## 3 Results and Discussion
### Accelerated Tests--Stability to Centrifugation and Extreme Heat Treatment  
Accelerated tests, such as centrifugation and extreme heating to 140 \({}^{\circ}\)C, are essential for evaluating the stability of emulsions, even if these conditions do not represent a real-life scenario. Through these tests, it is possible to determine the performance of emulsions under stress and predict their long-term behavior under normal storage and used conditions. Oil and water emulsions that are stabilized only by plant proteins, such as lentils, peas, and broad beans, may exhibit separation or structural loss under adverse conditions, revealing weaknesses that would not be detected under normal conditions. These accelerated tests allow researchers to observe instability phenomena such as flocculation and coalescence and identify components that can be optimized. They also ensure the safety and quality of the final product. The coalescence of the emulsion droplets can be accelerated by mechanical stirring or by centrifugal force, as the frequency of collision of the emulsion droplets is increased. Centrifugation is a simple and practical method for determining the effects of formulation on the coalescence stability of emulsions by forcing the droplets to collide with each other through centrifugal force 24. Table 2 lists the stability constants (KE). T3 with 100% fava bean protein was the most stable emulsion and resisted centrifugal force better. By adsorbing at the interface and forming an interfacial film, the steric hindrance formed can inhibit the movement of small droplets [61]. These results are in agreement with the discovery made by [43] that the fava bean protein adsorbs much better at the interface than the pea protein, followed by the lentil protein. It was observed that all the emulsions that contained a higher percentage of fava bean in their formulation showed higher stability after centrifugation [12; 22]. According to [43], the adsorption rate of fava bean protein when added to an oil-water emulsion is much higher than that of pea > lentil protein at the same concentrations, which could explain the lower contribution of lentil proteins to emulsion stability. Indeed, both protein solubility and surface charges are important for the stability of emulsion systems [62]. Gravity separation often causes droplets to remain in contact for prolonged periods of time, which can lead to increased flocculation or coalescence. The highest coalescence was observed in T8 (50% lentil, 25% pea, 25% fava) and T2 (100% lentils) after centrifugation, with a thicker oil layer forming. Samples with a higher proportion of lentils in the formulation had a thick oil layer. In sample T3, the presence of pure broad beans in the emulsion improved the resistance of the oil droplets to high gravity, resulting in greater homogeneity with a creaminess threshold of less than 5%. An analysis of the contour plot (Figure 3C) shows untested areas responsible for better emulsion stability. Higher concentrations of fava beans may reduce the coalescence of the samples during centrifugation, resulting in more stable emulsions, but mixtures with lentils and peas may also exhibit the same properties. lentil protein, in combination with pea protein, did not lead to higher stability at the tested concentrations. Heat treatment can lead to greater movement of the oil droplets, their flocculation, and a loosening of the protein structure, resulting in the formation of interactions between the protein molecules (hydrophobic or disulfide bonds) [63]. These phenomena reduce the thermal stability of the emulsion [31]. When the samples were heated to 80 \({}^{\circ}\)C for 30 min and then centrifuged, only treatments T2 (100% lentil protein) and T4 (50% pea, 50% lentil) showed extreme phase separation, which completely changed the appearance of the samples.