Charge convection in electrically stressed, low-conductivity, liquids

On the electric field distribution in plane and axisymmetrical partially charged stationary jets

“…Concerning the analogy with hydrodynamic jets, we should note that it is widely used in magnetic hydrodynamics, for example, in [12]; however, a (32)-type criterion of the pointness of the Ampere force causing magnetohydrodynamic jets has not been obtained. In the limiting case (32A) for velocities of undeveloped jets, according to [2], we find u ~ U 5/2 , which is in agreement with the results of Gibbins' experiments [19]. In the other limiting case (32B) and d ӷ r = ӷ r 0 for prebreakdown flows of viscous liquids for a Schlichting jet (Fig.…”

“…The volume charge being formed in the first approximation over δ influences the cumulative value Its density q in this approximation is determined from equations obtained from (19). In dimensional variables, (20) Similar to as in [16], it is possible to obtain additional conditions of dissociation (ionization) equilibrium in the case of moving fluids.…”

“…Then, system of equations (5) and (18) has the following form: (19) In (19), differentiation with respect to the dimensionless coordinate takes place (with the characteristic…”

“…Herein, in the analysis of the mathematical relations of the densities of the resultant external forces, according to the properties of the ions, the forces due to their viscosity may be regarded or disregarded. In Fick's approximation [15][16][17][18], the viscosity for the charged components, in contrast to the neutral components, at condition (3) is not regarded; however, their formation, for example, according to [2,19], should be taken into account. Written macroscopic equations (15) may be obtained not only by the continuum mechanics methods described, for example, in [10,13], but also by microscopic methods in determination of the respective moments from the Boltzmann kinetic equation for the microparticle distribution functions [8,15].…”

Distribution of electric fields in certain types of stationary weakly ionizing jets

“…Depending on the properties of ions, in analyzing mathematical relationships for the densities of the resulting external forces, the forces related to viscosity may be taken into account or neglected. In Fick's approximation [15][16][17][18], viscosity is not taken into account for charged components (unlike the neutral component) under condition (3); however, according to [2,19], it should be taken into account when those components are created. Macro-…”