Mathematical model of CO₂ release during milk fermentation using natural kefir grains

Milk fermentation takes place in the presence of various micro-organisms, producing a variety of dairy products. The oldest of them is kefir, which is usually produced by the fermentation of milk with kefir grains. Carbon dioxide (CO₂ ), as one of the process products, also contributes to the characteristic flavor of kefir. The amount of CO₂ generated during fermentation depends on bioprocessing conditions and may change, which is not desirable at the industrial level.

In this study we developed a simplified mathematical model of CO₂ release in the milk-fermentation process. An intuitive approach based on superposition and experimental analysis was used for the modeling. The chemical system studied was considered as a two-input (temperature, rotational frequency of the stirrer) one-output (CO₂ concentration) dynamic system.

Based on an analysis of CO₂ release transients in the case of non-simultaneous stepwise changed input quantities, two differential equations were defined that describe the influence of the two input quantities on the output quantity. The simulation results were verified by experiments. The proposed model can be used for a comprehensive analysis of the process that is being studied and for the design and synthesis of advanced control systems, which will ensure a controlled CO₂ release at the industrial level. © 2018 Society of Chemical Industry.