Comparison of Two-Phase Numerical Modelling Techniques in Applications with Electrohydrodynamics

Abstract

Three two-phase numerical modelling techniques were employed to study the effect of electrohydrodynamics (EHD) on the redistribution of fluid and flow patterns created. One model uses an interface tracking technique to differentiate the fluids in different domains. The other modelling techniques have a volume of fluids approach that uses a variable to represent the volume of each phase that is present in a control volume and is subjected to advection from the velocity field and diffusion to stabilize the interface. These models were testing in two cases, the deformation of a bubble from EHD forces and liquid redistribution in a stratified pipe cross-section causing liquid extraction, to investigate the limitations of each of the modelling techniques and compare the results to find the right model to use in different situations. It was found, in the bubble deformation model, that the EHD polarization forces are centralized on the interface between the fluids. Both the dielectrophoretic and electrostrictive forces were found to be significant in this scenario where previous models thought the electrostrictive component to be negligible [1]–[4]. These forces act to spread the phase parameter in the volume of fluids methods due to the force being variable across the interface control volumes which leads to a destabilization of the model. This unstable interface expansion degrades the forces dependent on the gradient of the phase parameter, in particular EHD and surface tension forces. The surface tension degradation led to bubble detachment or phase infiltration across the interface which made the model results nonphysical. The interface tracking method maintained stability as the force applied was a surface pressure on the moving interface and could not expand as the interface was infinitesimal. The steady state results of this method matched experimental data from previous investigations within 5% of interface position [5]. In the liquid extraction model, the forces were located along the interface and both components of the polarization forces were significant similar to the bubble deformation case. The volume of fluids models eventually destabilized at the interface which caused a degradation of EHD and surface tension forces, The result was a faster extraction time compared to the interface tracking method due to reduced surface tension. The volume of fluid models were compared to past numerical research [6] for the same geometry it was found that the factor that weighs the advection to the diffusion of the phase parameter is crucial in time dependent models. Increasing this parameter stabilizes the boundary of the fluid but suppresses advection leading to much slower extraction times but when the components are balanced, when large EHD forces are applied the boundary destabilizes. This shows the importance of finding the right value for this parameter in cases that are time dependent and illustrates the variation in time dependent results in volume of fluid models. The interface tracking model was compared to previous experimental work and with a different interpretation of the experimental results than the original author the results were within the experimental error [7]. The interface tracking method is shown to be the best option for stable models with good time dependent and steady state results. This model’s limitation is its inability to experience topological changes to the domains whereas the volume of fluid models were able to reach a steady state solution after the liquid rose and made contact with the electrode. In cases with topological changes during the experiment the volume of fluid methods must be used with much caution taken regarding the phase parameter weighting factor.