Electrospray of a very viscous liquid in a dielectric liquid bath

Numerical computations and order-of-magnitude estimates are used to analyze a jet of a very viscous liquid of finite electrical conductivity that is injected at a constant flow rate in an immiscible dielectric liquid under the action of an electric field. The conditions under which the injected liquid can form an elongated meniscus with a thin jet issuing from its apex (a cone-jet) are investigated by computing the flow, the electric field, and the transport of electric charge in the meniscus and a leading region of the jet. The boundaries of the domain of operation of the cone-jet mode are discussed. The current transfer region determining the electric current carried by the jet is analyzed taking into account the viscous drag of the dielectric liquid surrounding the jet. Conditions under which the electric current/flow rate characteristic follows a square root law or departs from it are discussed.