Models and problems in electrohydrodynamics

A survey of mathematical models employed in modern electrohydrodynamics of weakly conducting fluids is given. The models are described in the order of increasing complexity. Some results obtained in the framework of each model are presented. The models considered include: the model of a unipolarly charged medium consisting of a continuous carrier fluid and an admixture of charged particles of the same sign; a more sophisticated two-ion model containing two charged admixtures of opposite signs; and the model with three different kinds of ions. In the framework of the aforementioned models, it is possible to adequately interpret almost all experimental data related to electrohydrodynamic flows that can be found in the literature. Further elaboration of the model may be needed to simulate particular electrochemical processes without introducing averaged (“effective”) macroscopic parameters. Four basic phenomena of fluid electrization (generation of an uncompensated electric space charge in the fluid) are described and analyzed.