Date of Award


Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Kathleen Feigl

Advisor 2

Franz Tanner

Committee Member 1

Amitabh Narain

Committee Member 2

Alexander Labovsky


The production of uniformly-sized droplets has numerous applications in various fields including the biotechnology and chemical industries. For example, in the separation of mixtures based on their relative absorbency, an optimal arrangement of monodispersed droplets in columns is desired for an effective separation. However, very few numerical studies on the formation of viscoelastic droplets via cross-flow shear are available, none of which have considered the case when the flow of the continuous phase is Couette. In this work, a new solver capable of automatic mesh refinement is developed for the OpenFOAM CFD toolbox to solve viscoelastic two-phase flow problems. The finite volume method is used to discretize the governing equations while employing the Volume of Fluid (VOF) coupled with the level set method to accurately describe the interface. The fourth-order least squares method is applied to the reinitialization of the level set function. Mesh refinement and coarsening procedure is based on a specified range of the volume fraction field. To validate the numerical technique, two-dimensional numerical simulation is conducted for a drop under static conditions, drop deformation in shear flow, the rise of a Newtonian drop in a Giesekus liquid and formation of viscoelastic droplet in a microfluidic T-junction. Furthermore, the effect of flow type and fluid elasticity on drop size and droplet formation dynamics was investigated in a viscoelastic-Newtonian system. The results obtained show good qualitative agreement with experimental work. In both cases where the flow of the continuous phase is pressure-driven (P-flow) and plane Couette (C-flow), there was a decrease in drop size as the cross-flow shear rate increased. However, for a fixed average shear rate, the drop sizes generated in C-flow were found to be smaller than that in P-flow. It was also found that the influence of elasticity on drop size became accentuated as the cross-flow shear increased. An increase in elasticity was accompanied by a decrease in drop size.