Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

Abstract

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918)10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Mixing and Reactive Fronts in the Subsurface

“…The impact of these processes on mixing enhancement for continuously emitted plumes has been studied in detailed 3-D numerical simulations at the field scale (Cirpka et al 2015). At the pore scale, the topology of threedimensional streamlines is expected to generate stretching and folding processes characteristic of chaotic mixing dynamics (Lester et al 2013;Turuban et al 2018). This leads to an exponential increase of mixing fronts, which is expected to dominate asymptotically the linear deformation created by shear (Lester et al 2016).…”

“…3a) lead to a linear increase of elongation. As discussed above, chaotic flows are generated by stretching and folding processes in three-dimensional porous media both at the pore scale and in anisotropic porous media (Lester et al, 2013, Turuban et al 2018, Ye et al 2016. They can also be engineered designing transient pumping and injection schemes to enhance mixing (Piscopo et al 2013).…”

Stretching and folding sustain microscale chemical gradients in porous media

“…Recent theories (19,20) have suggested that laminar flow through three-dimensional porous media may possess the basic ingredients for chaotic advection (e.g., the exponential deformation of fluid elements), which would represent a possible mechanism for the enhancement of microscale chemical gradients and the persistence of incomplete mixing at the pore-scale. These chaotic dynamics may have particularly important consequences for microbial processes, a broad range of which are hosted in porous environments (21).…”

Plume deformation, mixing, and reaction kinetics: An analysis of interacting helical flows in three-dimensional porous media

“…Mixing processes are crucial in many subsurface applications including contaminant transport and (bio)degradation, mineral precipitation and dissolution, viscous fingering, densitydriven convection, and groundwater-surface water interaction * masro@env.dtu.dk [21][22][23][24][25][26][27][28]. Most studies of mixing in heterogeneous porous media have been performed in two-dimensional (2D) setups including quasi two-dimensional flow-through experiments and detailed 2D numerical simulations [12,[29][30][31][32][33], whereas fewer contributions have investigated mixing in fully three-dimensional (3D) systems [34][35][36][37][38][39][40][41][42][43][44]. Complex flows can develop in fully three-dimensional anisotropic porous media, entailing whirling and twisting streamlines [35,[45][46][47][48][49][50][51][52].…”