Imaging critical fluctuations of pure fluids and binary mixtures

We use optical microscopy techniques to directly visualize the structures that emerge in binary mixtures and pure fluids near their respective critical points. We attempt to understand these structures by studying the image formation using both a phase contrast and a dark field filter to our microscope. We found that images of critical fluctuations for both liquid-liquid and liquid-gas critical systems have gray level intensity histograms with Gaussian shape. For all fluids investigated, the temperature-dependent standard deviation of the Gaussian histogram follows a power law with the same exponent. Since the image intensity fluctuations are determined by order parameter fluctuations, this direct imaging method allowed us to estimate the critical exponent of compressibility with very good accuracy.

Figure 1

Schematic representation of the optical microscopy system (not at scale). A white light source and a collimator produced a parallel beam of light after passing through a 0.8-mm pinhole with two 50-mm lenses, $L_1$ and $L_2$. This light scattered by fluctuations in the turbid media is collected by a high-quality, 50-mm photographic lens $L_3$ (Olympus, OM). An image of the fluid is formed on the CCD camera that is ≈1 m from $L_3$.

Figure 2

Enhanced bright field (a), phase contrast (b), and dark field (c) images taken at approximately 1 mK above the critical temperature. The images are single frames extracted from video recorded at 25 frames/s and the correlation length at this temperature was ≈1 μm. The height of the image is 1.5 mm.

Figure 3

Log-linear plot of intensity distributions (histograms) of de-noised BF, PC, and DF images. The slight deviation from a Gaussian distribution is most likely determined by optical noise. The horizontal axis corresponds to the 256 intensity levels of the 8-bit images. The standard deviations of the three PDFs are 19.8 for BF, 20.3 for PC, and 22.8 for DF.

Figure 4

Temporal evolution of the intensity of a line of pixels. The BF (a) and PC (b) images show a slow evolution superposed over a fast evolution. The DF (c) image only shows the fast evolution. The long temporal persistence of fluctuations in both BF and PC images is lost in the DF image, presumably because the fluctuations are in the low-$q$ range that is filtered out in DF.

Figure 5

(a) Intensity distributions (histograms) for the fluctuation images of isobutyric acid and water mixture at $T-T_c=1\mathrm{mK}.$ The curve is the best fit to a Gaussian distribution (continuous line). (b) Temperature dependence of the standard deviation Δ of the Gaussian distribution reveals a power law with an exponent of $\gamma /2=0.62.$

Figure 6

Optical microscopy imaging reveals large density fluctuations in ${\mathrm{SF}}_6$ fluid under reduced gravity very close to its critical point $(T-T_{cx}=10\mu \mathrm{K}).$ The height of the image is 1 mm.

Figure 7

(a) Intensity distributions (histograms) for the fluctuation images of ${\mathrm{SF}}_6$ at $T-T_{cx}=10\mu \mathrm{K}.$ The curve is the best fit to a Gaussian distribution (continuous line). (b) Temperature dependence of the standard deviation Δ of the Gaussian distribution reveals a power law with the exponent of $\gamma /2\approx 0.62.$