Equilibrium and non-equilibrium concentration fluctuations in a critical binary mixture

Abstract

When a macroscopic concentration gradient is present across a binary mixture, long-ranged non-equilibrium concentration fluctuations (NCF) appear as a consequence of the coupling between the gradient and spontaneous equilibrium velocity fluctuations. Long-ranged equilibrium concentration fluctuations (ECF) may be also observed when the mixture is close to a critical point. Here we study the interplay between NCF and critical ECF in a near critical mixture aniline/cyclohexane in the presence of a vertical concentration gradient. To this aim, we exploit a commercial optical microscope and a simple, custom-made, temperature-controlled cell to obtain simultaneous static and dynamic scattering information on the fluctuations. We first characterise the critical ECF at fixed temperature $T$ above the upper critical solution temperature $T_c$, in the wide temperature range $T-T_c\in [0.1,30]$ ${}^o$C. In this range, we observe the expected critical scaling behaviour for both the scattering intensity and the mass diffusion coefficient and we determine the critical exponents $\gamma$, $\nu$ and $\eta$, which are found in agreement with the 3D Ising values. We then study the system in the two-phase region ($T<T_c$). In particular, we characterise the interplay between ECF and NCF when the mixture, initially at a temperature $T_i$, is rapidly brought to a temperature $T_f>T_i$. During the transient, a vertical diffusive mass flux is present that causes the onset of NCF, whose amplitude vanishes with time, as the flux goes to zero. We also study the time dependence of the equilibrium scattering intensity $I_{eq}$, of the crossover wave-vector $q_{co}$ and of the diffusion coefficient $D$ during diffusion and find that all these quantities exhibit an exponential relaxation enslaved to the diffusive kinetics.

11 pages, 4 figures

References in corpus (5)

• Critical Phenomena and Renormalization-Group Theory
• Differential Dynamic Microscopy: Probing wave vector dependent dynamics with a microscope
• Slowing-down of non-equilibrium concentration fluctuations in confinement
• Capillary to bulk crossover of nonequilibrium fluctuations in the free diffusion of a near--critical binary liquid mixture
• Equilibrium and nonequilibrium fluctuations at the interface between two fluid phases

Cited by in corpus (5)

• Giant fluctuations and structural effects in a flocking epithelium
• Correcting artifacts from finite image size in Differential Dynamic Microscopy
• Deformation profiles and microscopic dynamics of complex fluids during oscillatory shear experiments
• Uncertainty quantification and estimation in differential dynamic microscopy
• Motile bacteria in a critical fluid mixture