Microscale modelling of the cellularization of a rubber compound in injection moulding conditions

The objective of this work was to develop a microscale model allowing to describe the growth of gas bubbles during the foaming of a rubber matrix in injection moulding conditions. The description of the foaming at the level of the bubble is based on a model first proposed by Amon and Denson [1]. The model describes the growth of numerous cells in closed proximity of one another. Each one is formed by a bubble enveloped by a spherical fluid shell that contains a finite amount of dissolved gas homogenously distributed throughout its mass. The gas concentration gradient between the bubble/polymer boundary and the outside of the polymer shell cell will induce a gas diffusion towards the bubble (Fick law) and subsequently a gas pressure increase, which will induce the growth of the bubble. The bubble grows up to the moment when no more gas is available. By applying the conservation of momentum, mass and energy principles to this process, one can obtain a set of equations describing the evolution of the bubble radius, the pressure, and the concentration gradient inside the polymer. In addition to initial and boundary conditions (initial gas concentration, bubble density, temperature, pressure in the surrounding medium), different physical parameters need to be determined or estimated: the diffusivity, the Henry’s constant, the surface tension between the fluid and the gas, the matrix viscosity, density and heat capacity.As the rubber is vulcanizing during the molding step, the viscosity increase due to the vulcanization was implemented in the model. A chemo-rheological model developed by Castro and Macosko [2] was used to introduce a state of cure dependency into the viscosity term. The state of cure evolution was predicted by means of a Kamal-Sourour autocatalytic kinetic model [3]. In addition, one considers the coupling with kinetic reaction generating the gas from a chemical foaming agent (OBSH).The bubble growth kinetics will be first described and discussed in view of the gas concentration evolution and the vulcanization kinetics. A parametric study will be conducted to determine first order parameters of the bubble growth process. The predictions of the bubble growth model will be compared with experimental data (foam density and bubble size distribution measured on cellular injected molded parts based on an EPDM rubber formulation with OBSH). The effect of injection parameters (such as the molding temperature, injected volume of matrix relatively to the mold volume) on the foam density will be discussed.Acknowledgements.This work is performed in the framework of the chair DEEP, between Hutchinson, ESPCI and MINES ParisTech. Hutchinson SA is acknowledged for its financial and technical support. This work is also supported by the French Minister of Research (ANRT).References.1.M. Amon and D. Denson, Polym. Eng. Sci. 1984, 24, pp. 1026-1034. 2. J. M. Castro and C. Macosko, 38th Society of Plastic Engineering and Technical Papers Annual Technology Conference, 1980, New York, United States of America. 3. M. R. Kamal. Polym. Eng. Sci. 1974, 14, pp. 231-23