Electrodispersion of a liquid of finite electrical conductivity in an immiscible dielectric liquid

Abstract

Order-of-magnitude estimates and numerical computations are used to analyze an electrospray operating in the cone-jet mode in a bath of an immiscible dielectric liquid. In agreement with experimental results in the literature, the analysis predicts that the electric current carried by the jet increases as the square root of the flow rate of dispersed liquid in a wide range of conditions of the flow. The characteristics of the current transfer region determining the electric current are estimated taking into account the viscous drag of the dielectric liquid that surrounds the jet. The electric current is predicted to depart from the square root law for small flow rates, when charge relaxation effects become important in the current transfer region, and also when the flow rate increases to values of the order of QM=ϵ0γ2a/μ22K, where ϵ0 and μ2 are the permittivity and viscosity of the dielectric liquid, K is the electrical conductivity of the dispersed liquid, a is the radius of the capillary needle through which this liquid is injected, and γ is the interfacial tension of the liquid pair. When the flow rate becomes of order QM, the meniscus at the tip of the capillary ceases to resemble a Taylor cone, the current transfer region ceases to be short compared to the size of the meniscus, the electric current levels to a constant value, and the stationary jet cannot extend very far downstream of the meniscus.