Structure and dynamics of concentration fluctuations in a non-equilibrium dense colloidal suspension†
Linearised fluctuating hydrodynamics describes effectively the concentration non-equilibrium fluctuations (NEF) arising during a diffusion process driven by a small concentration gradient. However, fluctuations in the presence of large gradients are not yet fully understood. Here we study the giant concentration NEF arising when a dense aqueous colloidal suspension is allowed to diffuse into an overlying layer of pure water. We use differential dynamic microscopy to determine both the statics and the dynamics of the fluctuations for several values of the wave-vector q. At small q, NEF are quenched by buoyancy, which prevents their full development and sets an upper timescale to their temporal relaxation. At intermediate q, the mean squared amplitude of NEF is characterised by a power law exponent −4, and fluctuations relax diffusively with diffusion coefficient D1. At large q, the amplitude of NEF vanishes and equilibrium concentration fluctuations are recovered, enabling a straightforward determination of the osmotic compressibility of the suspension during diffusion. In this q-range we also find that the relaxation of the fluctuations occurs with a diffusion coefficient D2 significantly different from D1. Both diffusion coefficients exhibit time-dependence with D1 increasing monotonically (by about 15%) and D2 showing the opposite behaviour (about 17% decrease). At equilibrium, the two coefficients coincide as expected. While the decrease of D2 is compatible with a diffusive evolution of the concentration profile, the increase of D1 is still not fully understood and may require considering nonlinearities that are neglected in current theories for highly stressed colloids.