## 3 Results
### Effect of Grinding Time on the Particle Size Distribution Curves  
The particle size distribution of the powders (Figures 2 and 5) was studied as a function of the grinding time using a ball mill. The very large particles (population 1) are present in the powders only under moderate grinding conditions (i.e., short duration). This corresponds to pregrinding conditions. The results show that increasing the grinding time in the ball mill induces significant changes in the granulometric distribution curve (Figure 2), and in the volume fractions of the four populations (Figure 5), with a decrease in the coarsest population (population 1), an increase, stagnation, and then decrease in population 2, and a continuous, monotonic increase in populations 3 and 4. Under these grinding conditions, after 30 s of treatment, the very large particles (population 1) are still very present, representing about 40% by volume of the powder. As the grinding time is increased, their frequency decreased exponentially. After 120 s, the presence of very large particles (population 1) is \"residual\". The frequency of coarse particles associated with population 2 (<55-470 \(\upmu\)m) shows a particular curve pattern that can be divided into two phases:  
Phase 1: A first phase up to 90 s, in which the increase in grinding time leads to an increase in their frequency in the powder. This phase, which could be described as a growth phase, could be explained by the presence of a large proportion of the coarse population (population 1) at the start of the grinding, which feeds the production of the coarse particles. At the same time, two other phenomena occur:  
1. The fragmentation of the population 1 particles generates the release of smaller fragments (or cellular components). 2. The particles of the population already generated within population 2 are also reduced in some cases. Both mechanisms increase the frequency of populations 3 and 4. Phase 2: From 90 s, the increase in grinding time leads to a decrease in its frequency in the powder. This phase, associated with its decay, highlights the fragmentation of population 2 as the dominant mechanism feeding the frequency of populations 3 and 4. These populations, as defined in our study, could therefore be described as a \"transfer\" populations. However, the release of components or the parallel fragmentation of the already generated population 2 remains a minor phenomenon from the point of view of volume yield, hence this growth phase. At the end of the grinding process, this population remains at around 20% in relative terms. From the early stages of grinding and throughout the process, the volume proportions of fine particles (populations 3 and 4) follow an increasing trend (i.e., power law). The rapid and simultaneous formation of these fine particles, especially population 3 associated with free starch granules, suggests that the starch granules adhere poorly to the intracellular matrix. Figure 5: Population volume proportions of pea powders at different grinding times in the ball mill. In contrast to the coarsest particle populations (populations 1 and 2), whose median size varies with grinding time or conditions, populations 3 and 4 have a relatively stable median size regardless of grinding conditions or duration (indicated in Figure 2 by the granulometric stability of the peaks in the corresponding particle size range). This difference suggests that subcellular components are not subject to classical fragmentation mechanisms when released within powders, as indicated by the relative stability of the median diameter of populations 3 and 4 across all tests. With regard to populations 3 and 4, it should be noted that the frequency expression is described in terms of volume, which reduces the effect for populations with fine granulometry compared to their expression in numbers.