Two-dimensional numerical simulations are carried out to examine the problem of transient electroconvection stability of dielectric liquids subjected to unipolar injection. The entire set of electrohydrodynamics equations associated with the electroconvective phenomena that occur in a layer of a dielectric liquid between two parallel electrodes subjected to a potential difference are solved numerically. We first validate the numerical simulation by comparing our linear stability electroconvection criteria with those obtained by other authors with a stability approach. In this paper, we restrict the study to the strong injection case, which corresponds to values of the non-dimensional injection parameter C greater than or equal to 10. The numerical solution of the electroconvective problem is then presented for rigid lateral boundary conditions. A detailed analysis of the scenario that occurs for different characteristic values of the stability parameter T is provided. The flow structure and its behaviour highlight the existence of different regimes, from laminar to chaotic. The development of charged plumes has been observed in particular. We compute the electrical Nusselt number for different values of the stability parameter and ion mobility. The electrical Nusselt number saturates with increasing T, a fact that it is in agreement with available experimental data. Finally, a spectral analysis is conducted for different aspect ratios of the computational domain. The spectral analysis gives an insight into the physical origin of the velocity and current oscillations. C 2012 American Institute of Physics. [http://dx

Granular materials exhibit several regimes of behavior: plastic, inertial, fluidized, and entrained flow, but not all materials can pass through all of these states. Our concern is with the criteria that determine the transition from one regime to another and with the boundaries to the various flow regimes that these criteria define. Experimentally we have focused on fine, cohesive powders, where the interparticle cohesive force dominates over gravitational force and where entrained air can cause moving powder to become fluidized. [S0031-9007(98)08339-2] PACS numbers: 45.70.Mg, 81.20.Ev, 83.70.Fn The past decade has witnessed a strong interest in granular materials by the physics community, but there is an important class of granular materials that has been largely ignored in spite of its commercial importance; these materials can be classified as fine cohesive powders. In these powders, with particle diameters less than about 30 3 10 26 m, interparticle cohesive effects are dominant, and ambient gas plays an important role in the behavior of the powder. Granular materials display four different flow regimes: plastic behavior, inertial flow, fluidized flow, and entrained flow. Particle size, particle density, cohesivity, and gas flow determine which of these types of behavior occur.(i) The plastic regime is characterized by a small spacing between neighboring particles. Velocities are small or zero and the stresses are independent of velocity for simple geometries. Plastic behavior determines the stability of heaps and slopes and there is an extensive literature on the subject because of its importance in civil engineering.(ii) In the inertial regime the stresses are due to the transport of momentum by interparticle collisions. The spacing between particles is much smaller than the particle size but greater than in the plastic regime. In everyday life granular materials such as sand, sugar, and ground coffee exhibit the transition from plastic solid to inertial flow when the limit of plastic stability is reached. We note that the interstitial fluid plays no part in inertial flow.(iii) Powders are capable of being fluidized by gas flow provided their cohesivity is not too great. In this regime the interparticle distance is of the same order of magnitude as the particle size. The interstitial fluid is the agent of transfer of momentum between particles, and fluid velocity determines the stresses in the material. The best known example of this situation is the fluidized bed, in which gas is forced through a bed of particles and the gas flow causes a pressure drop across the powder. When the pressure drop is sufficient to support the weight of the powder and to overcome the interparticle cohesive forces, the bed expands and becomes fluidized. The powder then takes on many of the properties of liquid, its upper surface remaining horizontal when the container is tilted.(iv) A fourth regime is that of entrainment, or suspension of the particles by the gas. In this case the distance between particles is much greater ...

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The interplay of charge diffusion, a hitherto neglected phenomenon, and Coulomb repulsion in the finite-amplitude electroconvection of a layer of insulating liquid subjected to weak unipolar injection is discussed. Analytical considerations and numerical simulations show that there exists a fundamental nondimensional parameter that relates the strength of the Coulomb repulsion to the diffusion coefficient. Unless this parameter is much larger than 1, diffusion must be included. A projection of the two-dimensional charge conservation equation into a one-dimensional space allows us to obtain good estimates of the charge-density distribution for any value of this parameter.

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.