STREAMING CURRENT DEVELOPMENT IN A RECTANGULAR CHANNEL

In this paper, we first analyse the flow distribution in a metallic pi pe of rectangular cross section. In the case of a laminar flow, an ana lytical solution has been found for the velocity distribution in the p ipe cross section. Concerning the space charge density profile, in the case of weak space charge density in the whole section, the general s ystem of equations for a rectangular channel have first been solved. T hus, the space charge density profile can be expressed in terms of the channel dimensions, the diffusion constants and the total charge in t he diffuse layer, which is an indicator of the diffuse layer developme nt. Indeed, in the case of a diffuse layer development controlled by a weak wall current (as it is very often the case), the space charge de nsity profile is close to a quasi fully developed diffuse layer profil e for which the total charge in the diffuse layer increases slowly in order to reach a constant value. Then, the space charge density convec ted in a such rectangular pipe has been computed, in terms of the geom etry of the pipe and the state of development of the diffuse layer, th at is to say, in terms of the total space charge in a given cross sect ion. In the case of a turbulent flow, an analysis shows that in our ex perimental results, a large part of the diffuse layer is perturbed by the turbulence even for a relatively low Reynolds number. Therefore, t he space charge density convected in a given cross section is nearly p roportional to the mean space charge density in the whole section, or the total charge in this section. Thus, the mesurement of the space ch arge density convected in a given section indicates the mean space cha rge density in that section, and so the state of development. We prese nt new experimental streaming current results for a rectangular channe l. The experiments were conducted for Reynold's numbers varying from 2 000 to 5000 and channel lengths from the entry of the pipe varying fro m a few centimeters to one meter. These results give the evolution of the space charge density development for different Reynolds numbers an d for different lengths from the entry of pipe.