Exact solution of fluid momentum equations in the atmospheric plasma-jets

Summary form only given. An exact solution of the fluid momentum equation for the incompressible steady-state flow is obtained for the gas streams inside the jet-tube and outside the tube of open air-space. In the solutions the fluid channels of gases as well as the plasmas are described with respect to the reaching distance and the expansion of gases and plasmas with the effects of particle-diffusion and gravity. In the fluid dynamics, three pressure forces are considered. The pressure force of shear stress by the flow viscosity is balanced with the pressure force of gas stream to be ejected into the air space. The other force of pressure due to the radial expansion of fluid channel reduces the velocity of fluid to be zero so that we have the reaching distance of fluid after ejecting from the nozzle. The maximum distance of gas flow with the critical Reynolds number Rnc = 2000 is calculated to be less than a hundred of nozzle-diameter for Ar, Ne, and He, respectively. Since the radial expansion of plasma is ten-times larger than that of neutral gases, the length of plasma is shorter as a few tens of nozzle-diameter. In the experiments the plasma length is verified and it increases with the increase of gas flow rate until Rn ~ Rnc and then it shrinks as the flow becomes turbulent. The variations of plasma are observed inside the jet tube and outside the tube according to the operation voltage, the flow rate. The influence of gravitation is presented on the direction of plasma spouting according to the gases, Ar, Ne, and He, respectively.