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.

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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

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