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The description of the dynamics of a multicomponent fluid confined in a nano-porous medium is still challenging despite its wide interest for many applications related to chemical engineering and geosciences. Indeed, when the pore size becomes similar to that of the fluid molecules, surface effects overcome contributions from the bulk of the fluid, which requires to adapt the classical Darcy formulation [1]. However, such Darcy-like formulations face conceptual difficulties when they deal with multicomponent systems exhibiting different affinities with the porous medium. Thus, this work proposes a different paradigm to describe multicomponent transport in porous media. The idea is to base the formulation on one equation of momentum conservation per species at the pore scale following what proposed by Kerkhof and Geboers [2], which could be then homogenized at the Darcy scale. The coupling between these equations is achieved by a Maxwell-Stefan friction terms to ensure momentum exchange between different species. Such a formulation is appealing but was, until now, difficult to apply as it requires the knowledge of new fluid physical properties such as partial viscosities or slip lengths by species. However, using molecular dynamics simulations enable the computation of such quantities [3-4], which makes this new paradigm accessible.

Within this framework, the aims of this postdoctoral position will be to:

  1. develop a numerical strategy to solve this set of coupled PDEs at the
    pore scale,
  2. compare the results with reference cases based on molecular
    simulations of multicomponent mixtures (dense gas and liquids) in simple
    porous geometry,
  3. adapt the Kerkhof-Geboers model if necessary,
  4. propose an upscaling strategy of the pore scale model at the Darcy


[1] Bear J. (1988) Dynamics of Fluids in Porous Media. Dover Publications,
New York
[2] Kerkhof P.J.A.M., Geboers M.A.M. (2005) Chemical Engineering Science
60: 3129.
[3] Ameur D., Galliero G. (2013) Microfluidics and Nanofluidics 15: 183.
[4] Bhadauria R., Aluru N.R. (2016), Journal of Chemical Physics 145:

Required qualification:

PhD in Applied mathematics, Fluid Physics/Mechanics or related domains


Scientific computing and/or code development


CV + motivation letter to (deadline: 15 oct 2019)
Dr. Etienne Ahusborde,
Prof. Guillaume Galliero,
Prof. Mejdi Azaiez,