Electrohydrodynamic inter-electrode flow and liquid jet characteristics in charge injection atomizers

The governing equations of electrohydrodynamics pertinent to forced and free electroconvection have been examined in the context of an array of charge injection atomization systems for dielectric electrically insulating liquids. The underlying physics defining their operation has been described further by linking the internal charge injection process inside the atomizer with resulting charged liquid jet characteristics outside it. A new nondimensional number termed the electric jet Reynolds number ReE,j is required to describe charge injection systems universally. The electric jet Reynolds number ReE,j varies linearly with the inter-electrode gap electric Reynolds number ReE, and the inter-electrode gap Reynolds number ReE varies linearly with the conventional liquid jet Reynolds number Rej. These variations yield two new seemingly universal constants relevant in the description of two-phase charge injection systems. The first constant being QVdϵ1EdL∼0.06\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\frac{{Q_{{\text{V}}} d}}{\epsilon }} \right)\left( {\frac{1}{E}} \right)\left( {\frac{d}{L}} \right)\sim 0.06$$\end{document} which physically represents the ratio of jet to inter-electrode gap electric field multipled by a nondimensional geometric factor while it may also be physically seen as a forced flow charge injection strength term, analogous to the ‘C’ term described in single-phase free electroconvection. The second constant being κEUinjLd∼0.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(\frac{\kappa E}{U_{\rm inj}}\right)\left(\frac{L}{d}\right)\sim0.6$$\end{document} which physically represents the ratio of inter-electrode gap ionic drift velocity, to the liquid jet velocity, multipled by a nondimensional geometric factor. These scalings have been found to be valid for charge injection systems regardless of fuel, voltage pulsation, electrode shape, orifice diameter, and inter-electrode gap length.