## 3 Experimental Results
### Equations Solved  
The balance of solid mass is obtained using Equation (3) [9], considering the porosity \(n\) and the volume of solid mass \(\theta_{s}\). The solid mass balance equation is naturally equal to zero because the quantity of solid particles in the system does not change. Porosity is also constant because there is no mechanical load applied and the material investigated is a non-swelling soil. In addition, volume changes due to temperature variations can be disregarded for the temperature intervals applied in the tests because they are very small. \[\frac{\partial}{\partial t}\left[\theta_{s}(1-n)\right]=0 \tag{3}\]  
The balance of water is computed with Equation (4) [9]:  
\[\frac{\partial}{\partial t}\left[\theta_{l}^{\text{av}}S_{r}n+\theta_{g}^{ \text{av}}\right]+\
abla\cdot\left(\dot{l}_{l}^{\text{av}}+\dot{l}_{g}^{\text{ av}}\right)=f^{\text{av}} \tag{4}\]  
where water in the liquid and in the gas phases has \(\theta_{l}^{\text{av}}\) and \(\theta_{g}^{\text{av}}\) volumetric densities, respectively. \(S_{r}\) is the degree of saturation, obtained using the water retention curve (Equation (2), constants in Table 3), and \(f^{\text{av}}\) is the final water balance. Terms \(\dot{j}_{l}^{\text{av}}\) and \(\dot{l}_{g}^{\text{av}}\) are, respectively, the flux of water in the liquid phase (advective flux) and in the gas phase (vapor, non-advective flux). Flux \(\dot{j}_{l}^{\text{av}}\) is caused by changes in liquid pressure \(P_{l}\) and is computed with Equation (5), where \(q_{l}\) is obtained by the generalized Darcy's law for the unsaturated case, given by Equation (6). In this equation, \(P_{l}\) is the liquid pressure already defined; \(\rho_{l}\) is the water density (1000 kg/m\({}^{3}\) at 20 \({}^{\circ}\)C); \(g\) is the acceleration of gravity (9.8 m/s\({}^{2}\)); \(\mu_{l}\) is the viscosity of water (8.9 \(\times\) 10\({}^{-7}\) kPa\(\cdot\)s at 20 \({}^{\circ}\)C); \(k_{rl}\) is the liquid phase relative permeability, which represents the percentage of void area, which is filled with water (Equation (7), where \(A\) and \(\lambda\) are constants; see Table 3); and \(K\) is the intrinsic permeability (values in Table 3) obtained from the saturated permeability \(k_{sat}\) through Equation (8) [9]. \[\dot{j}_{l}^{\text{av}}=\rho_{l}q_{l} \tag{5}\]  
\[q_{l}=K\frac{k_{rl}}{\mu_{l}}(\
abla P_{l}-\rho_{l}g) \tag{6}\]  
\[k_{rl}=AS_{r}^{\lambda} \tag{7}\]  
\[K=\frac{k_{sat}}{\rho_{l}}\ \ \sim\frac{k_{sat}}{10^{7}} \tag{8}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{5}{c}{**Retention Curve (Drying Branch)**} & \multicolumn{3}{c}{**Hysteresis (Transition to Wetting Branch)**} \\ \hline P (MPa) & \(\lambda\) & Srl & Sls & dSr & P (MPa) & \(\lambda\) wetting \\
0.15 & 0.26 & 0 & 0.89 & 0.035 & 0.03 & 0.25 \\ \hline \multicolumn{5}{c}{**Intrinsic Permeability ***} & \multicolumn{3}{c}{**Liquid Phase Relative Permeability**} & \multicolumn{3}{c}{**Conductive Flux of Heat**} \\ \hline K (m\({}^{2}\)) & n & A & Power 1 & \(\lambda_{\text{dry}}\) (W mK\({}^{-1}\)) & \(\lambda_{\text{sat}}\) (W mK\({}^{-1}\)) \\
1.10 \(\times\) 10\({}^{-17}\) & 0.4661 & 1 & 3 & 0.1 & 0.6 \\ \hline \multicolumn{5}{c}{*isotropic.} \\ \end{tabular}
\end{table} 
Table 3: Hydraulic and thermal data. Flux \(j_{g}^{w}\) is the sum of a component computed using [PERSON]'s law for gas (dry air and vapor) movement driven by changes in gas pressure and a component computed using [PERSON]'s law (Equation (9)) for molecular diffusion and dispersion. In this work, gas pressure is assumed to be constant and equal to the atmospheric pressure and dispersion is disregarded for simplification, and therefore, vapor transport only by diffusion is considered. In Equation (9), \(\tau\) is a tortuosity parameter (\(\tau\) = 1 default value), \(\rho_{g}\) is the gas density, \(D_{g}^{vap}\) is molecular vapor diffusion coefficient (Equation (10)) and \(\omega_{g}^{w}\) is vapor mass fraction.