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

Cerbino R, Sun Y, Donev A, Vailati A - Sci Rep (2015)

Bottom Line: 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.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.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.

View Article: PubMed Central - PubMed

Affiliation: Università degli Studi di Milano, Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Milan, I-20133, Italy.

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.

No MeSH data available.


Related in: MedlinePlus

Dynamic scaling of the spectra of the non-equilibrium fluctuations during the approach to steady state.The inset shows the unscaled structure factors. Times span the range  and are distributed geometrically with a multiplier of 1.21 (for a total of 13 curves).
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f6: Dynamic scaling of the spectra of the non-equilibrium fluctuations during the approach to steady state.The inset shows the unscaled structure factors. Times span the range and are distributed geometrically with a multiplier of 1.21 (for a total of 13 curves).

Mentions: Qualitatively, this behavior is similar to that reported for spinodal decomposition27282930 and other phenomena, such as colloidal aggregation37. The growth dynamics of the structure factor of the concentration perturbations associated to these phenomena is such that the structure factor exhibits dynamic scaling , where F(k, km) is a time independent master curve and α a power law exponent, which in the case of spinodal decomposition corresponds to the dimensionality of the space. This suggests that our results are compatible with a scaling law akin to that of spinodal decomposition with a power law exponent α = 1/β ≈ 8. By scaling the structure factors of simulations in the time range 200s ≤ t ≤ 2000s using the relation we get that the curves nicely collapse onto a single, time-independent, master curve F(k/km) (Fig. 6).


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

Cerbino R, Sun Y, Donev A, Vailati A - Sci Rep (2015)

Dynamic scaling of the spectra of the non-equilibrium fluctuations during the approach to steady state.The inset shows the unscaled structure factors. Times span the range  and are distributed geometrically with a multiplier of 1.21 (for a total of 13 curves).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4588591&req=5

f6: Dynamic scaling of the spectra of the non-equilibrium fluctuations during the approach to steady state.The inset shows the unscaled structure factors. Times span the range and are distributed geometrically with a multiplier of 1.21 (for a total of 13 curves).
Mentions: Qualitatively, this behavior is similar to that reported for spinodal decomposition27282930 and other phenomena, such as colloidal aggregation37. The growth dynamics of the structure factor of the concentration perturbations associated to these phenomena is such that the structure factor exhibits dynamic scaling , where F(k, km) is a time independent master curve and α a power law exponent, which in the case of spinodal decomposition corresponds to the dimensionality of the space. This suggests that our results are compatible with a scaling law akin to that of spinodal decomposition with a power law exponent α = 1/β ≈ 8. By scaling the structure factors of simulations in the time range 200s ≤ t ≤ 2000s using the relation we get that the curves nicely collapse onto a single, time-independent, master curve F(k/km) (Fig. 6).

Bottom Line: 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.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.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.

View Article: PubMed Central - PubMed

Affiliation: Università degli Studi di Milano, Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Milan, I-20133, Italy.

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.

No MeSH data available.


Related in: MedlinePlus