An interface tracking model for droplet electrocoalescence.

Abstract

This report describes an Early Career Laboratory Directed Research and Development (LDRD) project to develop an interface tracking model for droplet electrocoalescence. Many fluid-based technologies rely on electrical fields to control the motion of droplets, e.g. microfluidic devices for high-speed droplet sorting, solution separation for chemical detectors, and purification of biodiesel fuel. Precise control over droplets is crucial to these applications. However, electric fields can induce complex and unpredictable fluid dynamics. Recent experiments ) have demonstrated that oppositely charged droplets bounce rather than coalesce in the presence of strong electric fields. A transient aqueous bridge forms between approaching drops prior to pinch-off. This observation applies to many types of fluids, but neither theory nor experiments have been able to offer a satisfactory explanation. Analytic hydrodynamic approximations for interfaces become invalid near coalescence, and therefore detailed numerical simulations are necessary. This is a computationally challenging problem that involves tracking a moving interface and solving complex multi-physics and multi-scale dynamics, which are beyond the capabilities of most state-of-the-art simulations. An interface-tracking model for electro-coalescence can provide a new perspective to a variety of applications in which interfacial physics are coupled with electrodynamics, including electro-osmosis, fabrication of microelectronics, fuel atomization, oil dehydration, nuclear waste reprocessing and solution separation for chemical detectors. We present a conformal decomposition finite element (CDFEM) interface-tracking method for the electrohydrodynamics of two-phase flow to demonstrate electro-coalescence. CDFEM is a sharp interface method that decomposes elements along fluid-fluid boundaries and uses a level set function to represent the interface.3

Electric Field Driven Separation of Oil–Water Mixtures: Model Development and Experimental Verification

“…The electrostatic field E is defined as the gradient of the electric potential ϕ: ,, A Poisson equation is used to represent the voltage equation, which describes how the electric field is affected by the electric charge density ρ el : ,, with the absolute permittivity ε being obtained from harmonic averaging weighted according to the phase fraction. Assuming no free charges in the bulk phases, ρ el becomes zero.…”

“…Assuming no free charges in the bulk phases, ρ el becomes zero. The electric field is coupled to the Navier–Stokes equation via the Maxwell stress tensor M , with its divergence giving the electric force: , The Maxwell stress tensor is represented by where I denotes the identity matrix. Rewriting eq including eq and assuming ρ el = 0 obtains: From the above equation, it is clear that only dielectrophoretic attractive forces are considered in the numerical simulations.…”