Abstract
Abstract In this work, we carried out numerical modeling of the large deformation of a shear thinning droplet suspended in a Newtonian matrix using the constrained volume model. The adopted approach was to consider making incremental corrections to the evolution of the droplet anisotropy equation in order to capture the experimental behavior of a shear thinning droplet when subjected to deformation due to imposed flow. The constrained volume model was modified by using different models to describe the viscosity of droplet phase: the Bautista et al. model, the Carreau-Yasuda model and the Power-law model. We found that by combining the constrained volume model with a simple shear thinning viscosity model we were able to describe the available experimental data for large deformation of a shear thinning droplet suspended in a Newtonian matrix. Moreover, we developed an equation approximating flow strength during droplet retraction, and we found that the model can accurately describe the experimental data of the retraction of a shear thinning droplet.
Highlights
The modeling of polymer blends composed of Newtonian fluids have been extensively investigated by researchers [1,2,3,4,5,6,7,8], and their flow behavior—to a great extent—is well understood
In this work, we carried out numerical modeling of the large deformation of a shear thinning droplet suspended in a Newtonian matrix using the constrained volume model
We found that by combining the constrained volume model with a simple shear thinning viscosity model we were able to describe the available experimental data for large deformation of a shear thinning droplet suspended in a Newtonian matrix
Summary
The modeling of polymer blends composed of Newtonian fluids have been extensively investigated by researchers [1,2,3,4,5,6,7,8], and their flow behavior—to a great extent—is well understood. Elmendorp and Maalcke [20] investigated a variety of combinations of droplet and matrix phase fluids, including moderately shear thinning droplets in a Newtonian matrix and the opposite setup Both systems were studied at small droplet deformation conditions. Favelukis et al [23] theoretically studied the deformation of a shear thinning single droplet suspended in a Newtonian matrix during uniaxial extensional flow. The approach used by Peters et al in their original work was to model the blend’s microstructure by assuming passive mixing, i.e., the droplet deforms passively with the imposed flow, and the droplet phase deformation is independent of the viscosity ratio between the droplet and matrix phases. Droplet elasticity can play a role in large deformation shearing flow taking place at high flow rates, this topic is outside the scope of this current work
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