STREAMING CURRENTS IN TURBULENT FLOWS AND METAL CAPILLARIES II. THEORY (2). CHARGE TRANSPORTED BY THE FLOW OF LIQUID by A. A. BOUMANS Stichting veer fundamenteel onderzoek der materie, Utrecht
Synopsis
The mean charge density/] which appears if a liquid flows through a tube is calculated. The following dimensionless numbers are used. 1 °. KR~, i.e. the ratio of the tube's hydraulic radius R~ and the diffuse layer thickness 1/K.
2 °. 12vK/v,, i.e. the ratio of the laminar sublayer thickness 12v/v, and the diffuse layer thickness l/K, where v is the kinematic viscosity of the liquid and v, the friction velocity as defined in 1.5. 3 °. ~,K, i.e. the ratio of the distance traveled with velocity v, in the relaxation time r and the diffuse layer thickness 1/K. 4 °. /~/p0, i.e. the ratio of the mean charge density/~ in the liquid and the mean charge density p0 = --2¢~/nR~ which appears in a laminar flow if KRh >~ 1, where ¢ is the dielectric constant of the liquid and ~ the wall potential. 5 °. Reynolds number Re = 2~Rh/v and friction number Jl =--(4Rh/s~2)dp/dl
where s is the specific density of the liquid, ~ the mean velocity across the tube cross section and dp/dl the pressure gradient along the tube axis. Hydrodynamics teaches that 2 is a function of Re, which is drawn in fig. 1234567.
The following relations are deduced for KRh>~ 1. In a laminar flow ~/po = 1. In a turbulent flow, as long as 12vK/v, >~ 1, ~/po = Re 2/64, but if 12vK/v, ~ 1, ~/po=KRh/4.