Dynamic analysis of lactic acid fermentation in membrane bioreactor

Area of Science:

• Biochemical Engineering
• Mathematical Modeling
• Fermentation Technology

Background:

• Lactic acid fermentation is crucial for various industries.
• Membrane bioreactors offer advantages for continuous fermentation processes.
• Controlling substrate concentration is key to optimizing lactic acid yield.

Purpose of the Study:

• To develop a novel mathematical model for lactic acid fermentation in membrane bioreactors.
• To establish an objective criterion for controlling substrate concentration.
• To ensure sustainable and steady lactic acid production.

Main Methods:

• Investigated continuous and impulsive substrate input.
• Analyzed existence and stability of equilibria using Poincaré-Bendixson Theorem.
• Applied Floquet's theorem and small-amplitude perturbation for stability analysis.

Main Results:

• Conditions for globally asymptotical stability of equilibrium were determined.
• A biomass-free periodic solution was found to be locally stable under specific conditions.
• A nontrivial periodic solution emerged via supercritical bifurcation in a limiting case.

Conclusions:

• The developed mathematical model provides a framework for controlling lactic acid fermentation.
• The findings offer insights into achieving stable and sustainable lactic acid output.
• Numerical simulations confirmed the theoretical results and model validity.