Electrical conductivity fluctuations in a binary liquid mixture near its critical point

Abstract

We have measured fluctuations in the dc electrical conductivity of isobutyric acid-water mixtures near the critical temperature $T_c$. Power spectra $S_V\mathrm{}\left(f\right)\mathrm{}$ were measured in the frequency range $0.04\le f\le 100$ Hz and temperature range $1\lesssim T-T_c\lesssim 1000$ mK. Near $T_c$ the spectra cannot be characterized by a simple power law. Rather $S_V\mathrm{}\left(f\right)\mathrm{}$ has a shoulder, which is theoretically expected to occur near a frequency $f_o=\frac{D}{{\xi }^2}$, where $D$ is the composition diffusivity and $\xi$ is the correlation length. The measurements are only in qualitative agreement with our calculations. Far from $T_c$, $S_V$ is proportional to $\frac{1}{f^{\psi }}$ with $\psi =0.95\mathrm{}\pm 0.1$. This $\frac{1}{f}$ noise is presumably not associated with critical thermodynamic fluctuations.