Electric and viscous correction for viscous potential flow analysis of electrohydrodynamic instability of an electrified leaky-dielectric jet

Abstract

The electric and viscous correction of viscous potential flow (EVCVPF) is developed for analyzing the electrohydrodynamic instability of an electrified leaky-dielectric viscous jet. The EVCVPF model is based on the viscous potential flow (VPF) and the viscous correction of VPF (VCVPF), proposed by Joseph and Wang [“The dissipation approximation and viscous potential flow,” J. Fluid Mech. 505, 365–377 (2004)]. The purpose is to resolve the discrepancy between the non-zero irrotational viscous and the electric tangent stresses. The power of the pressure correction is introduced to compensate the neglected viscous dissipation in the flow bulk in VPF, which is equal to the average power of the irrotational viscous and the electric tangent stresses. The model has been validated by comparing it to the exact normal-mode solution of the linearized Navier–Stokes equations (fully viscous flow, FVF). The energy budget is also performed to assist in understanding underlying mechanisms. Results show that EVCVPF is accurate for charged jets with low and moderate viscosities, i.e., the Ohnesorge number approximately Oh ≤ 0.1. The inaccuracy for highly viscous jets are the limitations of VPF itself. The electric field has less influence compared to the fluid viscosity. To achieve more accurate approximations, VCVPF and VPF are chosen for axisymmetric and non-axisymmetric modes under weak electric fields. EVCVPF is in remarkably good agreement with FVF under moderate and strong electric fields. In general, as VCVPF extends the applicability in fluid viscosity of VPF, EVCVPF further improves the adequacy when studying the electrohydrodynamic instability.