## Results and Discussion

Table 4: Metrics of production of citric acid by yeasts belonging to the species _Yarrowia_ (_Candidà—Saccharomyces—Endomycopsis—Endomycopsis) lipolytica_, during growth on various substrates in bioreactor experiments. Comparisons with the current study. present work, a Verhulst-type equation [79] in which the glycerol decreasing ratio, \(Gly\)/\(Gly_{0}\), according to the approach proposed by [PERSON] and colleagues [80; 81; 82], was used in order to quantitatively describe the specific growth rate (\(\mu\)). Note that the treatment of biomass concentration at the beginning of the experiments (i.e., \(X\) at \(t=0\)) as an adjustable parameter (Table 5) highly improved the quality of the fitting. Comparisons between experimental data and theoretical concentration values are depicted in Figure 5a-c, demonstrating a very satisfactory fitting for all runs performed. The kinetic parameter values are comparable to the theoretical and experimental values recorded in the literature; specifically, the optimized parameter value for \(\mu_{\text{max}}\) in the current investigation (\(\approx\)0.03 h\({}^{-1}\)), presented slightly lower values than that reported for other optimized \(\mu_{max}\) values for various _Y. lipolytica_ strains cultivated batch-wise and producing a plethora of secondary metabolites (optimized \(\mu_{max}\) values ranged between 0.16 and 0.44 h\({}^{-1}\)) [68; 69; 79; 82]. Optimized \(q_{Pol\text{max}}\) values are found in the same order of magnitude with experimental values reported for other _Y. lipolytica_ strains cultured on glycerol in batch experiments (0.002-0.04 g\({}_{Pol}\)/g\({}_{N}\)/h; see: [PERSON] et al. [29]; [48]). The same can be stressed concerning the optimized \(Y_{X[Gly}\) values reported in the current investigation (Table 5), which presented remarkable similarities with optimized values achieved from application of several types of numerical modes for other _Y. lipolytica_ strains cultured on glycerol (=0.29-0.30 g/g) [82]. Equally, the above-mentioned optimized \(Y_{X[Gly}\) values (see Table 5) present important similarities with experimentally achieved \(Y_{X[Gly}\) values for various _Y. lipolytica_ strains cultured on crude glycerol in batch experiments (0.11-0.30 g/g) [18; 22; 29; 48]. Optimized \(Y_{Pol[Gly}\) values (ranging between 0.66 and 1.06 g\({}_{Pol}\)/g\({}_{Gly}\)--see Table 5) were somehow overestimated when compared to the experimental data (see Table 1 and Figure 2). The biochemical patterns of polyols formation from glycerol fermentation, have not yet been completely elucidated [10; 13], therefore, it is not known which the maximum theoretical conversion yield of glycerol into mannitol/erythnitol and arabitol is. On the other hand, as previously stressed, with the exception of a scarce number of reports [50; 52; 54], experimental values of the \(Y_{Pol[Gly}\) yield have rarely been reported to be \(>\)0.60 g/g, therefore, the optimized \(Y_{Pol[Gly}\) parameter values seem to be overestimated. Finally, the rather high \(Pol_{\text{max}}\) value of 162.87 g/L obtained for the data of \(Gly_{0}\approx\) 150 g/L, is attributed to the fact that glycerol was not totally consumed and polyols formation was still rising for the duration of the experiment (Figure 5) making predictions of \(Pol_{\text{max}}\) ambiguous.