Electrostatic field theory and circuit analysis in the design of coalescers with pulsed dc voltage

This paper presents a mathematical analysis of the electric field and interfacial free charge experienced by the emulsion in an electrostatic coalescer that is subjected to a pulsed dc voltage. Previous work in this area is re-assessed, but the analysis is expanded. A novel static analysis of the system is presented, giving valuable physical insight. It becomes obvious that there must be a limited range of frequencies that are effective in a pulsed dc scheme. Thereafter, analytical expressions for the steady-state solution, where both the switching frequency and duty ratio (or mark space ratio) can be varied, are presented for the first time. These expressions are used to derive voltage and charge profiles for a specific example under various circumstances. In addition, a previously found criterion for optimum switching frequency is analyzed, and it is found that there are actually three physical parameters that all would show the same correlation with coalescer performance, not only charge as previously found, but also voltage and current. An analytical expression for the correlation quantity is derived, and the numerical example indicates that there is a narrow range of frequencies and duty ratios that are effective.