Towards an improved conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid

In [1], the authors proposed a charge-conservative numerical framework for simulating electrohydrodynamic two-phase flows where the electric force was discretely treated as the divergence of Maxwell stress tensor because the use of volume-averaged electric force was found to be inaccurate. In this letter, we show that this framework still suffers from inaccuracies, particularly at high permittivity ratios and propose a simple solution that involves reconstruction of electric displacement rather than the electric field. We demonstrate the efficacy of the new remedial approach through simple numerical experiments for different electrical behaviour of the fluids over a range of permittivity ratios.