文献类型：期刊文献

英文题名：Establishment of a quantitative mathematical model with expressive formulation based on the basic laws and physical essences of bubble growth in polymer foaming

作者：Jiang, Tuanhui Xing, Jingfu Zeng, Xiangbu Li, Shengnan Zhang, Xiaodie Zhang, Chun He, Li Gong, Wei

第一作者：Jiang, Tuanhui

通信作者：He, L[1];Gong, W[2]

机构：[1]Guizhou Univ, Coll Mat & Met, Guiyang 550025, Guizhou, Peoples R China;[2]Guizhou Mat Ind Technol Inst, Guiyang 550014, Guizhou, Peoples R China;[3]Guizhou Inst Technol, Sch Mat & Met Engn, Guiyang 550025, Guizhou, Peoples R China;[4]Guizhou Minzu Univ, Guiyang 550025, Guizhou, Peoples R China

第一机构：Guizhou Univ, Coll Mat & Met, Guiyang 550025, Guizhou, Peoples R China

通信机构：corresponding author), Guizhou Univ, Coll Mat & Met, Guiyang 550025, Guizhou, Peoples R China;corresponding author), Guizhou Minzu Univ, Guiyang 550025, Guizhou, Peoples R China.

年份：2026

卷号：344

外文期刊名：POLYMER

收录：;EI(收录号：20260319912366);Scopus(收录号：2-s2.0-105027284175);WOS:【SCI-EXPANDED(收录号:WOS:001658158300001)】；

基金：This work was supported by the "Thousand" Level Talents of High-Level Innovative Talents Selection and Cultivation Project of Guizhou Province (No. QCC [2025] 003) .

语种：英文

外文关键词：Mechanical equilibrium; Phase equilibrium; Bubble growth; Mathematical model; Visualization

摘要：Understanding and predicting bubble growth is fundamental to controlling the cellular structure of polymer foams. Over the past five decades, researchers have combined experimental and theoretical approaches to investigate bubble growth behavior. However, existing models fail to clearly elucidate the physical essence of bubble growth and often exhibit significant deviations when quantitatively validated against experimental data. Firstly, based on classical thermodynamic principles, we proposed that bubble formation in polymer melts required simultaneous satisfaction of both mechanical and phase equilibrium conditions. The three fundamental physical assumptions were proposed for establishing a mathematical model describing the bubble diameter evolution over time (D-t model): (1) The bubble diameter is inversely proportional to the final bubble density. (2) Employing the Logistic function to describe mechanical equilibrium dominated by gas molecular fluctuations. (3) The Boltzmann function is utilized to characterize the transport of gas molecules driven by chemical potential difference. Through mathematical simulation of bubble growth with different diameters and bubble growth nucleated at the same time during polypropylene chemical foaming injection molding, it has been revealed that the randomness and non-uniformity in the microscopic distribution and aggregation of gas are the primary factors influencing the differences in bubble diameter. The quantitative accuracy of the model was further validated across diverse polymer systems and processing conditions. This work not only offers a novel understanding of the physical essence of bubble growth but also provides an effective theoretical tool for the quantitative analysis and process optimization of polymer foaming processes.