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Buoyancy-driven dispersion in confined drying of liquid binary mixtures

Jean-Baptiste Salmon

Frédéric Doumenc

  • CNRS, Solvay, LOF, UMR 5258, Univ. Bordeaux, F-33600 Pessac, France

  • Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France and Sorbonne Université, UFR 919, 4 place Jussieu, F-75252 Paris Cedex 05, France

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Phys. Rev. Fluids 5, 024201 – Published 10 February, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.024201

Abstract

We investigate the impact of buoyancy on the solute mass transport in an evaporating liquid mixture (nonvolatile solute + solvent) confined in a slit perpendicular to the gravity. Solvent evaporation at one end of the slit induces a solute concentration gradient which in turn drives free convection due to the difference between the densities of the solutes and the solvent. From the complete model coupling mass transport and hydrodynamics, we first use a standard Taylor-like approach to derive a one-dimensional nonlinear advection-dispersion equation describing the solute concentration process for a dilute mixture. We then perform a complete analysis of the expected regimes using both scaling analysis and asymptotic solutions of this equation. The validity of this approach is confirmed using a thorough comparison with the numerical resolution of both the complete model and the 1D advection-dispersion equation. Our results show that buoyancy-driven free convection always impacts solute mass transport at long timescales, dispersing solutes in a steadily increasing length scale along the slit. Beyond this confined drying configuration, our work also provides an easy way for evaluating the relevance of buoyancy on mass transport in any other microfluidic configuration involving concentration gradients.

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Phys. Rev. Fluids 5, 024201– Published 10 February, 2020
  • Received 8 October 2019
  • Accepted 13 January 2020
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