#### Date of Award

Fall 2004

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)

#### Department

Mechanical Engineering

#### First Advisor

Pushpendra Singh

#### Second Advisor

N. Aubry

#### Third Advisor

Anthony D. Rosato

#### Fourth Advisor

Denis L. Blackmore

#### Fifth Advisor

I. Joga Rao

#### Abstract

A finite element code based on the level set method is developed for performing two and three dimensional direct numerical simulations (DNS) of viscoelastic two-phase flow problems. The Oldroyd-B constitutive equation is used to model the viscoelastic liquid. The code is used to study transient and steady state shapes of Newtonian and viscoelastic drops in simple shear and buoyancy driven flows. The roles of the governing dimensionless parameters: Capillary number (Ca), Deborah Number (De) and the polymer concentration parameter c, in determining deformation of drops and bubbles, are also analyzed.

The numerical code permits us to vary Ca, De and c independently, which is difficult to achieve experimentally. This capability is used to isolate the roles of these parameters on the nature of viscoelastic stress near the drop surface and their effect on drop deformation. Results for simple shear flows indicate that when the drop phase is Newtonian and the matrix phase viscoelastic, the viscoelastic stresses pull the ends of the drop near the tips of the major axis and near the tips of the minor axes they are tangential, and thus have the net effect of increasing drop deformation. Viscoelastic stresses have the opposite effect when the drop phase is viscoelastic and the matrix phase is Newtonian. Additionally, due to the extensional nature of viscoelastic stresses, drops sheared by viscoelastic fluids develop pointed ends, a phenomenon observed experimentally and popularly known as tip-streaming.

For buoyancy driven bubbles rising in quiescent viscoelastic fluids, simulations show that the rise velocity oscillates before reaching a steady value. The shape of the bubble, the magnitude of velocity overshoot and the amount of damping depend mainly on c and the bubble radius. Simulations show that there is a critical bubble volume range in which there is a sharp increase in the terminal velocity with increasing bubble volume similar to the behavior observed in experiments. An explanation for this phenomenon is offered based on the transient oscillations and shape change.

The structure of the wake of a bubble rising in a Newtonian fluid is strikingly different from that of a bubble rising in a viscoelastic fluid. In addition to the two recirculation zones at the equator of the bubble rising in a Newtonian fluid, two more recirculation zones exist in the wake of a bubble rising in viscoelastic fluids which influence the shape of a rising bubble. Also, the direction of motion of the fluid a short distance below the trailing edge of a bubble rising in a viscoelastic fluid is in the opposite direction to the direction of motion of the bubble. The wake is 'negative' in the sense that the direction of fluid velocity behind the bubble is the opposite of that for a Newtonian fluid.

#### Recommended Citation

Pillapakkam, Shriram B., "Computational studies of viscoelastic multiphase flows" (2004). *Dissertations*. 681.

https://digitalcommons.njit.edu/dissertations/681