meter. It is obvious that the increase in the expression pressure $ p_{e} $ leads to a dramatic improvement in expression performance. The solid lines in the figure are the calculations obtained from Eq. (7), using the time variation of the cake thickness L calculated from Eq. (5). The calculations compare favorably with the experimental data.

In Fig. 16, the fractions, A, $ B_{1} $ , $ B_{2} $ , and $ B_{3} $ , of the moisture removal are plotted against the expression pressure $ p_{c} $ . The fraction A constitutes the major portion of consolidation and increases with increasing expression pressure $ p_{c} $ . Conversely, the fraction $ B_{1} $ decreases with increasing $ p_{c} $ . This implies that the primary consolidation based on the Terzaghi spring analogy plays a more important role in controlling ultrahigh-pressure expression. The fraction $ B_{2} $ is kept at an almost constant value regardless of the value of $ p_{c} $ , and $ B_{3} $ is negligibly small.

The modified consolidation coefficient $ C_{e} $ is plotted as a function of the expression pressure $ p_{c} $ in Fig. 17. The coefficient $ C_{e} $ increases with increasing $ p_{c} $ , but $ C_{e} $ is less affected by $ p_{c} $ in the pressure range above 5 MPa. This may be attributed to the high compressibility of the cake in the ultrahigh-pressure range, as expected from the definition of $ C_{e} $ given by Eq. (6) (lritani et al., 2003, 2008).

In Fig. 18, a set of creep constants, $ \eta_{1} $ , $ \eta_{2} $ , and $ \eta_{3} $ , are plotted against the expression pressure $ p_{c} $ . It can be seen that each creep constant is maintained roughly constant irrespective of the

Fig. 16. Effect of expression pressure on ratio of consolidation of each stage to overall consolidation.

Fig. 17. Effect of expression pressure on modified consolidation coefficient.

Fig. 18. Effect of expression pressure on creep constants.

pressure $p_{c}$. Each creep constant differs by more than one order of magnitude, thereby indicating that the creep phenomenon occurs in stages.

### 5. Conclusions

Ultrahigh-pressure expression combined with flocculation has been developed to achieve the high-rate and high-degree deliquoring of excess activated sludge. Flocculation of the sludge due to PACl addition brought about a marked increase in the filtration rate in low-pressure filtration. The moisture content of the compressed cake was finally reduced to 31 wt% by expression under action of an ultrahigh pressure of 15 MPa with the aid of pretreatment by water permeation through the filter cake, suggesting that the liquid contained within the microorganism cells was partially removed by the mechanical pressure. It was found from the analysis of ultrahigh-pressure expression that the equilibrium porosity in the compressed cake was empirically represented by a power function of the solid compressive pressure over a wide range of applied pressures from 0.5 to 15 MPa. Moreover, it was shown that the complicated kinetics of ultrahigh-pressure expression was accurately described on the basis of the modified Terzaghi and multi-stage Voigt combined model.

## Nomenclature

A ratio of primary consolidation to overall consolidation

B creep constant

$ C_{a} $ aluminum concentration in permeate (kg/m³)

$ C_{c} $ empirical constant in Eq. (2)

$ C_{e} $ modified consolidation coefficient (m²/s)

$ d_{f} $ diameter (m)

$ d_{s} $ specific surface area size of particles (m)

$ E_{0} $ empirical constant in Eq. (2)

e void ratio of compressed cake

f frequency

i number of drainage surfaces

L thickness of cake (m)

$ L_{1} $ thickness of cake at $ \theta_{c}=0 $ (m)

$ L_{\infty} $ thickness of cake at $ \theta_{c}=\infty $ (m)

$ p_{c} $ expression pressure (Pa)

$ p_{f} $ filtration pressure (Pa)

$ p_{p} $ water permeation pressure (Pa)

$ p_{s} $ solid compressive pressure (Pa)

R moisture content of cake on mass basis (wt%)