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.

Figure 1. Development of nonequilibrium fluctuations during diffusion processes occurring on Earth and in space.

False-colour shadowgraph images of nonequilibrium fluctuations in microgravity (a–d) and on Earth (e–h) in a 1.00-mm-thick sample of polystyrene in toluene. Images were taken 0, 400, 800, and 1,600 s (left to right) after the imposition of a 17.40 K temperature difference. The side of each image corresponds to 5 mm. Colours map the deviation of the intensity of shadowgraph images with respect to the time-averaged intensity.

Figure 2. Mean-squared amplitude of nonequilibrium concentration fluctuations in microgravity.

(a) Experimental results obtained in microgravity in the presence of temperature differences of 4.35 K (black circles), 8.70 K (blue circles) and 17.40 K (red circles). (b) Comparison of the experimental results with the theoretical predictions. The solid line represents the theoretical prediction for microgravity. The dashed lines are the theoretical predictions for the power spectra of the nonequilibrium concentration fluctuations on the Earth. In microgravity, the data scale onto a single universal curve, whereas on the Earth no such scaling occurs.

Figure 3. Relaxation time of non-equilibrium concentration fluctuations as a function of wave vector.

The black data correspond to a temperature difference of 4.35 K, the blue data to 8.70 K and the red ones to 17.40 K. The solid line represents the diffusive time τ_c(q)=1/(Dq²) as estimated from literature data for the diffusion coefficient.