## 3 Results and Discussions
### Fermentation Process Measurement
It was observed that temperatures above 25 \({}^{\circ}\)C did not fit the semi-logarithmic equation at 24 h of fermentation; therefore, it was concluded that after 24 h of fermentation the medium was below the established pH (4.5). Thus, the fermentation temperatures of 30, 35 and 40 \({}^{\circ}\)C were discarded as temperatures for the fermentation of kefir grains in a time of 24 h, where the lowest pH was reached in all samples (3.50-4.25 pH). High temperatures (30-40 \({}^{\circ}\)C) accelerate the metabolism of LAB's, generating a medium with an acidic pH in a shorter fermentation time; hence, such an acidic medium can decrease the functional activity of LAB and therefore the increase in biomass is reduced. At low temperatures (10-15 \({}^{\circ}\)C), which also presented a non-linear behavior, the low temperature could reduce the activity of LAB and consequently carry out a slow fermentation process, which is reflected in the low production of acid in the medium (pH 6.2) and therefore in the slow growth of a kefir biomass. Since it is essential that the LAB carry out fermentation to increase their biomass and in the same way to obtain simple sugars (galactose and glucose) through the degradation of lactose, these simple sugars could be assimilated and metabolized by the yeasts present in the medium and stimulate each other's growth [49], which will be reflected in the increase in the biomass of the conglomerate (LAB and yeast). The results showed that at 20 \({}^{\circ}\)C they were able to correlate to the linear behavior. Consequently, as a result, the experimental data obtained showed that the optimum temperature for fermentation was 20 \({}^{\circ}\)C for all examined media. The results indicate that the kefir grains have the potential to proliferate in the milk during fermentation at the selected temperature of 20 \({}^{\circ}\)C and 2% of kefir grains for GLU, SAC, FUC and GAL; moreover, the best substrates fitted to the model were R2, which was equal to 0.994, 0.991, 0.983 and 0.965, respectively (Table 1). \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Substrate**} & **R\({}^{2}\)** & **R\({}^{2}\)** & **R\({}^{2}\)** & **R\({}^{2}\)** & **R\({}^{2}\)** & **R\({}^{2}\)** \\  & **10 \({}^{\circ}\)C** & **15 \({}^{\circ}\)C** & **20 \({}^{\circ}\)C** & **25 \({}^{\circ}\)C** & **30 \({}^{\circ}\)C** & **35 \({}^{\circ}\)C** & **40 \({}^{\circ}\)C** \\ \hline Control & 0.565 & 0.768 & 0.983 & 0.997 & \(\ast\) & \(\ast\) & \(\ast\) \\ Fractans & 0.609 & 0.504 & 0.983 & \(\ast\) & \(\ast\) & \(\ast\) & \(\ast\) \\ Galactose & 0.358 & 0.827 & 0.965 & \(\ast\) & \(\ast\) & \(\ast\) & \(\ast\) \\ Fractose & 0.398 & 0.729 & 0.938 & 0.998 & \(\ast\) & \(\ast\) & \(\ast\) \\ Glucose & 0.543 & 0.852 & 0.994 & 0.866 & \(\ast\) & \(\ast\) & \(\ast\) \\ Lactose & 0.036 & 0.494 & 0.958 & 0.919 & 0.995 & \(\ast\) & 0.937 \\ Sucrose & 0.466 & 0.784 & 0.991 & 0.996 & \(\ast\) & \(\ast\) & \(\ast\) \\ \hline \end{tabular} \({}^{\ast}\) Means that the fermentation medium was below the established pH of 4.5.  
\end{table} 
Table 1: Rate of change of pH vs. time during fermentation of milk kefir grains. Figure 2: pH change kinetics fitted to log (pHt-pHinf / pHi-pHinf) media for growth: (**a**) nonfat milk powder (control) and nonfat milk powder with (**b**) 2% of fructans, (**c**) 2% of galactose, (**d**) 2% of glucose, (**e**) 2% of lactose, (**f**) 2% of sucrose and (**g**) 2% of fructose. 10 \({}^{\circ}\)C (–––); 15 \({}^{\circ}\)C (–\(\times\)–); 20 \({}^{\circ}\)C (–––); 25 \({}^{\circ}\)C (–––); 30 \({}^{\circ}\)C (–––); 35 \({}^{\circ}\)C (–––); 40 \({}^{\circ}\)C (–––).