Stability of electrohydrodynamic induction pumping of liquid film in vertical annular configuration

Instability of electrohydrodynamic (EHD) induction pumps can manifest itself in a sudden drop/jump in pump output. The instability can also result in alternating/bidirectional flow. To understand and avoid this erratic behavior of the pump operation, a nondimensional stability analysis of EHD induction pumping of liquid film in a vertical annular configuration in the presence of an external load (i.e., pressure gradient and gravitational force) for repulsion mode is carried out. A general nondimensional stability criterion is presented, indicating that the stability of the pump depends on the nondimensional geometric parameters of the pump as well as the nondimensional electric properties of the liquid film. A stability map based on dimensionless electric conductivity and liquid-film thickness is presented. The effect of the dimensionless angular velocity on the nondimensional interfacial velocity under the influence of a pressure gradient and gravitational force is investigated. It is also shown that the erratic behavior of the unstable pump can be eliminated by a proper selection of geometric and liquid-film parameters, as well as the traveling electric-wave frequency.