# Density and Viscosity in Biodiesel + Diesel Mixtures from Recycled Feedbacks
## 3 Results and Discussions
### Density  
The experimental density values (\(\rho\)) for waste beef fallow butyl ester diesel (1) + diesel (2) and waste cooking oil methyl ester biodiesel (1) + diesel (2) pseudobinary systems are depicted isothermally in Figure 3 and summarized in Table S1.  
Density was observed to increase as the biodiesel amount incremented in the pseudobinary solution at a stated temperature; in the case of temperature variations, density decreased as the temperature was rising. This last was ascribed to the constant increment of the space between molecules but without abrupt alterations that could evaporate the mixture. Contrasting the density between both systems at fixed composition and temperature, densities were lower for the system containing waste beef fallow butyl esters. This behavior was associated with the different alkyl radical; the biodiesel density for methyl ester group (FAME) is superior to longer alkyl carbon chains such as ethyl (FAEE), propyl (FAPE) or butyl (FABE) [7]. Moreover, the waste beef fallow butyl ester biodiesel contained a high proportion of saturated esters of about 77.735% of the relative area (constituted by butyl tetradecanoate, butyl hexadecanoate and butyl octadecanoate), as commonly occurs in fat materials. For the waste cooking oil methyl ester biodiesel, the saturated ester components comprised 13.942 mol\(\%\) (methyl tetradecanoate, methyl hexadecanoate, methyl octadecanoate). The cooking treatment of the fresh vegetable oils in restaurants could mean that the double C=C bonds of the unsaturated esters were converted to simple C-C bonds. Then, the saturated esters possess lower density than unsaturated ones, as previously reported for pure methyl esters; for instance, contrasting the saturated component methyl palmitate (C\({}_{17}\)H\({}_{34}\)O\({}_{2}\)) [45] and the unsaturated chemical methyl palmitate (C\({}_{17}\)H\({}_{32}\)O\({}_{2}\)) [46], the respective densities are 854.5 and 857.6 kg\(\cdot\)m\({}^{-3}\) at 308.15 K or 817.3 and 819.8 kg\(\cdot\)m\({}^{-3}\) at 358.15 K. In summary, those effects caused the densities of FAME biodiesel and their mixtures with diesel to be even higher than the corresponding for FABE + diesel blends. Complementarily, Figure 4 summarizes the trends for density of waste cooking oil biodiesel (FAME) [23; 47; 48] and tallow biodiesel (FAME [23; 49] or FABE) obtained in this work and those reported elsewhere as a function of temperature. This comparison yielded percent relative deviations from 0.24 to 3.71% for FAME and from 0.42 to 0.97% for FABE. In general, the density of biodiesel varies from 810 to 920 kg\(\cdot\)m\({}^{-3}\); these differences are attributed to the different chemical compositions of the ester profile, which alters the  
Figure 3: Density for biodiesel (1) + diesel (2) systems as a function of mole fraction of biodiesel (\(x_{1}\)). Red and blue symbols denote waste cooking oil methyl ester biodiesel and waste beef fallow butyl ester biodiesel, respectively.  
corresponding properties, such as cetane number and oxidation stability; a major presence of unsaturated bonds leads to lower density, cetane number and oxidation stability [50; 51].