This study numerically investigates the flow structures and bifurcation scenarios of three-dimensional (3D) laminar electroconvection (EC). An efficient parallel lattice Boltzmann model is undertaken to numerically solve the model problem. The results present three steady flow patterns and three pitchfork bifurcations. These three patterns each have one, two, or four charge void cells. The three critical values of electric Rayleigh number Tc are 242, 545, and 665, respectively. There are also two hysteresis loops whose nonlinear criteria Tf are 157 and 435, respectively. An unexpected flow pattern, which has two prism-shaped vortices demonstrates the importance of 3D analysis. Besides, we find that the 3D flow in the cavity is more stable by studying the correlation between the 3D and two-dimensional (2D) laminar EC. Using dynamic mode decomposition (DMD) for the flow structures, we reveal that the novel feature is the result of competition between the EC flow structure and the limitation of geometry.

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.

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