The Taylor Pump: Viscous-Free Surface Flow Driven by Electric Shear Stress

The pump invented by G.I. Taylor consists of low conductivity liquid in an insulated tank with electrodes at each end, one of which has an extension canted over the liquid/gas interface. When a potential difference is imposed between the electrodes, an electric shear stress acts on the interface and drives a Marangoni-like flow. The steady, two-dimensional flow of an incompressible, Newtonian, ohmic liquid in the tank is analyzed by solving simultaneously the Navier-Stokes equations for velocity and pressure in the tank and the Laplace equation for electric field in the liquid and the gas. The results show that an egg-shaped vortex develops in the liquid as the relative importance of inertial to viscous forces increases, in accordance with the experiments of Melcher and Taylor (1969). The methods developed here can be readily extended to analyze drop deformation and enhancement of mass transfer in two-phase systems due to an imposed electric field.