MODELING DROP SIZE DISTRIBUTION IN POLYMER BLEND INJECTION MOLDING Frederick R. Phelan Jr., Erik Hobbie, Hyunsik Jeon, Sharon C. Glotzer, Charles C. Han Polymers Division and Center for Theoretical and Computational Material Science National Institute of Standard and Technology Gaithersburg, MD 20899 Abstract An approach for modeling the drop size distribution in the injection molding of polymer blends is developed. The simulation directly uses experimental data correlated to functional forms in the FIDAP fluid dynamics package. As an example, experimental data for droplet size and shape in a Polyisoprene /Polybutadiene system was measured using an in-situ optical microscopy instrument designed for studying complex fluids under simple shear flow. The data is collected in the flow-vorticity plane as a function of temperature and shear rate. Size and shape distributions were calculated from the digitized micrograph using standard image analysis software. The shear viscosity of the blends, as well as that of the pure components, was measured as a function of shear rate and temperature using a commercially available parallel-plate rheometer. From theoretical considerations, the simulation is expected to provide good estimates of drop size distribution for flows with large aspect ratios of flow length to thickness where entrance effects are expected to be negligible, and there are no regions of recirculation. Introduction Polymer blend mixtures are generally injection molded while phase separated in which droplets of one phase are suspended in a matrix phase. The components are usually pre-mixed in an extrusion operation to form a finely dispersed mixture, and then injected into the molding cavity. Upon entering the cavity, the drops break- up into finer and finer sizes near mold walls where the shear rate is high, and coalesce/relax towards equilibrium sizes in regions of low shear near the center (Figure 1). This leads to a non-uniform “skin-core” microstructure in the final part, which highly affects the properties. The detailed morphology of the blend material after injection depends on the fluid mechanical deformation history, component rheological and interface properties, and blend thermodynamics. It is of great interest to develop a simulation that models not only the injection molding fluid mechanics, but also the evolution of the blend morphology during the injection. Because there are many thousands of drops in a typical injection molding operation, it is not practical to use microscale flow modeling methods such as Lattice Boltzmann (1-2) or continuum surface force methods (3-6) to model individual drops. Instead, one must use methods that compute the average microstructure within a meso- volume that is larger than the length scale of the mixture, but much smaller than overall volume, e.g., Batchelor (7), Doi and Ohta (8), and Wetzel and Tucker (9-10). This approach is characterized by the use of an area (or interface) tensor given by ∫ Γ = dS n n V A ˆ ˆ 1 ( 1 ) where nˆ is the unit normal at the drop surface. This tensor contains information about the average local morphology of the mixture. The trace of the area tensor yields an important quantity, the specific area, which is the surface area per unit volume ) ( A tr S V = ( 2 ) For spherical drops, the drop size radius is related to the specific surface by the relation R C V CS S drop drop V 3 = = ( 3 ) where C is the drop concentration. It is evident from this relation that an increase in the specific area corresponds to an increase in the fineness of the microstructure. The evolution of the area tensor is governed by the expression ∫ ∫ ∫ Γ Γ Γ + + = S d n n V dS n n V dS n n V A & & & & ˆ ˆ 1 ˆ ˆ 1 ˆ ˆ 1 ( 4 ) In addition, the area tensor is used in the formulation of the blend constitutive law. While the area tensor approach gives insight into the behavior of blends, the problem is that there does not exist at this time a formulation of Eq. (3) that accounts for both surface tension and drop breakup, both of which are very important phenomena in blends processing. The goal of this work is to put together a simulation that predicts drop size distribution and morphology in injection molded polymer blends. To overcome some of the theoretical difficulties involved in