## 3 Results
### Comparison of Hydrogen Generation and Reaction Efficiency  
The reaction was not as fast as expected for initial experiments with 1M alkaline and elevated temperature (40 \({}^{\circ}\)C) for better comparison with our previous results. The slowest H\({}_{2}\) generation reaction was recorded from the HDC sample, while RM showed the highest generation velocity/rate. However, we observed that some particles of SOW and RM samples did not react at all, which could potentially be solved with further grinding to smaller particle sizes, but this was not performed to maintain a relative comparison between dress and Alw1 samples. In the investigation of sample reaction efficiency, it seems that RM shows the highest efficiency, even though the initial expectation is that this sample has roughly 40% Al; in the composition, we see that it is mostly aluminium oxide, and XRD does not show much hydroxide. Other samples have impurities such as Si or N, C, which are expected to hinder the reaction. To increase the reactivity of samples, a mechanical pre-treatment of samples to a comparable particle size, then gas generation and reaction kinetics are compared. The cumulative hydrogen production is shown in Figure 4a, and reaction efficiencies are depicted in Figure 4b. As the samples were pre-treated with a file/crushing, the particles were more spherical than cylindrical, resembling plates or films. This means that in the first degree of monodisperse approximation, the geometry of particles is described only by the single radius. With respect to volumetric bodies, in the chemical reaction, the shrinking of the solid reactant occurs. Hence, the radius is time-dependent, _r(t)_. The base of the shrinking \begin{table}
\begin{tabular}{c c c c c} \hline
**Element** & **SOW** & **RM** & **HDC** & **Alw1** \\ \hline Argon & 0.5 & 0.0 & 0.0 & 0.0 \\ \hline Carbon Dioxide & 0.1 & 0.1 & 0.0 & 0.1 \\ \hline Ethane & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline Hydrogen & 68.3 & 94.4 & 99.3 & 98.2 \\ \hline Methane & 0.0 & 0.0 & 0.2 & 0.0 \\ \hline Nitrogen & 24.8 & 4.21 & 0.3 & 0.4 \\ \hline Oxygen & 6.1 & 0.1 & 0.1 & 0.1 \\ \hline Water & 0.2 & 0.2 & 0.1 & 1.1 \\ \hline \end{tabular}
\end{table} 
Table 2: Hydrolysis gas analysis in the FC setup. Figure 4: **(a)** Cumulative hydrogen volume produced in hydrolysis cross sample with comparison to industrial waste Alw1; **(b)** reaction efficiency for uniform size samples, with comparison between samples. core model for a spherical particle is the expression that links the molar aluminium reaction rate \(dn_{Al}/dt\) on the surface with the diminishing size of a particular particle:  
\[4\pi r^{2}(t)\frac{dn_{Al}}{dt}=-\frac{d}{dt}\left(\frac{4\pi}{3}\frac{\rho_{Al }}{M_{Al}}p^{3}(t)\right), \tag{8}\]  
where \(\rho_{Al}\) and \(M_{Al}\) are the density and molar mass of the solid aluminium particles. Equation (8) is correct for the first and more intensive so-called surface reaction rate step analysed in the present work. This equation is widely solved in literature [14], where it is shown that at a sufficient stirring, the following applies:  
\[\frac{r(t)}{r_{0}}=(1-f)^{\frac{1}{3}}, \tag{9}\]  
where \(r_{0}\) is the initial radius of the solid particle, and \(f\) is the normalised non-dimensional hydrogen yield (\(0<\)\(f<1\)), where \(f=1\) means the maximal theoretical yield calculated by the ideal (or real) gas equation of state. In the experimental case of gaining the pressure \(p\) of yielded hydrogen in a constant volume \(V\), the following applies:  
\[f=\frac{2}{3}\frac{V}{RT_{a}}(p-p_{0})\frac{W_{Al}}{M_{Al}}, \tag{10}\]  
Here, \(W_{Al}\) is the reacted aluminium mass, and \(p_{0}\) and \(T_{a}\) are the reference pressure and temperature, respectively. The coefficient 2/3 comes from the stoichiometry in the reaction between the solid and liquid (Equation (6)). Summarising [PERSON] et al.