An analysis of electrohydrodynamic stability and deformation in immiscible fluids
Creators: name: Zhang, Jia
Publisher: name: No Publisher Supplied
Year: 2012

description: The interactions between an electric field and fluid motion give rise to a class of complex and important phenomena known as electrohydrodynamics. In this work, we developed a set of analytical tools to provide basic understanding and quantitative prediction capabilities. Under this theme, three tasks have been accomplished. 1. A general solution approach for the electrohydrodynamic instability of stratified immiscible fluids is presented. The problems of two and three fluid layers subject to normal electric fields are analyzed. Analytical solutions are obtained by employing the transfer relations relating the disturbance stresses to the flow variables at the interface(s). The results assume a general format. Both new dispersion relations and those from various previous work are shown to be special cases when proper simplifications are considered. As a specific example, the stability behavior of a three-layer channel flow is investigated in details using this framework. This work provides a unifying method to treat a generic class of instability problems. 2. A transient analysis to quantify droplet deformation under DC electric fields is presented. The full Taylor-Melcher leaky dielectric model is employed where the charge relaxation time is considered to be finite. The droplet is assumed to be spheroidal in shape for all times. The main result is an ODE governing the evolution of the droplet aspect ratio. The model is validated by extensively comparing predicted deformation with both previous theoretical and numerical studies, and with experimental data. Furthermore, the effects of parameters and stresses on deformation characteristics are systematically analyzed taking advantage of the explicit formulae on their contributions. The theoretical framework lays the foundation for the study of a more complex problem, vesicle electrodeformation. 3. A transient analysis for vesicle deformation under DC electric fields is developed. The theory extends from a droplet model, with the additional consideration of a lipid membrane separating two fluids of arbitrary properties. For the latter, both a membrane-charging and a membrane-mechanical model are supplied. The main result is also an ODE governing the evolution of the vesicle aspect ratio. The effects of initial membrane tension and pulse length are examined. The model prediction is extensively compared with experimental data, and is shown to accurately capture the system behavior in the regime of no or weak electroporation. More importantly, the comparison reveals that vesicle relaxation obeys a universal behavior regardless of the means of deformation. The process is governed by a single timescale that is a function of the vesicle initial radius, the fluid viscosity, and the initial membrane tension. This universal scaling law can be used to calculate membrane properties from experimental data. Together, these projects provide powerful tools to analyze a broad class of problems involving electrostatics, hydrodynamics, and membrane mechanics.