# Density and Viscosity in Biodiesel + Diesel Mixtures from Recycled Feedbacks
## 1 Introduction  
Since the beginning of the 21 st century, global greenhouse gas (GHG) emissions have been steadily increasing due to the development of various countries. It is estimated that 71.6% of total GHG emissions come from the burning of fossil fuels [1]. Due to the desire to reduce or stabilize GHG emissions, together with the decrease in oil reserves, renewable energy sources such as biofuels have received increasing attention. An alternative renewable energy source is waste materials; fats and cooking oils are some of them. Through a transesterification process, these can be converted into biodiesel. This biofuel is classified as low-toxic, biodegradable and renewable. It has a higher cetane index, no sulfur content, good lubricity and about 10-12 wt% of oxygen [2; 3; 4; 5]. On the opposite hand, biodiesel has poor cold flow properties, tends to oxidize with air at high temperatures, and its calorific value is lower than that of fossil diesel [6; 7; 8; 9; 10; 11]. Based on the above, the current design of compression engines allows biodiesel or biodiesel + fossil diesel mixtures to be successfully applied without altering the durability and reliability of the engine if the material specifications are complied [5]. Some of these crucial specifications are volumetric and transport properties; the density of biodiesel must be in the range of 860-900 kg\(\cdot\)m\({}^{-3}\) and the viscosity between 3.50 and 5.00 mm\({}^{2}\cdot\)s\({}^{-1}\) at 313.15 K. Fuel viscosity affects the pump specifications, the atomization process and the performance of injectors [12; 13]; meanwhile, the density also affects the injector systems, the cetane number and the calorific value [14; 15]. All of these make it necessary to account for information about volumetric and transport properties for biodiesel + diesel mixtures at atmospheric pressure [3; 6; 13; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. The temperature interval ranges from 288.15 to 373.15 K, based on fatty acid methyl esters from vegetable feedstocks (canola, castor, coconut, corn, cotton, hazelnut, jatropha, mustard, neem, palm, rapeseed, safflower, soybean, sunflower) or waste materials (cooking oil, edible tallow) [19; 23]. Nevertheless, a limited number of research studies are focused on the analysis of derived volumetric properties for biodiesel + diesel systems [24; 25; 26]. The (fish or sunflower) biodiesel + diesel systems were reported to have negative viscosity deviation and positive excess molar volumes [24], while the (coconut or soybean) biodiesel + diesel mixtures exhibited positive and negative excess molar volumes [25; 26]. For mixtures of rich-unsaturated biodiesel and diesel, negative deviations for volume occurred [27]. Regarding viscosity, it has been found that predictive models can provide good results considering specific conditions and the biodiesel feedstock, which yields differences in the values of viscosity of biodiesel (from different raw materials) and diesel blends [28]. Besides, it was reported that the use of long-chain alcohols (i.e., butanol) improved some properties of biodiesel, like the cloud point, which decreased up to 8 \({}^{\circ}\)C (butyl esters) [29] from 20 \({}^{\circ}\)C (methyl esters) [30] for the same raw material, hence the necessity of studying the production of biodiesel using other long-chain alcohols. Apart from that, the development of models and correlations to describe properties of pure compounds and mixtures requires the knowledge of experimental data, which makes their study necessary. Considering the availability of waste materials as sources of biodiesel production, the need to study their volumetric and transport properties when mixed with diesel and the testing and development of models that represent those properties, in the present work, the density and viscosity of biodiesel + diesel pseudobinary mixtures are reported at 0.078 MPa. The biodiesel samples were based on fatty acid butyl esters (FABE) from waste beef tallow and fatty acid methyl esters (FAME) from waste cooking oil.