A Mathematical Treatment of the Electric Conductivity and Capacity of Disperse Systems ii. The Capacity of a Suspension of Conducting Spheroids Surrounded by a Non-Conducting Membrane for a Current of Low Frequency

Abstract

Mathematical theory.—The following formula for the specific capacity $C$ of the suspension, i.e., the parallel capacity of a one centimeter cube of the suspension, is derived in terms of the capacity $C_0$ of one ${\mathrm{cm}}^2$ of the membrane surrounding the spheroids, the major axis $2q$ of a spheroid, the specific resistances $r$ and $r_1$ of suspension and suspending phase, and a constant $a$ which depends only on the axis ratio $\frac{a}{b}$ of the spheroid: $C=C_{0}aq(1-\frac{r_1}{r})$. The values of $a$ are given in a table. One application of the formula is the determination of the thickness of interphasial membranes (biological, adsorptive, chemical). The formula can also be used for a suspension of polarizable homogeneous spheroids when the polarization resistance is small compared to the impedance of the polarization capacity.