A parabola-shaped free-fall arch in silos with centric and eccentric outlets

Koivisto, 2017, The sands of time run faster near the end, Nat. Commun., 8, 15551, 10.1038/ncomms15551

Hu, 2019, Size scaling relation of velocity field in granular flows and the Beverloo law, Granul. Matter, 21, 21, 10.1007/s10035-019-0872-z

Janda, 2012, Flow rate of particles through apertures obtained from self-similar density and velocity profiles, Phys. Rev. Lett., 108, 10.1103/PhysRevLett.108.248001

Uñac, 2012, Experimental study of discharge rate fluctuations in a silo with different hopper geometries, Powder Technol., 225, 214, 10.1016/j.powtec.2012.04.013

Saleh, 2018, A review on gravity flow of free-flowing granular solids in silos – basics and practical aspects, Chem. Eng. Sci., 192, 1011, 10.1016/j.ces.2018.08.028

Hilton, 2011, Granular flow during hopper discharge, Phys. Rev. E, 84, 10.1103/PhysRevE.84.011307

Rubio-Largo, 2015, Disentangling the free-fall arch paradox in silo discharge, Phys. Rev. Lett., 114, 238002, 10.1103/PhysRevLett.114.238002

Savage, 1967, Gravity flow of a cohesionless bulk solid in a converging conical channel, Int. J. Mech. Sci., 9, 651, 10.1016/0020-7403(67)90069-0

Henann, 2014, Continuum modeling of secondary rheology in dense granular materials, Phys. Rev. Lett., 113, 178001, 10.1103/PhysRevLett.113.178001

Tighe, 2007, Pressure and motion of dry sand: translation of Hagen’s paper from 1852, Granular Matter, 9, 141, 10.1007/s10035-006-0027-x

Brown, 1970

Tian, 2015, Study on free fall surfaces in three-dimensional hopper flows, Adv. Powder Technol., 26, 1191, 10.1016/j.apt.2015.05.015

Wang, 2021, Shape of free-fall arch in quasi-2D silo, Particuology., 55, 62, 10.1016/j.partic.2020.10.001

Medina, 2000, Gravity induced granular flow measurements in a 2D silo with a lateral bottom exit, Phys. Lett. A, 273, 109, 10.1016/S0375-9601(00)00473-4

Medina, 1998, Velocity field measurements in granular gravity flow in a near 2D silo, Phys. Lett. A, 250, 111, 10.1016/S0375-9601(98)00795-6

Wang, 2018, Numerical simulations of dense granular flow in a two-dimensional channel: the role of exit position, Chinese Physics B., 27, 124704, 10.1088/1674-1056/27/12/124704

Börzsönyi, 2013, Granular materials composed of shape-anisotropic grains, Soft Matter, 9, 7401, 10.1039/c3sm50298h

Altuhafi, 2013, Analysis of an image-based method to quantify the size and shape of sand particles, J. Geotech. Geoenviron., 139, 1290, 10.1061/(ASCE)GT.1943-5606.0000855

Nielsen, 1998, Pressures from flowing granular solids in silos, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., 356, 2667, 10.1098/rsta.1998.0292

Drescher, 2004, Revised model for plug/funnel flow in bins, Powder Technol., 141, 44, 10.1016/j.powtec.2004.02.011

Chen, 2021, Measurement of granular temperature and velocity profile of granular flow in silos, Powder Technol., 392, 123, 10.1016/j.powtec.2021.07.007

Medina, 2014, Discharge rates of dry granular material from bins with lateral exit holes, Powder Technol., 253, 270, 10.1016/j.powtec.2013.11.027

Lin, 2015, Numerical study of free-fall arches in hopper flows, Physica A: Stat. Mech. Appl., 417, 29, 10.1016/j.physa.2014.09.032

Walker, 1966, An approximate theory for pressures and arching in hoppers, Chem. Eng. Sci., 21, 975, 10.1016/0009-2509(66)85095-9

Walters, 1973, A theoretical analysis of stresses in silos with vertical walls, Chem. Eng. Sci., 28, 13, 10.1016/0009-2509(73)85081-X