Carpineti Marina, Sabato Matteo, Croccolo Fabrizio, Vailati Alberto
Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy.
Laboratoire des Fluides Complexes et leurs Réservoirs, IPRA, UMR5150 E2S-Université de Pau et des Pays de l'Adour, CNRS, TOTAL, F-64600, Anglet, France.
Eur Phys J E Soft Matter. 2019 Feb 27;42(2):25. doi: 10.1140/epje/i2019-11786-x.
A thermal diffusion process occurring in a binary liquid mixture is accompanied by long ranged non-equilibrium concentration fluctuations. The amplitude of these fluctuations at large length scales can be orders of magnitude larger than that of equilibrium ones. So far non-equilibrium fluctuations have been mainly investigated under stationary or quasi-stationary conditions, a situation that allows to achieve a detailed statistical characterization of their static and dynamic properties. In this work we investigate the kinetics of growth of non-equilibrium concentration fluctuations during a transient thermodiffusion process, starting from a configuration where the concentration of the sample is uniform. The use of a large molecular weight polymer solution allows to attain a slow dynamics of growth of the macroscopic concentration profile. We focus on the development of fluctuations at small wave vectors, where their amplitude is strongly limited by the presence of gravity. We show that the growth rate of non-equilibrium fluctuations follows a power law [Formula: see text] as a function of time, without any typical time scale and independently of the wave vector. We formulate a phenomenological model that allows to relate the rate of growth of non-equilibrium fluctuations to the growth of the macroscopic concentration profile in the absence of arbitrary parameters.
二元液体混合物中发生的热扩散过程伴随着长程非平衡浓度涨落。在大长度尺度下，这些涨落的幅度可能比平衡涨落的幅度大几个数量级。到目前为止，非平衡涨落主要是在稳态或准稳态条件下进行研究的，这种情况能够实现对其静态和动态特性的详细统计表征。在这项工作中，我们从样品浓度均匀的构型开始，研究瞬态热扩散过程中非平衡浓度涨落的增长动力学。使用高分子量聚合物溶液可以实现宏观浓度分布缓慢的增长动力学。我们关注小波矢处涨落的发展，在那里它们的幅度受到重力存在的强烈限制。我们表明，非平衡涨落的增长率作为时间的函数遵循幂律[公式：见正文]，没有任何典型时间尺度且与波矢无关。我们建立了一个唯象模型，该模型能够在没有任意参数的情况下，将非平衡涨落的增长率与宏观浓度分布的增长联系起来。
