## 3 Results and Discussions
### Kinetic Constants
Dashed lines indicate the values calculated for \(\upmu_{\text{max}}\) and Ks by the Contois model. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Monod**} & \multicolumn{4}{c}{**Contois**} & \multicolumn{4}{c}{**Logistic**} \\ \hline  & \(\upmu_{\text{max}}\) & \(\mathbf{K_{s}}\) (**g/L**) & **RSS** & **R\({}^{2}\)** & \(\upmu_{\text{max}}\) (**h\({}^{-1}\))** & \(\mathbf{K_{s}}\) (g/g**) & **RSS** & **R\({}^{2}\)** & \(\upmu_{\text{max}}\) (**h\({}^{-1}\))** & \(\mathbf{X_{m}}\) (g/L) & **RSS** & **R\({}^{2}\)** \\ \hline No pH & & & & & & & & & & \\ control & 0.811 & 10.124 & 0.1101 & 0.742 & 0.993 & 124.961 & 0.0041 & 0.990 & 0.619 & 0.437 & 0.0537 & 0.874 \\ pH control & 0.734 & 4.880 & 0.0061 & 0.987 & 0.517 & 0.001 & 0.0071 & 0.985 & 0.472 & 28.665 & 0.0338 & 0.928 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The growth kinetic constants of Monod, logistic, and Contois models (\(\upmu_{\text{max}}\): maximum specific growth rate; K\({}_{\text{s}}\): semi-saturation constant; \(X_{\text{m}}\): maximum biomass concentration), the residual sum of squares RSS, and the correlation coefficient R\({}^{2}\), calculated for fermentations with and without pH control. The results obtained could also justify the initial glucose addition to the rice suspension in view of the kinetic improvement of the process. In this work, the kinetic results indeed demonstrate that 1% glucose addition is still not sufficient to guarantee a suitable specific growth rate when pH is not controlled, but it can be considered adequate to satisfy the nutritional requirements of the microorganism when pH control is performed during the process. In Table 4, the kinetic constants \(\alpha\) and \(\beta\) for the lactic acid production rate, determined by the Luedeking-Piret model, are reported. For fermentations without pH control, constants \(\alpha\) and \(\beta\) were 0.001 g/g and 0.489 g/g h, respectively. As expected, the lactic acid production rate was mainly non-growth linked, with an \(\alpha\)/\(\beta\) ratio of 0.002. In fact, lactic acid started to increase after 8 h of process, reaching its maximum concentration during the stationary phase (1.987 g/L, at time t\({}_{24}\)). Conversely, [PERSON] et al. [14] and [PERSON] et al. [31] reported lactic acid production rates that were mainly associated with biomass growth, during a lactic acid fermentation process for milk whey using _Lactobacillus casei_ var. _rhammosus_ (\(\alpha\)/\(\beta\) = 9.47) and sugarcane molasses with _Lactobacillus casei_ MTCC 1423 (\(\alpha\)/\(\beta\) = 2.79), respectively. When pH control was applied, the Luedeking-Piret model fit the experimental lactic acid production rate with a low accuracy (R\({}^{2}\) = 0.762), providing an uncommon negative non-growth-linked constant \(\beta\) (\(-\)8.637 g/g h), which reproduced the decreasing tract of the lactic acid curve observed after 20 h of process. Future purposes will be a more appropriate kinetic modeling of the lactic acid production and a further optimization of the fermentation protocol with pH control in terms of added glucose percentage, in view of a future scale up of the process.