Transient dynamics of a highly viscous, poorly conducting liquid column in a uniform transverse electric field

The transient dynamic behavior of a leaky dielectric liquid column immersed in another leaky dielectric medium and subjected to a uniform transverse electric field is investigated within the Stokes flow regime. The ordinary differential equations governing the column's transient deformation are derived and solved numerically. The influence of the relevant dimensionless numbers, including the electric capillary number CaE, the electrical conductivity ratio kr, the electrical permittivity ratio εr, the relative charge relaxation time τr, and the viscosity ratio μr, on the transient characteristics of the system is examined. It is found that increasing the electric field strength accelerates transient deformation, whereas increasing the charge relaxation time or the viscosity of the surrounding medium decelerates deformation. The transient flow develops a reverse circulation, forming either at the center of the liquid column or in the far field of the surrounding medium, depending on kr and εr. During deformation, a transition from the lower to the upper branch of the hysteresis occurs at sufficiently large kr or sufficiently small kr with large εr. Transient deformation exceeding the steady-state value may occur at large τr or extremely small μr. The electrostatic pressure at the interface increases monotonically with time, overcoming the interfacial tension and driving transient deformation from the outset. The tangential electric force either promotes or resists the interfacial flow, depending on the fluids' electrical properties.