Mathematical model of polylactic acid biodegradation under controlled composting conditions

Abstract

The environment suffers constant damage due to the excessive manufacture of non-degradable materials. Since petroleum-derived plastic polymers degrade slowly, it is necessary to promote the use of biodegradable plastics, such as polylactic acid. Polylactic acid is produced from natural and renewable resources, it has suitable physical and chemical properties, and biodegrades under appropriate temperature and humidity conditions, which are achieved in the composting process. Currently, there are models that are based on the measurement of carbon dioxide, and mass loss, among others. However, there are no models that describe the biodegradation of polylactic acid considering the effect of the influencing factors of the composting process. The objective of this work is to model the dynamics of polylactic acid biodegradation under controlled composting conditions, considering the main influencing factors, such as temperature, moisture content, and oxygen. Using mathematical modeling from ordinary differential equations as a methodology, simulations were carried out based on the degradation of dry matter from different substrates. The results aim to predict the dynamics of polylactic acid biodegradation, through a model that integrates the influencing factors of the composting process.

A theoretical description of polylactic acid biodegradation in composting processes through mathematical modeling

“…The total dry mass of composting M can be expressed as the sum of the composting mixture and the PLA mass, as shown in Equation ( 1) [5]:…”

“…Finally, in the fast reaction phase, the degradation rate of PLA is higher, because microorganisms begin to metabolize the small PLA fragments to generate methane and carbon dioxide under anaerobic and aerobic conditions, respectively [41,52,61]. Thus, the dynamics of PLA mass degradation is represented by Equation (3) [5,50]:…”

“…In Table 1, the notations for each variable and their initial values are described. In addition, the values of the parameters used to perform the numerical simulations are detailed in Table 2, which are mostly taken from secondary sources [5,36,39,16,15,50,13,38,17,35,46,56,14].…”

“…Nowadays, there are some studies of mathematical models that evaluate the degradability of plastics based on the measurement of carbon dioxide, mass loss, Arrhenius equation, among others [4]. In the work of Baldera-Moreno et al (2023) [5], a model of PLA biodegradation under controlled composting conditions was proposed whose degradation rates are variable with respect to the influencing factors; but the influence of the C/N ratio is not considered. According to Chowdhury et al (2013) [11], the ideal range of the initial C/N ratio should be between 25 and 40 to perform well in the composting process.…”

“…) of the composting process, several assumptions were made (similar to the studies of ; Baldera-Moreno et al (2023)[5];Ekinci et al (2020) [39];Sokač et al (2022) [54]):…”