Response surface methodology for modeling of the critical electric field of a single drop subjected to different electric waveforms

Abstract

Electro-coalescence has been an environmentally friendly technology for decades. However, electric field strength should not exceed a critical value (Ecrit) to inhibit droplets from disintegrating during coalescence. In this study, response surface methodology (RSM) with a D-optimal design was utilized to develop a model to achieve the maximum Ecrit of a single drop. Waveform, frequency, drop diameter and interfacial tension were statistically significant. Frequency change revealed Ecrit increases with a moderate slope for all waveforms. This was attributed to less degree of drop deformation due to shorter on-time intervals of pulsatile electric field and non-compliance of drop vibration with field frequency. Following the revelation of interaction between diameter and frequency, it was observed elevated frequencies have a significant impact on larger droplets, and the sensitivity of Ecrit to the diameter decreases with frequency. This suggests higher frequencies as a useful and fast controllable variable to compensate for the effect of droplet size distribution. Optimization suggested a minimum drop diameter and a maximum frequency that can be used as two important limits for the robust design of electro-coalescers. The best and worst results in all cases corresponded to Pulse 90 and 10 waveforms respectively.