(221k) Electrohydrodynamics of Drops in Randomly Fluctuating Electric Fields

When an electric field acts across a drop suspended in a weakly conducting fluid, it generates electric stresses at the fluid-fluid interface. The drop deforms under the applied field, and if the field strength is large enough, it undergoes breakup into smaller drops. A steady fluid flow is generated in both the drop and medium phase fluids, if the drop is weakly conducting, or leaky dielectric. The response of a single drop to both D.C. and A.C. electric fields has been well studied, but in practice, systems consist of many drops of various sizes (e.g. in an electrocoalescer), being acted upon by a macroscopically uniform field. This system of interacting drops can be mimicked by assuming that the effect of the surrounding drops is to create a randomly fluctuating electric field around a test drop. We describe this fluctuating electric field by a stationary Markovian Gaussian process, characterized by a mean, variance and correlation time. The distribution of drop deformation is quantified as a function of the statistics field signal, for the case where the orientation of the field is fixed. When the mean is less than the critical field strength for breakup, the average drop deformation under random fields is larger than the deformation under a steady field of amplitude equal to the mean of the fluctuating field. The mean deformation is larger when the field is more strongly correlated. We also probe the statistics of drop breakup for different field signals. There is a finite probability of breakup at fields less than the critical D.C. field strength for breakup. Finally, the drop response to random fields is compared to other periodic time varying fields.