Lactic acid is a versatile chemical with wide application in many industries. It can be produced by the fermentation of different sugars by various lactobacilli and investigations on lactic acid production from different substrates and by different strains are still in progress. The present study aimed to study lactic acid production from lactose by Lactiplantibacillus plantarum AC 11S and to choose a mathematical model describing in the best way the experimental data obtained. The influence of initial substrate concentration was investigated, and optimal pH and temperature were determined. An unstructured mathematical model was developed comprising equations for bacterial growth, substrate consumption, and product formation. The model was solved with different terms for specific growth rates considering substrate and/or product inhibition. The best bacterial growth and lactic acid production were achieved at pH = 6.5 and 30 °C. Production of lactic acid was mainly growth-associated, and at initial substrate concentration over 15 g/L, a considerable product inhibition was observed. The parameters of different models were determined and compared. The modified Gompertz equation gave the best fit when solving only the equation for biomass growth at different initial substrate concentrations. Solving the entire set of differential equations for bacterial growth, substrate consumption, and product formation, the best results were obtained when using a variant of the logistic equation for biomass growth. This variant included a term for product inhibition and described in the best way all experimental data. Solving the model for different biomass concentrations showed that an increase in biomass led to a shorter lag phase and the stationary phase was reached faster. The results obtained, optimum conditions and the kinetic model, are good bases for studying pH-controlled fermentation, as well as a continuous process.

Lactic acid production from lactose by Lactiplantibacillus plantarum AC 11S was studied. The influence of initial substrate concentration was investigated, and optimal pH and temperature were determined. An unstructured mathematical model was developed comprising equations for bacterial growth, substrate consumption, and product formation. The model was solved with different terms for specific growth rates considering substrate and/or product inhibition. The best bacterial growth and lactic acid production were achieved at pH = 6.5 and 30 oC. Production of lactic acid was mainly growth-associated and at substrate concentration over 15 g/L a considerable product inhibition was observed. The parameters of different models were determined and compared. While the modified Gompertz equation gave the best fit for biomass growth, a variant of the logistic equation including a term for product inhibition described in the best way the entire set of equations comprising bacterial growth, substrate consumption, and product formation at different initial substrate concentrations.

Lactic acid (LA) is an important chemical with diverse applications in various industries. LA can be produced by the fermentation of different substrates by many microorganisms such as bacteria, fungi, yeasts, and algae. Lactic acid bacteria (LAB) are generally accepted as the main producers of LA. A distinct characteristic of LAB is the complexity of the fermentation media. Distiller’s dried grains with solubles (DDGS), a by-product from bioethanol production, represent a promising substitute for costly sugars in the nutrition media for LA production. In the present paper, the possibility of using dilute acid DDGS hydrolysates as a substrate for LA fermentation was investigated. The influence of different factors (acid concentration, time, pressure, solid-to-liquid ratio) on the reducing sugars (RS) obtained was studied. Additional enzyme hydrolysis was carried out to increase RS content in the hydrolysates. LA production from hydrolysates without and with control of the pH during fermentation was monitored and compared with lactose as a substrate. Inhibition of the process was observed in both substrates in the absence of pH control which was overcome in the case of pH control. A mathematical model based on the Verhulst and Ludeking–Piret equations was proposed and tested, showing very good agreement with experimental data.

This study proposes a mathematical modeling approach for evaluating the effect of applying a permanent electric field on the biodegradation of 1,2-dibromoethane by bacterial cells of Bradyrhizobium japonicum 273. Two models for inhibited microbial growth including product inhibition were composed—one using the Monod–Yerusalimsky approach and another one—the Levenspiel kinetic equation. The models were used to process own experimental data obtained without an electric field and ones obtained at the application of an electric field. The experiments were carried out at an optimum anode potential of 0.8 V vs. the standard hydrogen electrode (SHE). Three initial concentrations of substrate were tested: 0.05, 0.1, and 0.15 g dm⁻³. The modeling takes into account the product inhibition on microbial growth assuming 2-bromoethanol as the first biodegradation product. It was found that the positive effect of the electric field is the enhancement of microbial growth, expressed by the increase in the maximum specific growth rate and the increase in the inhibition constant when the model of Monod–Yerusalimsky is applied. The main effect of the electric field is in the increase in the rate constant of 2-bromoethanol removal by electrochemical oxidation, enabling the enhancement the microbial growth and substrate conversion to the product. The obtained results show that the application of a permanent electric field leads to a higher electrochemical oxidation rate (with a rate constant up to 60% higher than for the control experiments) and complete substrate and 2-bromoethanol biodegradation. The model of Levenspiel is not so sensitive to the effects of the electric field on product inhibition.