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Transport of volume in a binary liquid

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  • Bringuier, E.

Abstract

In this paper, the transport of volume in a binary liquid mixture is theoretically investigated in three steps, with strong implications for the measurement of mutual diffusivities in non-dilute mixtures. In a first step, the velocity of volume transport is determined from the transport velocities of the two components and the thermodynamic relation of state of the liquid mixture in equilibrium. The role played by Galilean invariance and the choice of a rigid frame of reference for reckoning current densities is highlighted. The divergence of the volume-transport velocity field is found to involve the isothermal compressibility and the thermal expansivity of the liquid together with the spatiotemporal variations of pressure and temperature. In a second step, a linear-response relation is introduced between the interdiffusion current density and the gradient of composition; this relation phenomenologically defines the mutual diffusivity of the binary liquid in a manifestly Galilean-invariant way. In a third step, it is examined whether the practical measurement of that diffusivity in a constant-volume container entails a vanishing mass-transport or volume-transport velocity. From a singular-perturbation analysis of the hydrodynamic equations, it is shown that the mass-transport velocity vanishes in the limit of a diffusion of composition that is much slower than the diffusion of momentum. As a consequence, the volume-transport velocity does not vanish during interdiffusion even though the law of additive volumes of the components holds. The physical meaning of the non-vanishing volume velocity is interpreted by means of the thermodynamic results obtained in the second step. Some of the conclusions carry over to multicomponent liquid mixtures.

Suggested Citation

  • Bringuier, E., 2012. "Transport of volume in a binary liquid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5064-5075.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:21:p:5064-5075
    DOI: 10.1016/j.physa.2012.05.065
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    References listed on IDEAS

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    1. Brenner, Howard, 2005. "Kinematics of volume transport," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 11-59.
    2. Bringuier, E., 2011. "Gauge-invariant approach to thermodiffusion in a liquid binary mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1861-1875.
    3. Lançon, P. & Batrouni, G. & Lobry, L. & Ostrowsky, N., 2002. "Brownian walker in a confined geometry leading to a space-dependent diffusion coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 304(1), pages 65-76.
    4. Lhuillier, Daniel, 2011. "Thermodiffusion of rigid particles in pure liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1221-1233.
    5. Kjelstrup, S. & Bedeaux, D. & Inzoli, I. & Simon, J.-M., 2008. "Criteria for validity of thermodynamic equations from non-equilibrium molecular dynamics simulations," Energy, Elsevier, vol. 33(8), pages 1185-1196.
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