## 3 Results and Discussion
### Stability to Flocculation and Coalescence  
Flocculation is a significant mechanism contributing to the destabilization of emulsions [56; 57]. It occurs when emulsion droplets aggregate, which can result from reduced electrostatic repulsion or inadequate protein adsorption at the interface [57; 58]. To calculate the flocculation and coalescence index, we used the d4.3 values. The value d4.3, also known as the volume mean diameter, is crucial for understanding the particle size distribution in emulsions. It represents the average size of particles, weighted by volume, which helps in evaluating the stability and quality of the emulsion. Larger d4.3 values often indicate larger particle sizes, which can lead to increased flocculation and coalescence, impacting the stability of the emulsion. The measurement of d4.3 provides insight into the behavior of the emulsion under different conditions and can guide the optimization of formulations for better performance. Emulsions stabilized with lentil proteins exhibited a lower flocculation index (3.93 \(\pm\) 0.09%) compared to those stabilized with pea proteins (5.72 \(\pm\) 0.01%) and fava bean proteins (25.80 \(\pm\) 0.12%) [8]. This discrepancy is likely due to the lower content of sulfhydryl (SH) and disulfide (SS) bonds in lentil proteins, as SH groups can form bridges that enhance droplet flocculation [8]. Conversely, emulsions stabilized with bean proteins showed an inverse relationship, where the flocculation index increased with higher bean content (e.g., T3: 100% fava--FI: 25.80 \(\pm\) 0.12%). Flocculation can lead to coalescence, a process where droplets merge to form larger aggregates, contributing to phase separation [59]. This phase separation occurs when the oil droplet size is sufficiently large to increase oil density. Table 2 presents data on coalescence and flocculation. Coalescence was minimized in treatments with lower flocculation indices. Treatment T4, containing 50% lentils, 50% peas, and 0% fava beans, showed the poorest emulsion stability, with a high flocculation index (26.02 \(\pm\) 0.12%), low flocculation stability (26.69 \(\pm\) 0.13%), and poor coalescence stability (78.39 \(\pm\) 0.38%), in addition to a larger particle size (650 nm) after 24 h (Figure 2). Most treatments exhibited an increase in droplet size after 24 h, except for T7, where the size remained constant, and T8 and T10, which showed a decrease in droplet size (Figure 2). Notably, pea protein, present in all three treatments, appears to be the most effective in reducing both coalescence and flocculation, as indicated by the contour plot (Figure 3A,D). Figure 1: Emulsion activity (EAI, m\({}^{2}\)/g) and stability indices (ESI, min) for 10 treatments of protein mixtures from peas, lentils, and fava beans. Data represent the mean \(\pm\) one standard deviation (n = 3). Means with similar superscripts in a column did not differ significantly (\(p\) > 0.5). Variations in emulsification behavior among proteins may stem from differences in their physicochemical properties, such as molecular weight, hydrophobicity, and the presence of free SH and SS bonds [58]. These properties affect the diffusion and interaction of plant proteins at the oil-water interface [49]. A study examining lentil, pea, soybean, and rapeseed proteins found that physicochemical properties were influenced by pH, protein type, and their interactions [49]. Differences in hydrophobicity among these proteins are thought to reflect inherent variations in protein composition, including the ratios of 11S to 7S proteins or globulins. In general, solubility depends on the balance between protein-protein and protein-solvent interactions [59]. Ref. [49] found that pea protein was  
Figure 3: Contour plots showing the effects of pea protein, lentil protein, and Java bean protein proportion on (**A**) flocculation stability (%); (**B**) EAI (m\({}^{2}\)/g); (**C**) Centrifugal stability constant—KE (%); (**D**) Coalescence stability—C (%); (**E**) Zeta potential (mV); (**F**) HCT (min).