Analyses on a charged electrolyte droplet in a dielectric liquid under non-uniform electric fields

Most of the analyses on the behaviors of a charged electrolyte droplet in a dielectric fluid have been performed based on the model of perfect conductor droplet. However, if the thickness of the electrical double layer (EDL) is not negligibly small with a finite thickness, the perfect conductor model must be corrected to some degrees. In this work, two analyses are performed for an electrolyte droplet in non-uniform electric fields based on the electrokinetic model. Firstly, the exact solution of electric potential is obtained for a spherical electrolyte droplet in a non-uniform electric field (uniform field + general linear field) under the Debye–Huckel approximation. The solution is used to derive the formula of the electrical force exerted on the droplet. The solution is also used for prediction of the first order deformation of droplet in the limit of small Weber number. Secondly, a new method is proposed for obtaining the first order correction to the solution of conductor model. This method is applicable to any deformed droplet shape. The key idea is that the volume charge density inside the thin EDL is integrated in the normal direction to the surface to be treated as the effective surface charge density. From the analysis, important features of the thin EDL are also revealed. When the EDL thickness decreases with O(κ−1), the difference between the droplet surface potential and the bulk potential also decreases with O(κ−1). Therefore, the slope of the electric potential change in the EDL remains as O(1). As a first concrete application, an ellipsoidal electrolyte droplet under a non-uniform electric field is studied.