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Chaotic mixing in three-dimensional porous media

Published online by Cambridge University Press:  17 August 2016

Daniel R. Lester ,
Marco Dentz  and
Tanguy Le Borgne
Daniel R. Lester*
Affiliation:
School of Chemical and Environmental Engineering, RMIT University, 3000 Melbourne, Victoria, Australia
Marco Dentz
Affiliation:
Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain
Tanguy Le Borgne
Affiliation:
Geosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, 35042 Rennes, France
*
†Email address for correspondence: [email protected]
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Abstract

Under steady flow conditions, the topological complexity inherent to all random three-dimensional (3D) porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a 3D fluid mechanical analogue of the baker’s map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence, pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW), which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that the chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with the longitudinal advection, whereas the topological constraints associated with two-dimensional porous media limit the mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.

JFM classification

Mixing: Chaotic advection Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 803 , 25 September 2016 , pp. 144 - 174
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Copyright
© 2016 Cambridge University Press 

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