No abstract

We used a form of schlieren interferometry to measure the mean-squared amplitude and temporal autocorrelation function of concentration fluctuations driven by the presence of a gradient during the free diffusion of a urea solution into water. By taking and processing sequences of images separated in time by less than the shortest correlation time of interest, we were able to simultaneously measure dynamics at a number of different wave vectors. The technique is conceptually similar to the shadowgraph method, which has been used to make similar measurements, but the schlieren method has the advantage that the transfer function is wave-vector independent rather than oscillatory.

We use dynamic near field scattering to measure the dynamics of concentration non equilibrium fluctuations at the steady-state of Soret separation. The analysis reveals that above a threshold wave vector q c , the dynamics is governed by diffusion while at smaller wave vectors, gravity dominates. From the measurements, we extract both the mass diffusion and the Soret coefficients. Comparing our results with literature data, we find good agreement confirming that the proposed experimental technique can be considered a sound approach for the study of thermodiffusion processes.

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, larger-scale fluctuations live shorter because of gravity, as theoretically and experimentally well-known. We explore here 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 in their dynamics. We recover diffusive behaviour 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. 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.PACS numbers: 05.70.Ln, 42.30.Va It is well established that fluctuations are long-ranged in systems out-of-equilibrium [1-3], even far from critical points where the long-range behaviour is observed also in equilibrium conditions [4]. In a binary fluid mixture subject to a stabilizing (vertical) temperature or concentration gradient, the coupling between the spontaneous velocity fluctuations and the macroscopic gradient results in giant concentration fluctuations in the quiescent state [3, 5]. Gravity quenches the intensity of fluctuations with length scales larger than a characteristic (horizontal) size 2π/q s related to the dimensionless solutal Rayleigh number Ra s of the system [5, 6]:where β s = ρ −1 (∂ρ/∂c) is the solutal expansion coefficient, ρ the fluid density, g the gravity acceleration, c the concentration (mass fraction) of the denser component of the fluid, ∇c the modulus of the concentration gradient, D the mass diffusion coefficient, ν the kinematic viscosity, and q s a characteristic solutal wave vector. Vertical boundaries suppress fluctuations larger than the confinement length L in the direction of the gradient [3, 7]. Gravity also accelerates the dynamics of the fluctuations for wavenumbers smaller than q s via buoyancy effects, leading to non-diffusive decay of large-scale fluctuations [8].The dynamics of concentration non-equilibrium fluctuations (c-NEFs) in the presence of a vertical concentration gradient in a binary liquid mixture can be characterized in terms of the Intermediate Scattering Function (ISF or, equivalently, normalized time correlation function) f (q, t), with f (q, 0) = 1. At first approximation the ISF can be modeled by a single exponential with decay time τ (q) depending on the analysed wave vector q.Available theories accounting for the simultaneous presence of diffusion (d) and gravity (g) [9, 10], but not for confinement, predict for a stable configuration (Ra s < 0):where the wave vector is expressed in its dimensionless formq = qL and τ s = L 2 /D is the typical so...

Diffusion is commonly believed to be a homogeneous process at the mesoscopic scale, being driven only by the random walk of fluid molecules. On the contrary, very large amplitude, long wavelength fluctuations always accompany diffusive processes. In the presence of gravity, fluctuations in a fluid containing a stabilizing gradient are affected by two different processes: diffusion, which relaxes them, and the buoyancy force, which quenches them. These phenomena affect both the overall amplitude of fluctuations and their time dependence. For the case of free diffusion, the time-correlation function of the concentration fluctuations is predicted to exhibit an exponential decay with correlation time depending on the wave vector q. For large wave vector fluctuations, diffusion dominates, and the correlation time is predicted to be 1 / (Dq2). For small wave vector fluctuations, gravitational forces have time to play a significant role, and the correlation time is predicted to be proportional to q2. The effects of gravity and diffusion are comparable for a critical wave vector q(c) determined by fluid properties and gravity. We have utilized a quantitative dynamic shadowgraph technique to obtain the temporal correlation function of a mixture of LUDOX(R) TMA and water undergoing free diffusion. This technique allows one to simultaneously measure correlation functions achieving good statistics for a number of different wave vectors in a single measurement. Wave vectors as small as 70 cm(-1) have been investigated, which is very difficult to achieve with ordinary dynamic light-scattering techniques. We present results on the transition from the diffusive decay of fluctuations to the regime in which gravity is dominant.