Thermal Fluctuations in a Layer of Liquid ${\mathrm{CS}}_2$ Subjected to Temperature Gradients with and without the Influence of Gravity

We report data for nonequilibrium density fluctuations in a layer of liquid ${\mathrm{CS}}_2$ subjected to temperature gradients on Earth and in a satellite. The structure factor $S(q)$ was measured using a calibrated shadowgraph. Upon removing gravity, $S(q)$ increased dramatically at small wave vector, until the fluctuations generated by thermal noise were limited only by the 3 mm sample thickness. The results agree with theory to within a few percent on Earth and are $\sim 14\%$ below theory in microgravity, demonstrating that the use of equilibrium Langevin forces is appropriate in this nonequilibrium situation.

Figure 1

Data (circles) and theory (line) for $T(q)S(q)$ in absolute (dimensionless) units for fluctuations in a 3.00 mm thick layer of ${\mathrm{CS}}_2$, on Earth, vs the dimensionless wave vector $qL$, with a stabilizing gradient of $17.9\mathrm{K}/\mathrm{cm}$.

Figure 2

Fits of theory to dynamic data taken in microgravity with a gradient of $101\mathrm{K}/\mathrm{cm}$. The data for the upper panel were taken at 2 Hz, while a frame rate of 0.5 Hz was used for the lower one. Points shown as crosses were excluded from the fits.

Figure 3

Data (circles) and theory (line) for $T(q)S(q)$ in absolute terms for a 3.00 mm thick layer of ${\mathrm{CS}}_2$, subjected to a $17.9\mathrm{K}/\mathrm{cm}$ gradient in microgravity, vs the dimensionless wave vector $qL$. Comparison with Fig. 1 shows the striking effect of removing gravity.

Figure 4

Log-log plots of experimental results for $S(q)$ vs $qL$, with applied gradients of 17.9 (squares), 34.5 (triangles), and 101 (circles) $\mathrm{K}/\mathrm{cm}$, in microgravity (upper curves) and on Earth. The lines are the theoretical predictions.