Universality in early-stage growth of phase-separating domains near the critical point

Abstract

We present both the experimental and computational methods and results of phase-separating experiments performed with sulfur hexafluoride (SF6) close to its critical density. These experiments were performed in microgravity to suppress buoyancy and convection-driven effects. Phase separation under reduced gravity is analyzed for both 0.3 mK and 3.6 mK temperature quenches in order to derive the early-stage growth law. We found a 1/3 growth law for early stages of phase separation for a volume fraction of minority domains of 50%. Our findings support the hypothesis of a crossover between Brownian motion and hydrodynamic effects in the early stages of phase separation. The temperature inside the bulk of the pure fluid was estimated using a proposed histogram method. Our histogram method allowed temperature estimation below thermistors' sensitivity and detected small temperature variations inside the bulk of the pure fluid.

Dynamic structure factor of density fluctuations from direct imaging very near (both above and below) the critical point of SF6

“…based on the dynamic structure factor algorithm place the critical point somewhere between 15 and 42 μK above the lower temperature plateau. This value is in agreement with our previous estimation obtained with a different method [34] for the same set of experiments. Based on the histogram method [34], T c was found between 36 and 67 μK (with the average at 47 μK) above the lower temperature plateau.…”

“…Phase separation occurs during this 300 μK thermal quench (a). Based on the histogram method, the estimated position of critical temperature is 47 μK above the lower plateau (a) [34]. Our current estimation based on the thermal diffusivity coefficient is between 15 and 42 μK above the lower plateau (b).…”

“…On the other hand, for qξ − 1 (critical regime), the correlation time should scale as τ −1 ∝ Aq 3.068 , where A is a constant [38]. For the temperature quench of T = T − T c ≈ 300 μK, the estimated average correlation length is ξ − ≈ 1.95 × 10 −4 cm [34]. Since in our experiment 17 cm −1 < q < 2285 cm −1 , the product qξ − is in the range 3.3 × 10 −2 < qξ − < 0.4, which is definitely not qξ − 1 as it is required for the critical regime.…”

“…In order to uncover possible universal growth laws for the interconnected clusters during the very early stages of phase separation, we plotted in Fig. 6 the normalized crossover wave vector k * = q c ξ − versus the normalized time t * = t/t ξ [34]. The correlation length is computed according to [18,19,42] …”

“…Based on a different image processing technique (histogram method), we previously estimated for the same set of images that T c is about 47 μK above the lower temperature plateau shown in Fig. 1 [34]. Based on data in Fig.…”