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A theoretical description of polylactic acid biodegradation in composting processes through mathematical modeling
  • Yvan Baldera-Moreno,
  • Alejandro Rojas,
  • Rodrigo Andler
Yvan Baldera-Moreno
Universidad Catolica del Maule

Corresponding Author:[email protected]

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Alejandro Rojas
Universidad Catolica del Maule
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Rodrigo Andler
Universidad Catolica del Maule
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Polylactic acid (PLA) is a bio-based plastic that is biodegradable under appropriate conditions of temperature, humidity and oxygen, which are achieved in the composting process. The objective of this work is to formulate a mathematical model that predicts the biodegradation of polylactic acid in composting processes. We performed a qualitative analysis of the reduced composting mass system, which is non-linear and non-autonomous. First, the reduced model was transformed into an autonomous system, showing that their solutions are positive, bounded and non-periodic. Furthermore, it was shown that the origin is locally and globally exponentially stable, the axial equilibrium is unstable and that a degenerate transcritical bifurcation exists at the origin. Simulations of the reduced system indicated that the PLA mass is completely biodegraded when the time tends to infinity, which was shown theoretically. In addition, numerical simulations of the complete composting system were performed considering three initial values of the carbon/nitrogen ratio. It was concluded that the initial carbon/nitrogen ratio of 32.5 reached 90% of PLA biodegradation in approximately 150 days. This work provides a mathematical tool applied to the field of biotechnology of biodegradable plastics.
09 Sep 2023Submitted to Mathematical Methods in the Applied Sciences
09 Sep 2023Assigned to Editor
09 Sep 2023Submission Checks Completed
15 Sep 2023Review(s) Completed, Editorial Evaluation Pending
25 Sep 2023Reviewer(s) Assigned