Development of charge in low-conductivity liquids flowing past surfaces: Engineering predictions from the theory developed for tube flow

Abstract A theory, developed earlier by the authors, which describes charge generation in the turbulent flow of low-conductivity (hydrocarbon) liquids in tubes, is recapitulated. The theory is extended, by use of well known correlations of turbulent mass transfer, into a form which may be easily tested experimentally, and from which engineering predictions may be made. The charging current is shown to be a universal function of a dimensionless group—four times the square of the tube radius divided by the product of the kinematic viscosity of the hydrocarbon, its relaxation time and the seven-fourths power of the Reynolds number—which turns out to be related to the ratio of the laminar subzone thickness to the diffuse double-layer thickness in the liquid. For small enough values of this group the current can be predicted by the theory; for larger values of the group the theory is unable to predict the current. The highest value of the dimensionless group where the theory can predict the current must be obtained experimentally.