Deformation of a conducting drop in a randomly fluctuating electric field

We quantify the transient deformation and breakup of a conducting drop suspended in a dielectric medium and subjected to a fluctuating electric field. Specifically, the magnitude of the field fluctuates randomly in time, while its orientation is fixed. Hence, the deformation of the drop is axisymmetric about the direction of the field. The temporal fluctuations are described by a stationary Markovian Gaussian process, characterized by a mean, variance, and correlation time. Small deformation theory predicts that the fluctuations produce a larger deformation than under a steady electric field of strength equal to the mean of the fluctuating electric field. Next, we utilize boundary integral computations to quantify the deformation and breakup of drops beyond the small deformation regime. When the mean of the fluctuating field is greater than the critical field for breakup under a steady field, we find that the average time taken to undergo breakup is less than that under an equivalent steady field. More interestingly, a certain fraction of drops are observed to undergo breakup even when the mean field is less than the critical field. The fraction of drops undergoing breakup and the range of mean electric field below the critical where breakup is observed depends on the strength of fluctuations of the electric field. An operating map is presented for the percentage of drops undergoing breakup as a function of the dimensionless mean field for different strength of field fluctuations. The present study sheds light on the response of drops in applications such as electrocoalescence and electroemulsification, where interactions with surrounding drops or disturbances in operating conditions can produce a random field around a drop, even when the applied macroscopic field is uniform.