RESEARCH ARTICLE Development of a bubble growth model for natural rubber-based foams Hessam Ferasat 1 | Mohammad Fasihi 1 | Mir Hamid Reza Ghoreishy 2 | Mojtaba Ajorloo 3 1 School of Chemical, Petroleum and Gas Engineering, Iran University of Science and Technology, Tehran, Iran 2 Department of Rubber Processing and Engineering, Faculty of Processing, Iran Polymer and Petrochemical Institute, Tehran, Iran 3 School of Engineering and Information Technology, The University of New South Wales, Canberra, Australian Capital Territory, Australia Correspondence Mohammad Fasihi, School of Chemical, Petroleum and Gas Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran. Email: mfasihi@iust.ac.ir Abstract The modeling of bubble growth was employed as a technique to control the cellular structure and by taking the equations of bubble growth and rubber curing into account simultaneously, the instantaneous radius of cells as a func- tion of time was predicted. Side-by-side solves of the Kamal–Sourour kinetic model, as well as the heat transfer equation, led to the development of temper- ature variation function. Also, the predictions of the employed model con- cerning the effects of different parameters like the temperature of the foaming process, the level of foaming agent, and various physical attributes such as vis- cosity, gas diffusion coefficient, thermal conductivity, density, and surface ten- sion on the bubble growth and radius alterations were analyzed. Based on the obtained scanning electron microscopy image from the cellular structure, there was only a 15% disparity between the predicted and experimental data about the bubble radius. Contrary to temperature, viscosity, and thermal conductiv- ity, an increment in the level of foaming agent, diffusion coefficient, and den- sity caused a rise of bubble radius. Also, the surface tension had an insignificant impact on the volume of the bubbles. Based on the findings, the applied model has proper credibility and can predict the influences of the abovementioned factors with satisfying accuracy. KEYWORDS bubble growth modeling, cellular structure, crosslinking, foam, rubber 1 | INTRODUCTION Lightweight polymeric materials are attracting immense attention in many industries. [1–6] Foaming is one of the most practical techniques causing a remark- able decrease in the density of polymers. [7,8] It is worth stating that the foam quality is chiefly determined by the properties of the used polymer, density and also the cellular structure achieved by the bubble growth stage through a foaming in physical or chemical process. [9] The focus of recent studies in association with the modeling of the bubble growth stage of foam samples has been mostly on polyurethane foams, [10–12] food foams, [13] and thermoplastics, and few pieces of researches have documented the modeling of rubber-based foams consid- ering the simultaneous effects of foaming conditions and curing process on the foam structure. Gent et al. [14] stud- ied experimentally the changes of bubble radius in the physical foaming process of elastomer/CO 2 . Chemical foaming of natural rubber was experimentally studied in previous works. [15–17] Street et al. [18] assessed the bubble Received: 11 August 2020 Revised: 8 November 2020 Accepted: 10 November 2020 DOI: 10.1002/pen.25592 Polym Eng Sci. 2020;1–12. wileyonlinelibrary.com/journal/pen © 2020 Society of Plastics Engineers 1