IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i21p5064-5075.html
   My bibliography  Save this article

Transport of volume in a binary liquid

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112004839
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2012.05.065?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Brenner, Howard, 2005. "Kinematics of volume transport," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 11-59.
    2. Lhuillier, Daniel, 2011. "Thermodiffusion of rigid particles in pure liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1221-1233.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Janusz Badur & Michel Feidt & Paweł Ziółkowski, 2020. "Neoclassical Navier–Stokes Equations Considering the Gyftopoulos–Beretta Exposition of Thermodynamics," Energies, MDPI, vol. 13(7), pages 1-34, April.
    2. Svärd, Magnus, 2018. "A new Eulerian model for viscous and heat conducting compressible flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 350-375.
    3. Bardow, André & Christian Öttinger, Hans, 2007. "Consequences of the Brenner modification to the Navier–Stokes equations for dynamic light scattering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 88-96.
    4. Brenner, Howard, 2010. "Bi-velocity transport processes. Single-component liquid and gaseous continua," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1297-1316.
    5. Brenner, Howard, 2013. "Bivelocity hydrodynamics. Diffuse mass flux vs. diffuse volume flux," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 558-566.
    6. Asinari, Pietro & Chiavazzo, Eliodoro, 2014. "The notion of energy through multiple scales: From a molecular level to fluid flows and beyond," Energy, Elsevier, vol. 68(C), pages 870-876.
    7. Qi, Yingxia & Meng, Xiangqi & Mu, Defu & Sun, Yangliu & Zhang, Hua, 2016. "Study on mechanism and factors affecting the gas leakage through clearance seal at nano-level by molecular dynamics method," Energy, Elsevier, vol. 102(C), pages 252-259.
    8. Zhong, Jie & Wang, Pan & Zhang, Yang & Yan, Youguo & Hu, Songqing & Zhang, Jun, 2013. "Adsorption mechanism of oil components on water-wet mineral surface: A molecular dynamics simulation study," Energy, Elsevier, vol. 59(C), pages 295-300.
    9. 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.
    10. Silvano, Nathan O. & Barci, Daniel G., 2023. "The role of multiplicative noise in critical dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    11. Abramov, Rafail V., 2017. "Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 532-557.
    12. Brenner, Howard, 2011. "Steady-state heat conduction in quiescent fluids: Incompleteness of the Navier–Stokes–Fourier equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3216-3244.
    13. Brenner, Howard, 2010. "Diffuse volume transport in fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(19), pages 4026-4045.
    14. Brenner, Howard, 2011. "Derivation of constitutive data for flowing fluids from comparable data for quiescent fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3645-3661.
    15. Ahmadi, Mohammadali & Chen, Zhangxin, 2022. "Molecular dynamics simulation of oil detachment from hydrophobic quartz surfaces during steam-surfactant Co-injection," Energy, Elsevier, vol. 254(PC).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:391:y:2012:i:21:p:5064-5075. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.