A Mathematical Treatment of the Electric Conductivity and Capacity of Disperse Systems I. The Electric Conductivity of a Suspension of Homogeneous Spheroids

Abstract

Conductivity measurements may give values for (1) the specific conductivity, (2) the concentration or (3) eccentricity of form of the suspended particles of suspensions such as biological tissues, blood and cream. Mathematical theory. The following relation is derived: $\frac{(\frac{k}{{k}_{1}\ensuremath{-}1})}{(\frac{k}{{k}_{1}+x})}=\frac{\ensuremath{\rho}(\frac{{k}_{2}}{{k}_{1}\ensuremath{-}1})}{(\frac{{k}_{2}}{{k}_{1}+x})}$, where $k$, ${k}_{1}$ and ${k}_{2}$ are the specific conductivities of the suspension, the suspending medium and the suspended spheroids, $\ensuremath{\rho}$ is the volume concentration of the suspended spheroids, and $x$ is a function of the ratio $\frac{{k}_{2}}{{k}_{1}}$ and the ratio $\frac{a}{b}$ of the axis of symmetry of the spheroids to the other axis. For the case of spheres, $x=2$ and the formula reduces to that of Lorentz-Lorentz and Clausius-Mossotti. Curves are given showing the variation of $x$ with $\frac{{k}_{2}}{{k}_{1}}$ for various values of $\frac{a}{b}$. Comparison with experimental data of Stewart for the conductivity of the blood of a dog (${k}_{2}=0$, $\frac{a}{b}=\frac{1}{4.25}$, $x=1.05$) shows excellent agreement for concentration from 10 to 90 per cent. Also the observations of Oker-Blom for two suspensions of sand in salted gelatine, give in each case constant values of $x$ for various concentrations.