A happel flow model—streaming current relationship for determining the zeta potential of cylindrical fibers

Abstract

A relationship between the zeta potential and the streaming current from mats of cylindrical fibers was derived using the model developed by Happel for flow perpendicular to cylinders. Silver-silver chloride electrodes were used to measure the streaming current produced by liquid permeation of 3-inch diameter Dacron fiber mats of uniform porosity. The calculated zeta potentials were independent of mat porosity in the range 0.60 to 0.85 for electrolyte concentrations of 1–4 × 10 −4 M KCl and 0.5–2 × 10 −4 M CaCl 2. The changes in zeta potential as a function of electrolyte concentration and valence were similar to those reported in the literature. Reproducibility between mats was not obtained when Nylon fibers were used; nonetheless, the zeta potentials calculated at the various porosities for a given mat were as constant as those for mats made with Dacron fibers. Reasons for this variability are discussed. The new streaming current relationship represents an improvement over the usual capillary-flow-model approach to the streaming current phenomenon in fiber mats. The influence of fiber orientation in the flow direction on the Biefer and Mason empirical capillary flow model relationship is discussed.