Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

Abstract

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection

“…We estimate as Ra s −10 4 the range of solutal Rayleigh numbers at which an acceleration in the dynamics associated to bouyancy is observable. Without gravity, c-NEFs exhibit the usual diffusive scaling with the standard Fickian diffusion coefficient for all wave numbers, as predicted by linearized fluctuating hydrodynamics [52] and observed in the GRADFLEX microgravity experiments [58][59][60].…”

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

“…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]. Recent experiments showed that finite-size effects also affect the dynamics of the fluctuations in the presence of gravity [17].…”

“…The power-law dependence led to the conclusion that the fluctuations are self-similar in a wide range of wave vectors, and to the argument that the fronts of diffusion are fractal (see, for example, the discussion in [26] and references therein). The analysis of experimental results obtained in microgravity confirmed the power-law behavior of the static structure factor of the fluctuations over a wide range of wave vectors, but it was not able to provide further insights about the fractal structure of the fronts of diffusion [14][15][16]. As pointed out by Alexander [27], a reliable experimental determination of the fractal dimension of rough surfaces is often prevented by the fact that the structures are not scale-invariant, but instead self-affine.…”

The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids

“…Linearized fluctuating hydrodynamics provides a satisfactory description of NEFs in binary liquid mixtures [10,11], that found experimental confirmation in several experiments, both on Earth [12][13][14][15][16][17][18][19] and in microgravity [20][21][22]. However, theory and experiments refer only to ideal conditions as for example stationary states, small gradients, and diluted systems.…”

“…The goal of the project is to deal with several challenging problems that emerged during the latest years, such as: i) the theoretical prediction of Casimir-like forces induced by non-equilibrium fluctuations [23,24,26,27]; ii) the understanding of the non-equilibrium fluctuations in multi-component mixtures, in relation to the transport coefficients [32,33]; iii) the understanding of the non-equilibrium fluctuations in polymer solutions, in relation to their behavior close to a glass transition [34,35]; iv) the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions [36,37,31], a problem closely related with the detection of Casimir forces; v) the investigation of the onset of fluctuations during transient diffusion [21].…”