Drop dynamics in polymer processing flows

Mechanically mixing two or more polymers to produce blends is an attractive route to novel polymer products. Blend properties are intimately related to the size, shape and orientation of dispersed drops. A fundamental understanding of how drops deform during processing is therefore a precursor to successful prediction and control of material properties. This thesis contributes to such an understanding by applying the Finite Element Method (FEM) to simulate deformable drop dynamics in viscoelastic fluids. A robust 3-dimensional adaptive FEM framework allowing large deformations to be accurately tracked is also developed for multi-particle Newtonian systems.; The first part of the thesis involves simulating axisymmetric single drop deformations with either or both fluid phases being viscoelastic. Drop and outer fluid constitutive behavior are described using the Oldroyd-B relation. Mass and momentum conservation equations in the creeping flow limit are solved using a finite element (FEM) formulation providing numerical stability via stress splitting and upwinding, the DEVSS-G FEM. Time stepping is performed fully implicitly using modified Newton iterations. Results show the influence of viscoelasticity on drop deformation and on retraction following cessation of the imposed extensional flow. Viscoelastic drops are predicted to deform less when stable shapes are possible and to retract more quickly than Newtonian drops of the same viscosity. A mechanism involving elastic energy storage is invoked to explain both. Viscoelasticity in the outer fluid produces larger drop deformations at steady state and can dramatically influence the mode of drop retraction. The former is due to additional squeezing of the drop from first normal stresses and the latter to the coupling of the far-field boundary conditions to the way in which stored elastic energy is permitted to release.; The second part addresses very large drop deformations in fully 3D flows of Newtonian fluids. Adaptive remeshing is employed to maintain a prescribed resolution of local length scales associated with surface curvature. The solution process decouples solution of the Stokes problem from mesh movement via an explicit time integration scheme. Drop free surfaces are remeshed after each time step with corresponding 3D meshes of unstructured tetrahedra created by interfacing with commercial software.