Electrohydrodynamic conduction pumping of a viscoelastic dielectric fluid with the Onsager–Wien effect

Abstract

Due to the Onsager–Wien effect (enhanced electric field dissociation), electrohydrodynamic (EHD) conduction pumping problems in the Oldroyd-B viscoelastic dielectric liquid are solved using the finite volume method. Fully coupled nonlinear equations, including the Naiver–Stokes (N–S) equation, the Nernst–Plank equation of the ion conduction mechanism, and the constitutive equation of viscoelastic fluid, are thoroughly implemented. Our numerical model is fully verified with two benchmark cases, and simulations are performed under different conduction numbers C0 (0.01–103), Weissenberg numbers Wi (0.01–50), and viscosity ratios (0.3–0.9). Two limiting operating states of EHD conduction pumping, the Ohmic and the saturation regimes, are discussed in detail. Elastic instability is more likely to occur in the Ohmic regime, and the thickness of the heterocharge layer (called the dissociation layer) remains sensitive to C0 and the elasticity values. Current density and pressure generation show crucial degrees of dependence on the fluid elasticity and viscosity ratio.

Working Regime Criteria for Microscale Electrohydrodynamic Conduction Pumps

“…The working regime of the EHD conduction pumps can be divided into the ohmic regime and the saturation regime . The previous studies , commonly adopt the dimensionless numbers C 0 = d /2λ H = d /2 KE 0 τ c to distinguish the working regimes of macroscale EHD conduction pumps, where C 0 denotes the ratio of the system characteristic length d to the heterocharge layer thickness λ H . When C 0 ≪ 1, EHD conduction pumps work in the saturation regime, and vice versa.…”