Nonequilibrium fluctuations in time-dependent diffusion processes

Abstract

A fluctuating hydrodynamics approach is presented for the calculation of the structure factor for timedependent nonequilibrium diffusive processes in binary liquid mixtures. The hydrodynamic equations are linearized around the time-dependent macroscopic state given by the usual phenomenological diffusion equation. The cases of free diffusion, thermal diffusion, and barodiffusion are considered in detail. The results are used to describe the low-angle scattered intensity distributions from the time-dependent concentration profiles during the approach to steady state. The theoretical predictions are found to be in agreement with experimental data from thermal diffusion and free diffusion experiments. It is shown that in general the presence of nonequilibrium concentration fluctuations yields a substantial increase in the static structure factor over the equilibrium value, at least for the cases of free diffusion and thermal diffusion. As in the case of nonequilibrium fluctuations at steady state, the static structure factor displays a fast k Ϫ4 divergence at larger wave vectors k, and saturation to a constant value for k smaller than a critical wave vector k RO. It is also shown that the static structure factor from a sedimenting mixture is actually temporarily lowered below the equilibrium value for k smaller than k RO. As the steady state is approached, the structure factor loses any k dependence and it attains the equilibrium value. ͓S1063-651X͑98͒14910-3͔

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

“…Further theoretical [7] and experimental [8] investigation showed that on Earth, the scale invariance of the fluctuations is broken by the force of gravity, which stabilizes long-wavelength fluctuations and thus prevents their divergence. The same gravitational stabilization of the fluctuations was shown to be present during timedependent isothermal diffusion processes [9][10][11][12], proving that nonequilibrium fluctuations are a general feature of diffusive processes, irrespective of the origin of the concentration gradient driving them. An additional mechanism breaking the scale invariance of the fluctuations at small wave vectors was predicted theoretically to be the finite size of the sample [13], a finding confirmed experimentally during the GRADFLEX experiment by the European Space Agency [14][15][16].…”

Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

“…Under non-equilibrium conditions, the gradient of one variable couples the spontaneous fluctuations of the velocity of the fluid molecules with the fluctuations of the relevant variable, thus providing a huge enhancement of the intensity of the fluctuations, increasing with their size. This phenomenon has been widely investigated in the latest decades and a sound theoretical description (see for example [59][60][61][62][63]) as well as many experimental studies [46,47,49,[64][65][66][67] can be found in the literature. Here, we would like to recall the essential equations that describe the intensity of the light scattered by concentration fluctuations generated in a fluid out of equilibrium and in the presence of the terrestrial gravitational field.…”

Evidence for the Existence of an Effective Interfacial Tension between Miscible Fluids: Isobutyric Acid−Water and 1-Butanol−Water in a Spinning-Drop Tensiometer

“…60,61 Careful experiments have demonstrated that diffusion, especially for a system near a critical solution point, can be affected by gravitational acceleration. [62][63][64][65][66][67] We are currently studying both the IBA-water and 1-butanolwater systems by laser line deflection 52 to determine how the diffusion under 1 g compares to what is seen in the tensiometer.…”