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On the electrolyte convection around a hydrogen bubble evolving at a microelectrode under the influence of a magnetic field
Water electrolysis was carried out in a 1 M H2SO4 solution under different potentiostatic conditions in the presence of a magnetic field oriented normal to the horizontal microelectrode (100 μm in diameter). The imposed magnetohydrodynamic (MHD) electrolyte flow around the evolving hydrogen bubble was studied to clarify the effect on the detachment of the bubble from the electrode and the mass transfer toward the electrode. Different particle imaging and tracking techniques were applied to measure the three-dimensional flow in the bulk of the cell as well as in close vicinity of the evolving bubble. The periodic bubble growth cycle was analyzed by measurements of the current oscillations and microscopic high-speed imaging. In addition, a numerical study of the flow was conducted to support the experimental results. The results demonstrate that the MHD flow imposes only a small stabilizing force on the bubble. However, the observed secondary flow enhances the mass transfer toward the electrode and may reduce the local supersaturation of dissolved hydrogen.
On weak solutions to the stationary MHD-equations coupled to heat transfer with nonlocal radiation boundary conditions
We study the coupling of the stationary system of magnetohydrodynamics to the heat equation. Coupling occurs on the one hand from temperature-dependent coefficients and from a temperature-dependent force term in the Navier-Stokes equations. On the other hand, the heat sources are given by the dissipation of current in the electrical conductors, and of viscous stresses in the fluid. We consider a domain occupied by several different materials, and have to take into account interface conditions for the electromagnetic fields. Since we additionally want to treat high-temperatures applications, we also take into account the effect of heat radiation, which results in nonlocal boundary conditions for the heat flux. We prove the existence of weak solutions for the coupled system, under the assumption that the imposed velocity at the boundary of the fluid remains sufficiently small. We prove a uniqueness result in the case of constant coefficients and small data. Finally, we discuss the regularity issue in a simplified setting.
Kinetic slow mode-type solitons
One-dimensional hybrid code simulations are presented, carried out in order both to study solitary waves of the slow mode branch in an isotropic, collisionless, medium-β plasma (βi=0.25) and to test the fluid based soliton interpretation of Cluster observed strong magnetic depressions (Stasiewicz et al., 200; Stasiewicz, 2004) against kinetic theory. In the simulations, a variety of strongly oblique, large amplitude, solitons are seen, including solitons with Alfvenic polarization, similar to those predicted by the Hall-MHD theory, and robust, almost non-propagating, solitary structures of slow magnetosonic type with strong magnetic field depressions and perpendicular ion heating, which have no counterpart in fluid theory. The results support the soliton-based interpretation of the Cluster observations, but reveal substantial deficiencies of Hall-MHD theory in describing slow mode-type solitons in a plasma of moderate beta.
Magnetohydrodynamic flow with hysteresis
We consider a model system describing the 2D flow of a conducting fluid surrounded by a ferromagnetic solid under the influence of the hysteretic response of the surrounding medium. We assume that this influence can be represented by the Preisach hysteresis operator. Existence and uniqueness of solutions for the resulting system of PDEs with hysteresis nonlinearities is established in the convexity domain of the Preisach operator.