Phase separation under a weak concentration gradient

Abstract

Phase separation dynamics is studied in a density-matched liquid mixture in the presence of a weak linear concentration gradient. This novel situation enables nucleation and spinodal decomposition to be studied simultaneously. We observe at all quench depths (i) a central zone of nearly constant concentration width where interconnected domains grow linearly with time, surrounded by (ii) a zone of isolated droplets whose width increases with time, with the droplet growth compatible with a j law. These findings suggest generalized nucleation as the phase separation process.PACS numbers: 64.70.Ja, 05.70.Jk, In this Letter we report the phase separation dynamics of a binary liquid mixture under a weak concentration gradient when it is quenched from a temperature at which it is homogeneous to a temperature where it is a two-phase mixture. This is a general process that occurs in many areas of scientific and technological interest such as material science and heat and mass transfer [1][2][3]. The experiment has been carried out near a critical point where the phase separation behavior can easily be generalized by the use of scaling functions. We have chosen the density-matched mixture cyclohexane (C) -f deuterated cyclohexane (C*) + methanol (M) in order to maintain the concentration gradient against gravitydriven convection and to suppress the influence of gravity during phase separation [4]. The phase separation process is expected to proceed [1] through spinodal decomposition (SD) or through nucleation and growth. During SD spontaneous fluctuations grow and generally give rise to interconnected domains. For nucleation and growth an energy barrier exists that prevents the droplets with a radius smaller than a critical radius /?* from growing. Classical theories predict a sharp limiting boundary called the spinodal curve between these two separation processes [2]. However, for real systems, Binder [3] proposes a smooth transition zone (spinodal nucleation) between the two processes at early stages. At late stages, during coarsening, additional effects like hydrodynamic flows in percolating clusters are expected to enhance the growth of the domains for volume fractions exceeding the percolation limit [5]. Wong and Knobler [6] report this expected crossover in the growth exponent from t^ io t '-^ (here / is the time elapsed after the quench) as the volume fraction decreases below 10%.In the present study the sample is submitted to a weak concentration gradient over its height. This enables the phase separation structures to be observed simultaneously in the unstable and metastable regions for the same quench depth. Our purpose is to determine the concentration dependence of the phase separation structures and the growth laws. In a computer simulation study of spinodal decomposition under concentration gradients, Kolb et al. [7] do not see any specific eff'ect of the gradient.Although they do not take into account hydrodynamics in their analysis, we expect a similar insensitivity to the gradient.The experimental cell is ...

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