## 2 Materials and Methods
### Experimental Method
#### Theoretical Design of a Cellular Concrete Mixture.  
Table 1 shows the theoretical proportions of the control and lightened samples. CPC-30-R cement with a density of 3000 kg/m\({}^{3}\) graded natural sand and contaminant-free water. The sand was studied using granulometric analysis to determine its properties according to the standard NMX-C-077-ONNCCE-1997 [61]. These analyses showed that the sand has a density of 2560 kg/m\({}^{3}\) and an absorption percentage of 1.5%, a contamination percentage of 5.8%, a fineness modulus of 2.8, and 4.5% loss on washing [62]. The recommended foam density to achieve good mix stability is approximately 60 kg/m\({}^{3}\). This is assured by using an additive and an instrument that converts the additive to the foam using pressurized air. The volume that the foam will occupy within the mixture must be considered and adjusted through laboratory tests for its proportioning.  
The cellular concrete volume ratio concerning the original mortar's total volume was determined to obtain a cellular concrete mix of specific density. This was achieved by dividing the desired density by the density of the control mix; in other words, the foam will fill the difference between these volumes; according to these criteria, the proportions were calculated to obtain cellular concrete of different densities, with a fluidity range of \(105\pm 15\%\).  
Conventional laboratory equipment and tools such as a mixer, molds for samples, basic tools, and test equipment to obtain the mortar characteristics in a fresh state were used for the manufacture and tests of the samples. Initially, the control mixture was fabricated with natural cement-sand mortar in a 1:4 ratio, according to the dosages presented in [62].  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Property** & **Control** & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** \\ \hline Mixture density (kg/m\({}^{3}\)) & 2135 & 1800 & 1600 & 1400 & 1200 & 1000 & 800 \\ Mixture volume (m\({}^{3}\)) & 1.000 & 0.8432 & 0.7496 & 0.6569 & 0.5622 & 0.4685 & 0.3748 \\ Cement CPC 30R (kg) & 6.225 & 5.243 & 4.661 & 4.078 & 3.495 & 2.913 & 2.330 \\ Sand (kg) & 21.225 & 17.896 & 15.91 & 13.91 & 11.93 & 9.942 & 7.95 \\ Water (kg) & 4.575 & 3.861 & 3.43 & 3.00 & 2.574 & 2.145 & 1.71 \\ Foam (kg) & 0 & 0.141 & 0.22 & 0.31 & 0.39 & 0.478 & 0.563 \\ Fluidity (\%) & 106 & 124 & 125 & 125 & 122 & 122 & 122 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Proportion of cellular concrete for different densities in a volume of 15 L and percentage of fluidity.  
Cellular concrete lightened mortars were also manufactured, adding the foaming agent according to the proportions shown in Table 1, which correspond to the densities of 800, 1000, 1200, 1400, 1600, and 1800 kg/m\({}^{3}\). The brand of the additive used to generate the foam is BUINY A.E./C.C.100, a foaming additive.  
The equipment used to generate preformed foam for the cellular concrete is called: UTC 400-E/simple. Once the mixtures were made, their properties in the fresh state were measured in the laboratory; in relation to the fluidity and according to NMX-C-144-ONNCCE-2015 [63], the tests determined that the mixture presents an adequate fluidity and an air content of 15-70%. Then, three cubic samples of \(0.05\times 0.05\times 0.05\) m were manufactured both for the control sample and for each of the cellular concrete samples of different densities; they were tested to determine compression strength after 28 days, according to the standard NMX-C-061-ONNCCE-2015 [64]. Additionally, samples with dimensions of \(0.15\times 0.15\times 0.04\) m were manufactured to measure thermal conductivity and specific heat.