Eur. Phys. J. E (2019) 42: 25
https://doi.org/10.1140/epje/i2019-11786-x

Regular Article

Kinetics of growth of non-equilibrium fluctuations during thermodiffusion in a polymer solution

¹ Dipartimento di Fisica, Università degli Studi di Milano, I-20133, Milano, Italy
² 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

^* e-mail: marina.carpineti@unimi.it

Received: 19 October 2018
Accepted: 24 January 2019
Published online: 27 February 2019

Abstract

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 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.