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Mixing across fluid interfaces compressed by convective flow in porous media

Published online by Cambridge University Press:  10 January 2018

Juan J. Hidalgo Open the ORCID record for Juan J. Hidalgo [Opens in a new window]  and
Marco Dentz Open the ORCID record for Marco Dentz [Opens in a new window]
Juan J. Hidalgo*
Affiliation:
IDAEA-CSIC, Barcelona, 08034, Spain Associated Unit, Hydrogeology Group (UPC-CSIC), Barcelona, Spain
Marco Dentz
Affiliation:
IDAEA-CSIC, Barcelona, 08034, Spain Associated Unit, Hydrogeology Group (UPC-CSIC), Barcelona, Spain
*
†Email address for correspondence: [email protected]
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Abstract

We study mixing in the presence of convective flow in a porous medium. Convection is characterized by the formation of vortices and stagnation points, where the fluid interface is stretched and compressed enhancing mixing. We analyse the behaviour of the mixing dynamics in different scenarios using an interface deformation model. We show that the scalar dissipation rate, which is related to the dissolution fluxes, is controlled by interfacial processes, specifically the equilibrium between interface compression and diffusion, which depends on the flow field configuration. We consider different scenarios of increasing complexity. First, we analyse a double-gyre synthetic velocity field. Second, a Rayleigh–Bénard instability (the Horton–Rogers–Lapwood problem), in which stagnation points are located at a fixed interface. This system experiences a transition from a diffusion controlled mixing to a chaotic convection as the Rayleigh number increases. Finally, a Rayleigh–Taylor instability with a moving interface, in which mixing undergoes three different regimes: diffusive, convection dominated and convection shutdown. The interface compression model correctly predicts the behaviour of the systems. It shows how the dependency of the compression rate on diffusion explains the change in the scaling behaviour of the scalar dissipation rate. The model indicates that the interaction between stagnation points and the correlation structure of the velocity field is also responsible for the transition between regimes. We also show the difference in behaviour between the dissolution fluxes and the mixing state of the systems. We observe that while the dissolution flux decreases with the Rayleigh number, the system becomes more homogeneous. That is, mixing is enhanced by reducing diffusion. This observation is explained by the effect of the instability patterns.

JFM classification

Convection: Convection in porous media Geophysical and Geological Flows: Geophysical and Geological Flows Mixing: Mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 838 , 10 March 2018 , pp. 105 - 128
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Copyright
© 2018 Cambridge University Press 

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