Streaming currents in turbulent flows and metal capillaries. I. Theory (1). Distribution of charge in the liquid

Abstract

Since the idea occurred to Professor Dr. W. J. D. Van Dijck to construct a h.t.-generator in which the high tension is built up by the streaming current, a detailed theoretical and experimental investigation of this phenomenon has been undertaken.

After a general introduction the distribution of charge in an electrolytic solution in a tube is calculated following the procedure of Debije and Hückel.

An exchange of charge between wall and liquid appears to influence this charge distribution not perceptibly if the wall current density J causes a voltage across the diffuse layer thickness 1/κ which is small with respect to the ζ-potential, i.e. J σκζ where σ is the conductivity of the liquid. In relevant cases the influence of this exchange on the ζ-potential can be neglected.

It is shown that turbulence does not influence the charge distribution if the time required to travel with the r.m.s. value of turbulent cross velocity (roughly equal to friction velocity υ*) across the diffuse layer thickness 1/κ is large compared with the liquid's relaxation time τ, i.e. τυ*κ 1. Charge distribution in the turbulent core of the flow becomes homogeneous if τυ*κ 1.