# High-Expansion Foam: A Risk Control Option to Increase Passenger Ship Safety during Flooding
## 3 Solutions for Damage Stability Protection Using Foam: AREST System
### Foam Characteristics
#### 3.3.1 Permeability  
In order to determine the permeability of foam utilised within the previously described risk control options, it was deemed necessary to conduct a water absorption test on the proposed foam technology. By doing so, the mass of water absorbed by the foam can be quantified as a function of time and varying external water pressure. From these results, a determination can be made regarding an appropriate foam permeability value, with due consideration given to the anticipated exposure time of the foam to water and the pressures under which this might occur. To this end, two water absorption tests were conducted, the first under atmospheric pressure conditions and the second with incremental overpressure. The first water absorption test was conducted at atmospheric pressure, with a foam specimen of 100 \(\times\) 200 \(\times\) 300 mm anchored fully immersed in water for a period of 28 days. The specimen was removed from the water and weighed at several intermediate stages to compare the wetted mass with its dry weight, thus determining the water absorbed as a function of the time exposure. Table 1 reports the results of the test at atmospheric pressure, highlighting that the foam water absorption ranges from 2% in weight after one day up to 2.7% after 28 days of exposure. From the observed data, it is evident that the rate of water absorption decreases with time, reaching an asymptotic value around about 3% conditioned on 28 days of exposure at atmospheric pressure. Having to deal with flooding of internal spaces of a ship, it is also necessary to check the behaviour of permeability with pressure values greater than atmospheric by means of an additional water absorption test, varying the level of overpressure on a fixed time interval. For this test, a cubic foam specimen of 100 \(\times\) 100 \(\times\) 100 mm was used. Foam sample specimens were fully immersed in water within a pressure vessel, see Figure 6. Compressed air was then injected into the vessel in a controlled manner, generating water overpressures acting on the foam of 0.5, 1, and 1.5 bars, with watertight integrity typically rated up to 1.5 bar (15 m water head). The test was carried out for a time interval of 3 h, being an appropriate time scale compliant with Safe Return to Port regulations. Table 2 reports the results, where an increase in foam permeability can be observed at water \begin{table}
\begin{tabular}{c c} \hline
**Exposure Time (Days)** & **Water Absorption (\%)** \\ \hline
1 & 2.1 \\
2 & 2.1 \\
3 & 2.2 \\
14 & 2.5 \\
28 & 2.7 \\ \hline \end{tabular}
\end{table} 
Table 1: Foam water absorption as a function of time at atmospheric pressure. pressures ranging up to 0.5 bar, moving from 1% to 2% permeability. Interestingly, at pressures beyond this point, it was found that the foam permeability was insensitive to increasing pressure, remaining at a constant value of approximately 2%. With respect to the above-mentioned results outlined within the foregoing, it is important to consider the effects of scale and their impact on the permeability value calculated. The sample sizes used within the experiments are of the order of 0.001 m\({}^{3}\) in comparison to the static foam installations, which are of the order of 200-300 m\({}^{3}\) in size. This is important, as the manner in which the foam absorbs water is such that smaller sample sizes will demonstrate higher permeability than large ones. Consequently, the experiments are inherently conservative due to the scale at which they are conducted. This means that the wetted volume of foam relative to the specimen size will decrease with increasing foam volume. This effect is further described in Figure 7, where an example of the general relationship between the sample size and the value of permeability determined is illustrated. Furthermore, the experiments conducted have assumed the entirety of the foam surface area to be in contact with water, thus increasing water uptake.