Fig. 9 Effect of consolidation pressure on time variation of cake moisture content in expression

Fig. 10 Relation between cake moisture content at different consolidation times and consolidation pressure

for treated carrots in an early stage remarkably increases and the cake moisture content after 24 h undergoes a marked decrease. The cake moisture content R after 24 h dramatically decreases from 69 to 47% by increasing the pressure from 0.5 to 10 MPa. Thus, it is found that the cake consisting of treated carrots behaves as the compressible material in expression operation (Iritani et al., 2007). In contrast, whilst the expression performance is improved with increasing pressure also in expression of raw carrots, the degree of deliquoring is less marked than that for treated carrots and the deliquoring rate is slightly improved particularly in early times.

In order to compare the cake moisture content R more clearly, the values of R at the consolidation time $ \theta_{c} $ of 1, 5, and 24h are plotted in Figure 10 against the consolidation pressure $ p_{2} $ . Although the cake moisture content R for treated carrots remarkably decreases with the increase in the consolidation pressure, R at the consolidation time $ \theta_{c} $ of 5h is very close in value to that at $ \theta_{c} $ of 24h for each pressure. It should be noted that the cake moisture content R for treated carrots at $ p_{2} $ of 0.5 MPa and $ \theta_{c} $ of 1h corresponds to that for untreated carrots at $ p_{2} $ of ca. 7MPa and $ \theta_{c} $ of 24h. Accordingly, the use of ultrasonicated carrots in expression can significantly shorten the consolidation time required to reduce the cake moisture content at lower pressures.

## Conclusion

This work has been partially supported by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan and from the Ministry of the Environment, Japan, and by the Steel Foundation for Environmental Protection Technology. The authors wish to acknowledge with sincere gratitude the financial support leading to the publication of this article.

Liquid expression from carrots assisted with ultrasonic pretreatments was conducted to investigate the promoting effect of sonication on mechanical deliquoring of carrots, and the time variations of the moisture content in the compressed cake were measured during the course of expression conducted under the different values of applied consolidation pressure. The deliquoring rate of carrots was significantly enhanced by the pretreatment of ultrasonic irradiation, and the moisture content in the compressed cake was finally reduced to 47% at the pressure of 10MPa. It turned out that the control of sample temperature was of extreme importance in sonication as the pretreatment and that the sample temperature should be kept to above 50°C. It was apparent from the model analysis that the deliquoring behavior was markedly influenced by the creep phenomenon. It was also found that the specific ultrasonic energy dissipated in the sample by the sonication treatment served as an indicator representing the degree of ultrasonic pretreatment. The elevated operating pressure was highly effective in reducing the cake moisture content as the result of the compressibility of the carrot cake.

## Acknowledgements

## Nomenclature

A = ratio of primary consolidation to overall consolidation [—]
B = creep constant [—]
$ C_{e} $ = modified consolidation coefficient [m²/s]
$ C_{p} $ = heat capacity of water [J/kg]
E = specific ultrasonic energy dissipated in sample [J/kg]
I = ultrasonic power dissipated into liquid [W]
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]
M = mass of water [kg]
P = load power [W]
$ p_{1} $ = pre-consolidation pressure [Pa]
$ p_{2} $ = consolidation pressure [Pa]
R = moisture content of compressed cake on mass basis [wt%]
T = sample temperature [°C]
t = net ultrasonic exposure time [s]