Analytical model of the breakdown mechanism in a two-phase mixture

Abstract

A two-phase mixture (TPM) is a mixture of gas and macroparticles of high concentration. It is of interest in many different areas, such as in macroparticle-contaminated insulated systems, gas–liquid discharges, dusty plasmas and processing plasmas. Based on Townsend's theory, a physical model in analytical form for the breakdown mechanism in TPM is presented. In this model, two factors that influence the electron avalanche propagation are considered: macroparticles distorting the electric field and capture of the electrons. According to this breakdown mechanism and the dipole-enhanced model for calculating the maximum local field strength in TPM, the modified Paschen' law for TPM is presented to calculate the breakdown voltage. When the number of series of macroparticles (m) between two plate electrodes is very small, such as when m = 1, the breakdown voltage of the TPM is always lower than that of gas. With an increase in m or a decrease in the radius of macroparticles, the breakdown voltage tends to increase gradually for the same volume fraction of macroparticles. When m ≫ 1, the breakdown voltage of TPM may be lower or higher than that of gas, depending on the ratio of the number of saturation electrons captured by a macroparticle to the cell primary electrons generated at the cathode. Some other relevant factors, such as the volume fraction of macroparticles, the dielectric mismatch, the charging rate and the product of gas pressure and the gas length, are also discussed.