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A Multi-Scale Polymer Foam Model and Its Application

Deming Mao1, Asjad Shafi1, Albert Harvey2, and Jack R. Edwards3. (1) Engineering and Process Sciences, The Dow Chemical Company, 2301 N. Brazosport Blvd, B-1226, Lake Jackson, TX 77566, (2) EP Americas, Shell Exploration and Production Company, 777 Walker Street, Houston, TX 77002, (3) Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695

Filling of a closed cavity with insulating foams requires balancing of many chemical and physical phenomena such as viscosity buildup, generation of blowing agent, and nucleation and growth of bubbles. We have developed a comprehensive foam model that can take into account these phenomena and can be used to simulate the flow of foam in closed as well as open cavities.

The math model employs a multi-scale approach. The bubble nucleation and growth are combined with the fundamental multi-phase transport equations for the whole process. Thus, the model can provide both bubble-scale and bulk polymeric liquid information. Bubble-scale information includes bubble size distribution, bubble number density and bubble shape; and bulk polymeric liquid information includes mixture mass density, species mass fraction, temperature, viscosity, reaction conversion, velocity and gel position.

The model takes into account the growth competition between large and small bubbles by using the concept of growing influence volumes and takes into account both the mass and momentum transfer limitations on the growth. The calculations for bubble growth are not limited to initial stages of foaming. No other model available at this time has all these features. The value of different parameters for reaction rates, viscosity buildup, and nucleation can easily be changed to simulate different foaming systems.

The model is integrated into a numerical scheme which was developed for gas-liquid two-phase flow with interface propagation and phase variation. Finally, the source codes are built on parallel structure, which can solve real industrial problems from a Linux cluster.

The foam model and numerical scheme can predict evolution of foam growth in closed or open cavities which can be used for process optimization. The model can also be used to generate information about the foam properties.