Percolation Through Voids Around Structurally Disordered Sand Grains

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Percolation Through Voids Around Structurally Disordered Sand Grains Nicholas J. Mc. Guigan, Donald J.

Percolation Through Voids Around Structurally Disordered Sand Grains Nicholas J. Mc. Guigan, Donald J. Priour Jr. April 19, 2018 1

Void Percolation: A Brief Tour 2

Void Percolation: A Brief Tour 2

What Drove Us to the Voids -We’re physicists; we like a challenge. -Seriously, due

What Drove Us to the Voids -We’re physicists; we like a challenge. -Seriously, due to the limiting factors tied to voids in disordered systems, calculations for percolation thresholds are largely unexplored. -Many examples in industry/nature *Recently increased interest in natural gas collection 3

A New Approach -Improve results from specular reflection method -Drude Model approach -Utilizing a

A New Approach -Improve results from specular reflection method -Drude Model approach -Utilizing a consistent electric field, direct charged tracer particles through system in parabolic bounces off barrier particles in the voids. 4

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Analysis Procedure: Crossing 7

Analysis Procedure: Crossing 7

Analysis Procedure: The Data Collapse 8

Analysis Procedure: The Data Collapse 8

Analysis Procedure: The Comparison 9

Analysis Procedure: The Comparison 9

Initial Disorder • To begin, we examine barrier systems containing only positional disorder. •

Initial Disorder • To begin, we examine barrier systems containing only positional disorder. • We then implement orientational disorder. Aligned Cubes Rotated Regular Tetrahedra 10

Cube Analysis 11

Cube Analysis 11

Platonic Solids Results 12

Platonic Solids Results 12

It’s Rough, Coarse, and it Gets Everywhere 13

It’s Rough, Coarse, and it Gets Everywhere 13

Structural Disorder • Systems of particles very irregular in reality. • Thus far, theoretical

Structural Disorder • Systems of particles very irregular in reality. • Thus far, theoretical studies on void networks were limited to systems of monodispersed, regular barriers. • Implement random perturbations in edge lengths and dihedral angles to generate irregular barriers. 14

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For Rectangular Solids 16

For Rectangular Solids 16

Fully Disordered Tetrahedra 17

Fully Disordered Tetrahedra 17

Conclusions • Sensitivity to orientational disorder only arises in the case of rectangular solids.

Conclusions • Sensitivity to orientational disorder only arises in the case of rectangular solids. • Implementing structural disorder raises the critical density as expected, yet appears to have little to no effect on the excluded volume in case of rectangular solids. 18

Future Considerations • Examine the effects of structural disorder on the remaining platonic solids.

Future Considerations • Examine the effects of structural disorder on the remaining platonic solids. • Investigate systems composed of barriers generated through the use of Voronoi Tesselation. • Etc, etc. , and etc. 19

References [1] D. J. Priour and N. J. Mc. Guigan, cond-mat/1801. 09970 [2] D.

References [1] D. J. Priour and N. J. Mc. Guigan, cond-mat/1801. 09970 [2] D. J. Priour and N. J. Mc. Guigan, cond-mat/1712. 10241 [3] Z. Koza, G. Kondrat, and K. Suszczyński, J. Stat. Mech. : Th. Exp. 11, P 11005 (2014). [4] D. J. Priour, Jr. , Phys. Rev. E, 89, 012148 (2014). [5] D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2 nd ed. (Taylor and Francis, Bristol, UK, 1992). 20