77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024;
Salt Lake City, Utah
Session X06: Drops: Electric Field Effects
8:00 AM–10:36 AM,
Tuesday, November 26, 2024
Room: Ballroom F
Chair: Yang Liu, City College of New York
Abstract: X06.00008 : Transient Electrohydrodynamic Behaviour of a Non-Newtonian Droplet in Another Non-Newtonian Medium: A Mathematical Exploration
9:31 AM–9:44 AM
Abstract
Presenter:
Pulak Gupta
(Indian Institute of Technology Ropar)
Authors:
Pulak Gupta
(Indian Institute of Technology Ropar)
PURBARUN DHAR
(Hydrodynamics and Thermal Multiphysics Lab (HTML), Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, West Bengal–721302, India)
Devranjan Samanta
(Department of Mechanical Engineering, Indian Institute of Technology Ropar, Punjab–140001, India)
Due to the encapsulated structure, small volume, and large surface area, droplets are ideally suited for use as specialized material carriers and reactors. Extensive studies of deformation and flow fields within droplets under an external electric field, among other fields such as magnetic, pressure, micropump, or combinations thereof, are well-known in the scientific community, particularly in microfluidic applications where deformation, manipulation, breakup, and coalescence are crucial. Many experimental, mathematical, and analytical work has been done on Newtonian droplets, considering both steady-state and transient conditions. However, in practical applications, the fluid often exhibits non-Newtonian behaviour, yet very few studies have addressed the non-Newtonian nature of droplets under transient conditions. This gap motivates the present study, which involves the mathematical analysis of an immiscible, leaky dielectric non-Newtonian droplet confined in a different surrounding medium under the small deformation regime, in the presence of an external, low-intensity DC electric field of irrotational nature. The study focuses on examining the transient deformation and flow fields within the droplet and the surrounding medium, considering various interfacial stresses. The investigation is constrained by a critical value of the Weissenberg number, set to 1, ensuring that the elastic nature remains less than or equal to the viscous nature without exceeding it. The mathematical analysis incorporates electrical phenomena via Laplace's equation and the charge conservation equation, hydrodynamic phenomena through the continuity equation and Cauchy momentum equation, and addresses the non-Newtonian behaviour using the upper convected Maxwell model. These equations are non-dimensionalized using appropriate characteristic scales and non-dimensional numbers, and solved with suitable non-dimensional forms of boundary and interfacial conditions. Validation of our mathematical model is conducted against existing experimental and mathematical literature. In addition to deformation, flow field patterns are analyzed by generating streamline patterns, suggesting deeper exploration in non-Newtonian fluids holds promise for advancing in the development of microfluidic devices.