression pressure.

Fig. 9 are illustrated in Fig. 10 in the form of a plot of $ (100-R_{c})/R_{c} $ vs. $ p_{c} $ . It is found that the plots show a linear relationship over a wide range of pressures.

In Fig. 11, $ w_{\infty}/w_{d} $ is plotted against the reciprocal expression pressure $ (1/p_{c}) $ , where $ w_{\infty} $ is the final wet cake mass per unit cross-sectional area, corresponding to the expression pressure, and $ w_{d} $ is the dry cake mass per unit cross-sectional area (Nakakura et al., 1996). The final wet cake mass at the infinite pressure, which is related to the amount of the bound water, has been frequently evaluated from the ordinate intercept of the straight line of experimental data (Kawasaki et al., 1990a; Matsuda et al., 1992). However, the plots deviate from a linear relationship at more than 2 MPa pressures, and thus it is essential to measure the moisture content of the compressed cake from the real experiments in order to obtain the cake moisture content attained by ultrahigh pressure expression.

Several types of expressions can be utilized to relate the porosity $ \varepsilon $ or void ratio e (the volume of liquid per unit volume of solid) to the solid compressive pressure $ p_{s} $ as follows (Tiller and Cooper, 1962)

$$ \varepsilon=\varepsilon_{1}p_{s}^{-\lambda} $$

$$ e=\frac{\varepsilon}{1-\varepsilon}=E_{0}-C_{c}\ln p_{s} $$

where $\epsilon_{1}, \lambda, E_{0}$, and $C_{c}$ are the empirical constants. The Terzaghi-Peck Eq. (2) has been frequently employed in the analysis of expression behaviors (Shirato et al., 1987; Iwata et al., 1991).

The porosity $\epsilon$ is related to the final moisture content $R_{e}$ by

$$ \varepsilon=\frac{e}{1+e}=\frac{\rho_{s}R_{e}}{\rho_{s}R_{e}+\rho(100-R_{e})} $$

where $ \rho_{s} $ is the true density of solids, and $ \rho $ is the density of the liquid. It should be noted that the solid compressive pressure $ p_{s} $ throughout the compressed cake is equal to the applied expression pressure $ p_{c} $ on the assumption that the effect of the side-wall friction is negligible. Therefore, the data of $ R_{e} $ vs. $ p_{c} $ shown in Fig. 9 are converted into the data of e or $ \varepsilon $ vs. $ p_{s} $ based on Eq. (3).

Fig. 12(a) and (b) shows the semi-logarithmic plot of e vs. $ p_{s} $ and the logarithmic plot of $ \varepsilon $ vs. $ p_{s} $ , respectively. As the liquid contained within the microorganism cells is partially removed in the course of expression, e and $ \varepsilon $ are rated on dry solid basis of microorganism cells for convenience. Whilst the semi-logarithmic plot of e vs. $ p_{s} $ cannot be represented by a linear relationship described by Eq. (2), the logarithmic plot of $ \varepsilon $ vs. $ p_{s} $ yields a straight line over a wide range of pressures in accord with Eq. (1). Therefore, the plot shown in Fig. 10 or Fig. 12(b) is available to examine the experimental data for ultrahigh-pressure expression of municipal excess activated sludge used in this study.

#### 4.5. Kinetics of ultrahigh-pressure expression

The semi-logarithmic plot of $ (1-U_{c}) $ vs. the consolidation time $ \theta_{c} $ is available to evaluate the creep effect in the consolidation

b

Fig. 12. Effect of solid compressive pressure on structure of compressed cake: (a) relation between void ratio and solid compressive pressure and (b) relation between porosity and solid compressive pressure.