The time evolution of the problem of Electrohydrodynamic (EHD) convection in a liquid between two plates is analysed numerically. The equations are nondimensionalized using the ion drift velocity and the viscous time scales. Following the non-dimensionalisation of the respective model, two different techniques have been used to describe the charge evolution, namely the Finite-Element Flux-Corrected Transport Method and the Particle-In-Cell technique. The results obtained with the two schemes, apart from showing good agreement, have revealed the appearance of a two-roll structure not described in previous works. This is investigated in detail for both strong and weak injection.

Numerical simulations are carried out for the characterization of injection instabilities in electrohydrodynamics and, in particular, the development of electroconvection between two parallel plates. The particle-in-cell and the finite element-flux corrected transport methods are used for the simulation of the test case, as they have proved very powerful and accurate in the solution of complex transport problems. Results are presented for unipolar injection (both strong and weak injections) between two plane electrodes immersed in a dielectric liquid, and the good agreement obtained by the two methods demonstrates not only their theoretical validity but also their practical ability to deal with transport problems in the presence of steep gradients. Some differences appear mainly in the prediction of small oscillations of the velocity and consequently of the electric current. These differences are highlighted and an explanation of their source is given.

This work addresses the stability of a two-dimensional plane layer of a dielectric liquid enclosed in wall bounded cavities of different aspect ratios and subjected to unipolar injection of ions. Numerical simulations have been conducted to investigate the effect of lateral walls, especially in the development of the electroconvective instability. It is found that an unexpected change of the bifurcation nature occurs for certain cavity aspect ratios. We show that above the linear stability threshold for the rest state a supercritical bifurcation arises. This bifurcation takes place at a given value T(c1) of the parameter T (the electric Rayleigh number). Then, a second subcritical bifurcation occurs at a second threshold T(c2), featuring a typical hysteresis loop with an associated nonlinear criterion T(f), which is very characteristic of the Coulomb-driven convection. This behavior has been confirmed by different numerical codes based on different numerical methods. The physical mechanism which leads to this situation is analyzed and discussed. The evolution of the bifurcation diagrams with the aspect ratio of the cavity is also provided and analyzed.

In this work we discuss fundamental aspects of Electrohydrodynamic (EHD) conduction pumping of dielectric liquids. We build a mathematical model of conduction pumping that can be applied to all sizes, down to micro-sized pumps. In order to do this, we discuss the relevance of the Electrical Double Layer (EDL) that appears naturally on non-metallic substrates. In the process we identify a new dimensionless parameter, related to the value of the zeta potential of the substrate-liquid pair, that quantifies the influence of these EDLs on the performance of the pump. This parameter also describes the transition from EHD conduction pumping to electroosmosis. We also discuss in detail the two limiting working regimes in EHD conduction pumping: ohmic and saturation. We introduce a new dimensionless parameter, accounting for the electric field enhanced dissociation, that along with the conduction number, allows to identify in which regime the pump operates.

This paper deals with self similar thermal and electrohydrodynamic (EHD) plumes. The former arises from hot lines or points, whereas the latter arises when sharp metallic contours submerged in non conducting liquids support high electrostatic potential, resulting in charge injection. Although the motive force is buoyancy in one case and Coulomb force in the other, it is shown that the solution for EHD plumes is the same as for thermal plumes in the limit of large Prandtl numbers. We present the analysis of axisymmetric plumes for large values of Prandtl number, and this analysis is subsequently applied to EHD plumes. The validity of the approximations for EHD plumes is discussed in the light of experimental data.