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Dispersion controlled by permeable surfaces: surface properties and scaling

Published online by Cambridge University Press:  19 July 2016

Bowen Ling ,
Alexandre M. Tartakovsky  and
Ilenia Battiato
Bowen Ling
Affiliation:
Mechanical and Aerospace Engineering Department, University of California San Diego, La Jolla, CA 92093, USA Mechanical Engineering Department, San Diego State University, San Diego, CA 92182, USA
Alexandre M. Tartakovsky
Affiliation:
Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99352, USA
Ilenia Battiato*
Affiliation:
Mechanical Engineering Department, San Diego State University, San Diego, CA 92182, USA
*
†Email address for correspondence: [email protected]
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Abstract

Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel–porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of the surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Péclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Péclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 801 , 25 August 2016 , pp. 13 - 42
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Copyright
© 2016 Cambridge University Press 

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