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Chaotic mixing in crystalline granular media

Published online by Cambridge University Press:  24 May 2019

Régis Turuban ,
Daniel R. Lester Open the ORCID record for Daniel R. Lester [Opens in a new window] ,
Joris Heyman Open the ORCID record for Joris Heyman [Opens in a new window] ,
Tanguy Le Borgne  and
Yves Méheust Open the ORCID record for Yves Méheust [Opens in a new window]
Régis Turuban
Affiliation:
Géosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, 35000 Rennes, France
Daniel R. Lester*
Affiliation:
School of Engineering, RMIT University, 3000 Melbourne, Victoria, Australia
Joris Heyman
Affiliation:
Géosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, 35000 Rennes, France
Tanguy Le Borgne
Affiliation:
Géosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, 35000 Rennes, France
Yves Méheust
Affiliation:
Géosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, 35000 Rennes, France
*
†Email address for correspondence: [email protected]
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Abstract

We study the Lagrangian kinematics of steady three-dimensional Stokes flow over simple cubic (SC) and body-centred cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing in these crystalline structures. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media, such as open pore networks, with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices posses the same symmetry point group, these differences are explained in terms of their space groups. This insight is used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation. These results point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.

JFM classification

Granular media: Granular media Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , pp. 562 - 594
Copyright
© 2019 Cambridge University Press 

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Luruban Supplementary Movie 1

Animation of the evolution of the inset in Figure 1(b) with downstream distance. This inset shows the cross-section (black line) of a material surface resulting from the continuous injection of a material line given by the red circle.

Download Luruban Supplementary Movie 1(Video)
Video 1.4 MB

Turuban Supplementary Movie 2

3D Animation of Figure 6(a), depicting a 3D view of the skin friction field, streamlines, stable and unstable manifolds associated with a sphere in the BCC lattice.

Download Turuban Supplementary Movie 2(Video)
Video 3.6 MB

Turuban Supplementary Movie 3

3D animation of Figure 9(c), depicting a smooth heteroclinic connection for the BCC lattice with $(\theta_{\text{f}}, \phi_{\text{f}}) = (3\pi/20, 0)$.

Download Turuban Supplementary Movie 3(Video)
Video 403.9 KB

Turuban Supplementary Movie 4

3D animation of Figure 9(d), depicting a transverse heteroclinic intersection for the BCC lattice with $(\theta_{\text{f}}, \phi_{\text{f}}) = (\pi/20, 0)$.

Download Turuban Supplementary Movie 4(Video)
Video 718.3 KB