## 3 Results and Discussions  
### Fermentation Process Measurement  
When the kefir grains encounter a nutrient-rich medium such as milk, the microorganisms that make them up begin to consume the nutrient to perform their vital functions. Their first task is always to reproduce and increase their biomass. One of the most important factors to control the growth of milk kefir grains is the pH. The fermentation produces a wide variety of organic acids such as acetic acid, lactic acid and malic acid, among others [41]. Acetic acid is derived from carbohydrate metabolism, but a proportion is originated during fermentation because of yeast metabolism, which has been derived from an incomplete tricarboxylic acid cycle. The production of these acids is directly related to the pH of the fermentation medium of the kefir grains. The balance involves various aspects of cell physiology and adaptation to different environmental factors [42]. To check the influence of temperature on the acidification medium, the pH values were followed along the kinetics, starting from an initial pH of the medium of 6.8 and considering an optimum of 4.5 to stop fermentation (Figure 1). As a consequence of the production of organic acids, pH values progressively decrease in all substrates, especially due to the production of lactic acid generated because of the growth of LAB [6; 14]. By increasing cell density, microorganisms must survive the byproducts of their own metabolism, such as the generation of organic acids, induced acidification and inhibition of fermentation ability, when cell density is exceeded and the amount of substrate decreases, there is cell lysis in the same medium. A mathematical model based on a fraction conversion model [43; 44] to describe the effect of temperature and fermentation time on the kinetic parameters of the pH change by kefir grains population was used with modifications for the present work, where the behavior of the pH medium vs. time was modeled to a mathematical model proposed by [PERSON] et al. [43] in order to select the best conditions to increase the biomass (temperature and substrate). To fit the mathematical model, the pH 4.5 was considered as the pH to stop the fermentation (pH\({}_{\rm{f}}=4.5\)); the selection of the pH was due to the pH of fermented milk kefir grains being between 4.2 and 4.6 [45,46]. A low pH of the substrate can slow the growth of kefir grains, and it can reduce the viability of microorganisms, but it is also related to the conservation and sensorial properties of the final product. [PERSON] et al. (2012) [47] mentioned that co-cultured kefir LAB and yeast are carried out faster and better in a pH close to 4.2 than at a pH of 6.2. During kefir fermentation, the pH change was recorded in 0 (initial), 2, 4, 6 and 24 h intervals. Before inoculation with kefir grains, the average milk pH was 6.8 by fitting the behavior of the medium to the model (Figure 2), and the R2 was adjusted (Table 1) using the Equation (1). Having new substrates is a continuous challenge, and in order to produce and obtain fermentation subproducts around milk kefir grains such as fermented beverages or byproducts of biotechnological interest such as exopolysaccharide, temperatures of 30 \({}^{\circ}\)C would be considered a better option for a continuous flow reactor, so that operation times can be reduced to 14-16 h with the use of FUC to obtain this metabolite, but not for cell growth, where a higher concentration was observed with GAL, which involves a constant change of substrate and medium to avoid cell lysis due to a fast decrease in pH. Variation on kefir microbiota by using different substrates has been demonstrated. Therefore, monitoring to maintain the characteristics of the culture in view of what is to be obtained (biomass or secondary metabolites) is crucial if industrializing its production and maintaining a sustainable culture are desired [48].