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

Abstract

In a recent letter [C. Giraudet et al., Europhys. Lett. 111, 60013 (2015)] we reported preliminary data showing evidence of a slowing down of non-equilibrium fluctuations of the concentration in thermodiffusion experiments on a binary mixture of miscible fluids. The reason for this slowing down was attributed to the effect of confinement. Such tentative explanation is here experimentally corroborated by new measurements and theoretically substantiated by studying analytically and numerically the relevant fluctuating hydrodynamics equations. In the new experiments presented here, the magnitude of the temperature gradient is changed, confirming that the system is controlled solely by the solutal Rayleigh number, and that the slowing down is dominated by a combined effect of the driving force of buoyancy, the dissipating force of diffusion and the confinement provided by the vertical extension of the sample cell. Moreover, a compact phenomenological interpolating formula is proposed for easy analysis of experimental results.

Coupled non-equilibrium fluctuations in a polymeric ternary mixture

“…In particular, only the full coupling of velocity, temperature and concentration NEFs in the bulk fluid can explain the appearance of propagating modes giving rise to a ( , ) that includes oscillations at very small wave numbers. This mechanism also induces a slowing-down of the non-propagating concentration NEFs similar to that caused by the confinement effect [41,42].…”

“…In these conditions, the effect of confinement should not be visible in the investigated wave number range. In fact, confinement effects appear only at dimensionless wave numbers ̃= < 5, corresponding here to dimensional wave numbers < 10/ , at the very bottom of the investigated range of q [41,42].…”

“…More recently [40], we have further developed the theory of NEFs to include the effect of gravity, but not confinement so that a direct comparison with the data of Ref. [14] is impossible since fluid layer thickness of only 2 mm makes confinement effects important, as evidenced in related literature for binary mixtures [41,42].…”

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

“…From eq. (29) follows that Ψ is invariant under the transformation to diagonal concentrations. Note that, from eq.…”

“…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.…”