Mathematical Modelling of Electrophysical Water Treatment

The problem of mathematical modeling the processes of water treatment from charged particles by electric field is considered. The problem is relevant due to the mass use of cleaning technologies in industry, medicine or the national economy. At the present stage, a significant improvement of purification system quality and the introduction of the technologies for the regeneration of their filtration components are required. Mathematical simulation using computer and supercomputer calculations helps to accelerate the development of new devices and cleaning technologies. On the basis of the chosen purification technology, it is important to create a numerical simulation apparatus with a controlled high accuracy of the calculations. For this purpose, we use a quasi-hydrodynamic (QHD) model of a viscous incompressible fluid flow, a system of convection-diffusion equations taking into account the action of the Lorentz force to describe the propagation of harmful impurities in aqueous medium, and an equation for the electric field potential [1, 2]. The numerical algorithm is based on the finite volume method. It is applied in the case of irregular unstructured meshes. This is important for problems of real two-dimensional (2D) and three-dimensional (3D) geometry. Time integration is performed according to an explicit scheme, which simplifies the procedure for parallelizing the algorithm. The proposed approach was tested on the examples of 2D and 3D geometry with various locations of the electrodes and various values of the potentials. The obtained results of the concentration of the ionic impurities show the possibility of this method to purify water from 10 to 40 percent. A design of a water purifier based on electrophysical purification technology can be developed on the base of this study.

The pre -breakdown characteristics of weakly ionized media in the high non-uniform electric field using calculations with refined grid cells

The theoretical model of a pre-breakdown ions formation in a liquid dielectric and their flows, caused by high non-uniform electric field is represented. The 3D system of the macroscopic pre-breakdown electrohydrodynamic equations is written. Influence of the electric field on the molecule dissociation rate is taken into account. The system includes the Poison equation for electric field potential, the equation of ions formation and the Navier-Stokes equations with electric force. In addition, results of modelling using refined mesh are presented.

Integral Equations for Problems on Wave Propagation in Near-Earth Plasma

We consider the solutions of two integrodifferential equations in this work. These equations describe the ultra-low frequency waves in the dipol-like model of the magnetosphere in the gyrokinetic framework. The first one is reduced to the homogeneous, second kind Fredholm equation. This equation describes the structure of the parallel component of the magnetic field of drift-compression waves along the Earth’s magnetic field. The second equation is reduced to the inhomogeneous, second kind Fredholm equation. This equation describes the field-aligned structure of the parallel electric field potential of Alfvén waves. Both integral equations are solved numerically.

Electric field assisted motion of a mercury droplet

Field-assisted self-assembly, motion, and manipulation of droplets have gained much attention in the past decades. We exhibit an electric field manipulation of the motion of a liquid metal (mercury) droplet submerged in a conductive liquid medium (a solution of sulfuric acid). A mercury droplet moves toward the cathode and its path selection is always given by the steepest descent of the local electric field potential. Utilizing this unique behavior, we present several examples of droplet motions, including maze solving, electro-levitation, and motion on a diverted path between parallel electrodes by controlling the conductivity of the medium. We also present an experimental demonstration of Fermat's principle in a non-optical system, namely a mercury droplet moving along a refracted path between electrodes in a domain having two different conductivities.

Annual variation of atmospheric electricity diurnal variation maximum in Kamchatka

Atmospheric electric field diurnal variation measured in fair weather conditions over the ocean surface has a typical form which is called a unitary variation. It is associated with the global time and occurs simultaneously all over the planet. However, the diurnal variation, measured over the ground, depends on many local factors. The diurnal variation maximum of the electric field potential gradient, measured at Paratunka observatory, has the maximum close in time to the unitary variation maximum. In the paper we show that this maximum is determined by local conditions and is associated in time with the sunrise. The diurnal variation maximum of the electric field potential gradient, measured at Paratunka observatory in fair weather conditions, has annual variation coinciding with the annual variation of local sunrise.

Earth electric field negative anomalies as earthquake precursors

In fair weather conditions, electric field potential gradient in the near-ground air takes positive values. Negative anomalies occur under the influence of different ionizing processes such as galactic cosmic ray flux and radioactive gas emanation from the ground. In the conditions of calm geomagnetic state and fair weather, anomalies can be used for earthquake forecast. In the paper, the efficiency of earthquake forecast based on negative anomalies is under the study. It was obtained that the efficiency of such a forecast during any weather conditions is 10%.

Negative Anomalies of the Earth’s Electric Field as Earthquake Precursors

Anomalies of the electric field potential gradient have been observed in the near-ground air before earthquakes in different regions of the world. Such anomalies are likely caused by radon air ionization. In this study, the impact of this precursor was estimated according to continuous observations of the electric field in Kamchatka in 1997–2002.

On classical solutions to the first mixed problem for the Vlasov-Poisson system in an infinite cylinder

The first mixed problem for the Vlasov-Poisson system in an infinite cylinder is considered. This problem describes the kinetics of charged particles in a high-temperature two-component plasma under an external magnetic field. For an arbitrary electric field potential and a sufficiently strong external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the cylinder. It is proved that the Vlasov-Poisson system with ion and electron distribution density functions supported at some distance from the cylinder boundary has a unique classical solution.