Title: Fluid Dynamics of Extensional Deformation and Capillary-Driven Breakup of Drops at Low Reynolds Number.
Author: Aditya N. Sangli
Day/Time: June 22nd, 12:00 pm – 2:00 pm
List of committee members
Professor David I. Bigio, Chair & Advisor
Professor Amir Riaz
Professor James H. Duncan
Professor Kenneth Kiger
Professor Richard V. Calabrese, Dean’s Representative
In this dissertation, extensional deformation and capillary-driven breakup of drops at low Reynolds number is investigated using a combination of theoretical, experimental, and numerical techniques. The dissertation introduces a new non-dimensional measure for drop deformation, rationalizes previously unseen drop breakup behavior, and extends our overall understanding of the fluid dynamics behind drop deformation and breakup.
First, non-stagnant extensional deformation of Silicone oil drops in Castor oil is experimentally studied over a wide range of capillary numbers by injecting the drops along the centerline of a flow through a hyperbolic converging channel. The unique design of the channel is capable of imposing a constant extensional rate and is validated using lubrication theory. Based on a careful analysis of drop deformation at both small and large capillary numbers compared to the critical capillary number, a new measure called the semi-minor capillary number is introduced to characterize drop behavior. Critical semi-minor capillary number is presented for a wide range of viscosity ratios and the significance of the new measure over the conventional capillary number measure is discussed.
During the course of the experiments, it was observed that drops undergoing non-stagnant extension exhibited a lag in velocity compared to the background flow velocity at the same point. This lag in velocity is attributed to flow induced deformation of the drops and the phenomenon is rationalized for a wide range of capillary numbers.
When drops are injected offset of the centerline of the channel, an anomalously large degree of deformation is observed even at low flow rates. A careful investigation of the phenomenon revealed that the strain rates along offset lines were at least an order of magnitude larger than the extensional rates along the centerline. A model is developed based on lubrication theory to predict the large deformation of drops and is successfully validated with experimental measurements.
Finally, when slender drops are allowed to develop under the effect of interfacial tension, they either retract into a sphere or breakup into multiple drops. This phenomenon is investigated using direct numerical simulations in a previously unexplored part of the parametric space where both inertial and viscous effects in the outside fluid are considered. A stability diagram is presented that shows a transition of drop states from asymptotically unstable to asymptotically stable states at different viscosity ratios. The drop behavior in different regimes is discussed and the significance of the balance between inertial and viscous forces is thoroughly described.