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Development and Validation of a Simple Kinetic‐Based Model to Simulate the Chemical Foaming Process During Rubber Vulcanization.

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Title: Development and Validation of a Simple Kinetic‐Based Model to Simulate the Chemical Foaming Process During Rubber Vulcanization.
Authors: Itriago, J.1,2 (AUTHOR), Pradille, C.3 (AUTHOR), Laure, P.1,4 (AUTHOR), Peuvrel‐Disdier, E.1 (AUTHOR) edith.peuvrel‐disdier@minesparis.psl.eu, Fabre, V.2 (AUTHOR), Bujeau, B.2 (AUTHOR)
Source: Polymer Engineering & Science. Jun2026, Vol. 66 Issue 6, p3961-3973. 13p.
Subjects: Vulcanization, Chemical kinetics, Porosity, Finite element method, Crosslinking (Polymerization), Foamed materials, Gases, Blowing agents
Abstract: A key issue in the modeling of the chemical foaming of rubbers is the description of the foam density evolution. This modeling must combine both a comprehensive physical description of the process and sufficient robustness and simplicity to be used in finite element computation software dedicated to reactive fluid injection. With this in mind, a simple model based on the kinetics of vulcanization and decomposition of the blowing agent was developed to simulate the chemical foaming process in rubbers. The kinetic parameters were identified by fitting the experimental data obtained using standard techniques (RPA, DSC) to autocatalytic models. In this model, the total foam volume is assumed to be the sum of the contributions from the rubber matrix and the gas bubbles it contains. The gas content of the system mainly depends on the extent to which the blowing agent decomposes. Free‐foaming dilatometry experiments under controlled non‐isothermal conditions were used to identify and validate the model. Agreement between the experimental data and the model predictions can be achieved by adjusting two parameters difficult to measure experimentally: Henry's constant, which represents the amount of dissolved gas in the rubber; and the gel point, which defines an upper limit for bubble growth. Highlights: Kinetic‐based model developed to predict the chemical foaming of rubbers.Foaming heat rate dependence explained by curing & gas generation balance.Gel point defined as an upper limit for bubble growth.Design of original free‐foaming experiments to validate the model.Additional source of gases (volatiles) in free‐foaming conditions.Experiment‐prediction agreement after adjusting gas solubility and gel point. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:A key issue in the modeling of the chemical foaming of rubbers is the description of the foam density evolution. This modeling must combine both a comprehensive physical description of the process and sufficient robustness and simplicity to be used in finite element computation software dedicated to reactive fluid injection. With this in mind, a simple model based on the kinetics of vulcanization and decomposition of the blowing agent was developed to simulate the chemical foaming process in rubbers. The kinetic parameters were identified by fitting the experimental data obtained using standard techniques (RPA, DSC) to autocatalytic models. In this model, the total foam volume is assumed to be the sum of the contributions from the rubber matrix and the gas bubbles it contains. The gas content of the system mainly depends on the extent to which the blowing agent decomposes. Free‐foaming dilatometry experiments under controlled non‐isothermal conditions were used to identify and validate the model. Agreement between the experimental data and the model predictions can be achieved by adjusting two parameters difficult to measure experimentally: Henry's constant, which represents the amount of dissolved gas in the rubber; and the gel point, which defines an upper limit for bubble growth. Highlights: Kinetic‐based model developed to predict the chemical foaming of rubbers.Foaming heat rate dependence explained by curing & gas generation balance.Gel point defined as an upper limit for bubble growth.Design of original free‐foaming experiments to validate the model.Additional source of gases (volatiles) in free‐foaming conditions.Experiment‐prediction agreement after adjusting gas solubility and gel point. [ABSTRACT FROM AUTHOR]
ISSN:00323888
DOI:10.1002/pen.70455