EHD equations and transport coefficients in a strong electric field

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

“…Thereupon, the rates of motion of the volume elements of the charged components are as follows: (8) Alongside with Fick approximation (8), other models may be used for determination of the macroscopic rates of the fluid components. Thus, for determination of (the neutral component rate), with regard for the viscosity, under conditions (3) and (4), the Navier-Stokes equations are most often applied [10]: (9) Here, p and ν are the pressure and the kinematic viscosity of the neutral component of the fluid, respectively, being close to the corresponding characteristics of the fluid itself under conditions (3) and (4); t is the time; and is the free-fall acceleration.…”

“…Herein, for the theoretical simulation and calculations of the macroscopic characteristics in the jets under consideration, it is sufficient to use electrohydrodynamics approximation [8], in which a system of Maxwell equations for a macroscopic magnetic field splits off from the principal system of equations, and it is possible not to consider it at all. The same is true of the equation for a change in the impurity concentration being low in comparison with the carrier fluid molecule concentration.…”

“…2 Herein, both in Onsager's model [9] and in the here-used model of Frenkel' for ionization [14] or of Plumley for dissociation [3], the classical statistics and kinetics of Arrhenius-Boltzmann-Gibbs are applied [15]. In the Onsager theory [9], the transition to macroscopic magnitudes is implemented after obtaining of a solution of a Boltzmann-type equation [8,15] for the function of the distribution of an assembly of free charges formed under dissociation in the applied electric field rather than after the solution of relatively simple equation (1). For obtaining of a solution of differential equation (1), the electric field influence on the integration constant C is considered (as well as in [3,4]) insignificant.…”

“…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]. In the derivation of the expressions for the force densities it is possible to take into account the influence on these forces exerted by collisions between charged and neutral components, which is often used in the physics of nonideal partially ionized plasma [20].…”

“…The continuity equations for the charged components with regard for (8) and Fick's diffusion law are written as follows [13]: (10) For the derivation of these equations, for example, in [13], the differentiation rules for the field of a vector being time-variant in the moving volume of a continuum are used (the substantiation for the correct application of the approximation of a continuum with a not very weak degree of ionization (dissociation) for its charged components is described, for example, in [8]). In isothermal conditions, as well as under the condition of a low impurity concentration (4) and constant density ρ = ρ 0 , system of equations (10), together with equations (6) and (9), becomes mathematically closed.…”