Modeling and Experimental Validation of Gradient Cell Density in PMMA Microcellular Foaming Induced by One-Sided Heating

Traditionally, the microcellular foaming process has aimed to generate uniform cell structures by applying heat uniformly to all surfaces of a polymer. Homogeneous cell distribution is known to enhance the mechanical properties and durability of the final product. However, the ability to engineer a gradient in cell density offers potential advantages for specific functional applications, such as improved sound absorption and thermal insulation. In this study, a controlled thermal gradient was introduced by heating only one side of a fully CO₂-saturated poly(methyl methacrylate) (PMMA) specimen. This approach allowed for the formation of a cell density gradient across the sample thickness. The entire process was conducted using a solid-state batch foaming technique, commonly referred to as the microcellular foaming process. A one-sided heating strategy successfully induced a spatial variation in cell morphology. Furthermore, a coalescence function was developed to account for cell merging behavior, enabling the construction of a predictive model for local cell density. The proposed model accurately captured the evolution of cell density gradients under asymmetric thermal conditions and was validated through experimental observations, demonstrating its potential for precise control over foam structure in saturated PMMA systems.