Structure of electrohydrodynamic shock waves in three-phase media containing two sorts of charged particles. Electrohydrodynamic flows from surface discontinuities

V. V. Gogosov - O. N. Grigor'eva - V. A. Naletova - N. L. Farber

Abstract
A study is made of the one-dimensional steady-state electrohydrodynamic flows of a medium consisting of three components: a neutral gas and two sorts of charged particles, each of which has its own coefficient of mobility. These can be either two sorts of ions, charged drops, or solid particles. The coefficients of mobility are assumed to be given functions, variable along the flow. An analysis is made of the structure of shock waves in such mixtures. The article considers flows when the current densities of the charged components coincide with the direction of the flow, when they are contrary to it, as well as the case when one of the currents flows along, and the other against the flow. From an analysis of the structure of the shock waves equations are written closing the system of relationships at the front of the shock wave. The form of the equations obtained essentially depends on the values of the mobility coefficients and on the signs of the current densities of the components. The distribution of the volumetric charge inside of the structure of the flow is found. It is shown that, when a surface charge is formed at the front of the shock wave, the distribution of the volumetric charge inside the structure of the wave can have either one or two maxima, approaching infinity when the width of the front of the shock wave approaches zero. It is shown that, with the motion of mixtures containing N sorts of ions or charged particles, each of which is characterized by its own mobility coefficient, the distribution of the density of the charge inside the structure of the charge, under determined conditions, can have N maxima. A study is made of the structure of the flows when, in some cross section of the flow, the current densities can undergo a discontinuity, may decrease to zero, or may appear. From an analysis of the structure of the shock wave, the lacking relationships at the front of the wave are written, when the corresponding discontinuity of the currents occurs inside the structure of the wave. The form of the relationships depends on the point inside the structure of the wave at which the discontinuity occurs, and on the value of the velocity and the mobility coefficient at this point. A study is made of the one-dimensional flow of a mixture of gas and charged particles with a discontinuity surface between the emitter and the receiver when, at the front of the discontinuity, the mobility coefficient undergoes a discontinuity and when, under the action of the forces of the electrical field, the current moves counter to the flow. The difference in the potentials between the emitter and the receiver, as well as the intensity and the position in the flow at which a surface charge is formed at the front of the discontinuity, are indicated. The distribution of the electrodynamic parameters along the flow is found as a function of the intensity of the discontinuity and the value of the applied potential difference.