Elastic effects in the foaming of thermoplastics

Abstract

We have investigated shear and bulk elastic stresses in non-Newtonian fluids in which bubble formation due to a blowing agent is taking place. In the absence of shear, these elastic fields manifest themselves strongly during the formation of bubbles, and during coalescence events. At later times, their activity is confined to the surface of the bubbles. These effects cause a significant slow-down in radial growth. In the presence of steady shear, elasticity tends to stabilize bubble shapes, as the maximum number of droplets decreases with shear rate, while their growth rate increases. @S1063-651X~98!16109-3# PACS number~s!: 83.80.Bp, 61.25.Hq, 82.70.Rr Polymeric foams have gained increasing technological importance due to their light weight, low density, and high impact resistance @1#. Inside an extruder, the foams are prepared by dissolving a small molecular species, such as CO2 , which acts as a blowing agent ~BA! within the polymer melt. A sudden drop in pressure results in the foaming of the thermoplastic, as bubble formation and growth of the BA occurs. After nucleating from the polymer melt, the bubbles grow by diffusion of the BA, by expansion of the vapor against the melt, and by coalescence. On extrusion to a cooler temperature, the thermoplastic hardens, freezing the bubble distribution in place. Since these foamed melts are non-Newtonian fluids, a description of bubble growth requires a set of coupled mass and momentum transfer equations augmented with the constitutive equation of the viscoelastic polymeric material. Indeed, considerable effort has been invested in such studies of bubble growth in melts @2#, most of it centered on isolated bubbles surrounded by liquid. However, as mentioned above, in a foaming process a large number of bubbles grow simultaneously and interact with each other; isolated bubble models are unable to address these important aspects of the growth process. Therefore, in this paper, we take a very different approach to the traditional study of foams. We present a study of bubble growth in a polymer melt where a large number of droplets are nucleated and interact through diffusion, velocity, and particularly highly-correlated elastic fields . We take a mesoscopic and hydrodynamic approach to polymers, which does not consider the details of molecular properties. Our model is a generalization of the two-fluid models introduced by several authors on a phenomenological basis to describe the dynamics of polymer melts and solutions @3‐6#. We define a relative polymer mass concentration f; the BA concentration is given by 12f. A GinzburgLandau approximation to the Flory-Huggins free energy density gives a mixture free energy of the form