Calculation of the charge trajectories in a streaming dielectric liquid by means of a compound stream function

The exact calculation of a charge trajectory in a streaming dielectric liquid requires the solution of the coupled Maxwell and Navier-Stokes equations, which can be solved using lengthy iterative numerical techniques. A simple alternative method is proposed which gives an analytical solution for the particular case when the spacecharge density is small. The technique is applied to a cylindrical wire located centrally between two parallel plates with a transverse liquid flow. Electrical and hydrodynamic stream functions are derived separately and are combined to give the charge trajectories for several values of the electric and flow parameters. The results are considered for the application to high-voltage streaming generators.