## 3 Measurement Procedure  
### Capillary Action  
Figure 2a shows the scheme of the test bench used for the capillary action measurement of different porous media (PM), together with the detail of the real picture of a sample silica gel (Figure 2b), in which the liquid (methanol) height can be clearly appreciated.  
It consists of:  
* A vessel to deposit the liquid;
* A wick sample clamping arm;
* A chronometer;
* A camera;
* A PC-data logger. PC: personal computer  
Figure 2: Capillary pumping measurement equipment; (**a**) scheme of the test bench and (**b**) detail of the sample.  
The vessel was filled up with methanol and a sample wick was set up at one end in the clamping arm to which the camera was also attached (see Table 1, showing the main equipment).  
Then, the holding arm with the wick sample was placed upright next to the vessel, submerging the other wick ends into the liquid contained in the vessel. The liquid immediately began to rise up through the wick, so the ascent of liquid was recorded [28]. The heights recorded in this way were plotted to obtain the wick capillary action curve (Figure 3). Each data point is the average result of 4 tests.  
The first step was to evaluate the suitability of the Washburn equation for determining the capillary curve. This evaluation was made by estimating whether the predicted values (Washburn) were within the \(\pm 5\%\) error of the experimental values. Considering the stainless-steel mesh of 60 \(\upmu\)m, it was observed (Figure 3) that most of the Washburn values were outside the \(\pm 5\%\) threshold.  
Therefore, a bi-exponential adjustment of the experimental data was done to obtain the analytical form of the liquid height, in a similar way to [29], with a view to the performance of further comparative capillary tests. This adjustment predicted values within the \(\pm 5\%\) threshold.  
\[\mathrm{y}\ =\ A_{1}\Big{[}1-\mathrm{e}^{(-\frac{t}{t_{1}})}\Big{]}+\mathrm{A}_{2} \Big{[}1-\mathrm{e}^{(-\frac{t}{t_{2}})}\Big{]} \tag{3}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & PENTAX Optio Z10 \\ \hline
**Resolution** & 8.0 Megapixels \\ \hline
**Optical Zoom** & \(7\times\) \\ \hline
**Size** & \(3264\times 2448\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main features of the PENTAX Optio Z10 camera (RICOH, Tokyo, Japan).  
Figure 3: Pumping curve for stainless-steel mesh of pitch 60 \(\upmu\)m in methanol.  
Deriving Equation (3) with respect to time yields the speed of advance of the liquid (4) [30]:  
\[\alpha=\frac{A_{1}}{t_{1}}e^{(-\frac{t}{t_{1}})}+\frac{A_{2}}{t_{2}}e^{(-\frac{t }{t_{2}})} \tag{4}\]  
where \(y\) represents the liquid height, \(\alpha\) the advance speed, and \(A_{1}\), \(t_{1}\), \(A_{2}\), and \(t_{2}\) are constants of the fluid and wick combination that were experimentally obtained. As the liquid ascended, the speed dropped to the point where it reached zero (maximum height reached = \(A_{1}\) + \(A_{2}\)).  
Two clearly differentiated regimes were observed on the curve; a first one in which the height varied very rapidly (initial regime) and a second one in which the variation of height was slightly slower (inertial regime). Regarding the advance speed, the maximum value corresponds to \(\alpha_{max}=\frac{A_{1}}{t_{1}}+\frac{A_{2}}{t_{2}}\). Constant \(t_{1}\) represents the time at which the height reached is 67% of the maximum height and \(t_{2}\) is the time at which the speed of advance is decreased to 37 % of maximum speed.