Percolation Through Voids Around Structurally Disordered Sand Grains
- Slides: 20
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
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 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: The Data Collapse 8
Analysis Procedure: The Comparison 9
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
Platonic Solids Results 12
It’s Rough, Coarse, and it Gets Everywhere 13
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
Fully Disordered Tetrahedra 17
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. • 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. 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
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