Slowing-down of non-equilibrium concentration fluctuations in confinement

¹ Laboratoire des Fluides Complexes et leurs Réservoirs, Université de Pau et des Pays de l'Adour 64600 Anglet, France
² Courant Institute of Mathematical Sciences, New York University - New York, NY 10012, USA
³ Departamento de Física Aplicada I, Universidad Complutense - 28040 Madrid, Spain

^(a) fabrizio.croccolo@univ-pau.fr

Received: 17 July 2015
Accepted: 21 September 2015

Abstract

Fluctuations in a fluid are strongly affected by the presence of a macroscopic gradient making them long-ranged and enhancing their amplitude. While small-scale fluctuations exhibit diffusive lifetimes, moderate-scale fluctuations live shorter because of gravity. In this letter we explore fluctuations of even larger size, comparable to the extent of the system in the direction of the gradient, and find experimental evidence of a dramatic slowing-down of their dynamics. We recover diffusive behavior for these strongly confined fluctuations, but with a diffusion coefficient that depends on the solutal Rayleigh number. Results from dynamic shadowgraph experiments are complemented by theoretical calculations and numerical simulations based on fluctuating hydrodynamics, and excellent agreement is found. Hence, the study of the dynamics of non-equilibrium fluctuations allows to probe and measure the competition of physical processes such as diffusion, buoyancy and confinement, i.e. the ingredients included in the Rayleigh number, which is the control parameter of our system.