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The effective diffusivity of ordered and freely evolving bubbly suspensions

Published online by Cambridge University Press:  09 February 2018

Aurore Loisy Open the ORCID record for Aurore Loisy [Opens in a new window] ,
Aurore Naso Open the ORCID record for Aurore Naso [Opens in a new window]  and
Peter D. M. Spelt
Aurore Loisy
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS, Université Claude Bernard Lyon 1, École Centrale de Lyon, INSA de Lyon, 36 avenue Guy de Collongue, 69134 Écully CEDEX, France
Aurore Naso
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS, Université Claude Bernard Lyon 1, École Centrale de Lyon, INSA de Lyon, 36 avenue Guy de Collongue, 69134 Écully CEDEX, France
Peter D. M. Spelt
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, CNRS, Université Claude Bernard Lyon 1, École Centrale de Lyon, INSA de Lyon, 36 avenue Guy de Collongue, 69134 Écully CEDEX, France
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Abstract

We investigate the dispersion of a passive scalar such as the concentration of a chemical species, or temperature, in homogeneous bubbly suspensions, by determining an effective diffusivity tensor. Defining the longitudinal and transverse components of this tensor with respect to the direction of averaged bubble rise velocity in a zero mixture velocity frame of reference, we focus on the convective contribution thereof, this being expected to be dominant in commonly encountered bubbly flows. We first extend the theory of Koch et al. (J. Fluid Mech., vol. 200, 1989, pp. 173–188) (which is for dispersion in fixed beds of solid particles under Stokes flow) to account for weak inertial effects in the case of ordered suspensions. In the limits of low and of high Péclet number, including the inertial effect of the flow does not affect the scaling of the effective diffusivity with respect to the Péclet number. These results are confirmed by direct numerical simulations performed in different flow regimes, for spherical or very deformed bubbles and from vanishingly small to moderate values of the Reynolds number. Scalar transport in arrays of freely rising bubbles is considered by us subsequently, using numerical simulations. In this case, the dispersion is found to be convectively enhanced at low Péclet number, like in ordered arrays. At high Péclet number, the Taylor dispersion scaling obtained for ordered configurations is replaced by one characterizing a purely mechanical dispersion, as in random media, even if the level of disorder is very low.

JFM classification

Multiphase and Particle-laden Flows: Gas/liquid flow Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 215 - 237
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Copyright
© 2018 Cambridge University Press 

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