Fractal fronts of diffusion in microgravity

Abstract

Spatial scale invariance represents a remarkable feature of natural phenomena. A ubiquitous example is represented by miscible liquid phases undergoing diffusion. Theory and simulations predict that in the absence of gravity diffusion is characterized by long-ranged algebraic correlations. Experimental evidence of scale invariance generated by diffusion has been limited, because on Earth the development of long-range correlations is suppressed by gravity. Here we report experimental results obtained in microgravity during the flight of the FOTON M3 satellite. We find that during a diffusion process a dilute polymer solution exhibits scale-invariant concentration fluctuations with sizes ranging up to millimetres, and relaxation times as large as 1,000 s. The scale invariance is limited only by the finite size of the sample, in agreement with recent theoretical predictions. The presence of such fluctuations could possibly impact the growth of materials in microgravity.

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.…”

“…Such a confinement is necessarily present in the case of concentration gradients generated by the Soret effect. In this case, both theoretical models [13] and experiments performed under microgravity conditions [14,16] have shown that the quenching of the fluctuations occurs at wave vectors smaller than Q ≈ π/L. Recently, the effect of confinement has been shown to affect the dynamics of the fluctuations on Earth, too [17].…”

“…In the presence of gravity, the cutoff is of the order of a fraction of a millimeter [8]; microgravity experiments [14,16] extended this cutoff by roughly a factor 30. 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).…”

Gravity effects on Soret-induced non-equilibrium fluctuations in ternary mixtures

“…One other notable example of FHD success is the prediction of the influence of gravity on the fluctuations [23], an effect initially considered to be not accessible to experiments, and later confirmed by novel optical techniques [24]. Similarly, detailed FHD predictions about finite size effects on non-equilibrium fluctuations [25][26][27] have been later experimentally verified, by Gradflex [28] in microgravity and by ground-based measurements [27,29] in the presence of buoyancy force. Hence, as a preliminary step in developing the theory of thermodynamic fluctuations in NE ternary mixtures, it was necessary to re-derive [30] the equilibrium results for ternary mixtures on the basis of FHD, for which the simplifications of Bardow [4] were adopted.…”