Skip to main content

Statistical Mechanics of Clogging

  • Living reference work entry
  • First Online:
Encyclopedia of Complexity and Systems Science

Glossary

Arch:

Set of mutually stabilizing particles, meaning that if any one of them is removed the whole set will collapse.

Clogging:

Halt of the flow of macroscopic particles caused by the development of a local structure (an arch in two dimensions or a dome in three) which brings the whole system to a rest state.

Granular matter:

Material composed of independent, macroscopic particles that interact solely by contacts or collisions. As the latter are intrinsically dissipative, energy is not conserved, and therefore, the system typically adopts metastable configurations.

Granular Silo:

Container in which granular matter is stored. The emptying of silos is generally performed through an orifice at the bottom, although other alternatives (such as the discharge through lateral orifices or by means of extraction belts) are also possible.

Unclogging:

Destabilization of a clogging arch by means of an energy input which must be external for the case of inert granular media, but can be also...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Bibliography

  • Ahmadi A, Hosseininia ES (2018) An experimental investigation on stable arch formation in cohesionless granular materials using developed trapdoor test. Powder Technol 330:137–146

    Google Scholar 

  • Arévalo R, Zuriguel I, Maza D, Garcimartín A (2014) Role of driving force on the clogging of inert particles in a bottleneck. Phys Rev E 89:042205

    ADS  Google Scholar 

  • Arnold P, McLean A (1976) An analytical solution for the stress function at the wall of a converging channel. Powder Technol 13(2):255–260

    Google Scholar 

  • Ashour A, Trittel T, Börzsönyi T, Stannarius R (2017a) Silo outflow of soft frictionless spheres. Phys Rev Fluids 2(12):123302

    ADS  Google Scholar 

  • Ashour A, Wegner S, Trittel T, Börzsönyi T, Stannarius R (2017b) Outflow and clogging of shape-anisotropic grains in hoppers with small apertures. Soft Matter 13(2):402–414

    ADS  Google Scholar 

  • Beverloo W, Leniger H, van de Velde J (1961) The flow of granular solids through orifices. Chem Eng Sci 15(3):260–269

    Google Scholar 

  • Cates ME, Wittmer JP, Bouchaud J-P, Claudin P (1998) Jamming, force chains, and fragile matter. Phys Rev Lett 81:1841–1844

    ADS  Google Scholar 

  • Chen K, Stone MB, Barry R, Lohr M, McConville W, Klein K, Sheu B, Morss A, Scheidemantel T, Schiffer P (2006) Flux through a hole from a shaken granular medium. Phys Rev E 74(1):011306

    ADS  Google Scholar 

  • Chevoir F, Gaulard F, Roussel N (2007) Flow and jamming of granular mixtures through obstacles. Europhys Lett (EPL) 79(1):14001

    ADS  Google Scholar 

  • Clément E, Reydellet G, Rioual F, Parise B, Fanguet V, Lanuza J, Kolb E (2000) Jamming patterns and blockade statistics in model granular flows. In: Helbing D, Herrmann HJ, Schreckenberg M, Wolf DE (eds) Traffic and granular flow ’99. Springer Berlin Heidelberg, Berlin/Heidelberg, pp 457–468

    MATH  Google Scholar 

  • Daniels KE, Kollmer JE, Puckett JG (2017) Photoelastic force measurements in granular materials. Rev Sci Instrum 88(5):051808

    ADS  Google Scholar 

  • Davies C, Desai M (2008) Blockage in vertical slots: experimental measurement of minimum slot width for a variety of granular materials. Powder Technol 183(3):436–440. Festschrift issue in honor of Professor Robert Pfeffer – articles presented at the honoring session of the AIChE annual meeting in 2006

    Google Scholar 

  • Divoux T, Gayvallet H, Géminard J-C (2008) Creep motion of a granular pile induced by thermal cycling. Phys Rev Lett 101:148303

    ADS  Google Scholar 

  • Dorbolo S, Maquet L, Brandenbourger M, Ludewig F, Lumay G, Caps H, Vandewalle N, Rondia S, Mélard M, van Loon J, Dowson A, Vincent-Bonnieu S (2013) Influence of the gravity on the discharge of a silo. Granul Matter 15(3):263–273

    Google Scholar 

  • Drescher A, Waters A, Rhoades C (1995) Arching in hoppers: II. Arching theories and critical outlet size. Powder Technol 84(2):177–183

    Google Scholar 

  • Endo K, Reddy KA, Katsuragi H (2017) Obstacle-shape effect in a two-dimensional granular silo flow field. Phys Rev Fluids 2:094302

    ADS  Google Scholar 

  • Evesque P, Meftah W (1993) Mean flow of a vertically vibrated hourglass. Int J Mod Phys B 7(09n10):1799–1805

    ADS  Google Scholar 

  • Garcimartín A, Zuriguel I, Pugnaloni LA, Janda A (2010) Shape of jamming arches in two-dimensional deposits of granular materials. Phys Rev E 82:031306

    ADS  Google Scholar 

  • Gella D, Maza D, Zuriguel I, Ashour A, Arévalo R, Stannarius R (2017) Linking bottleneck clogging with flow kinematics in granular materials: the role of silo width. Phys Rev Fluids 2:084304

    ADS  Google Scholar 

  • Gella D, Zuriguel I, Maza D (2018) Decoupling geometrical and kinematic contributions to the silo clogging process. Phys Rev Lett 121:138001

    ADS  Google Scholar 

  • Goldberg E, Carlevaro CM, Pugnaloni LA (2018) Clogging in two-dimensions: effect of particle shape. J Stat Mech: Theory Exp 2018(11):113201

    MATH  Google Scholar 

  • Guariguata A, Pascall MA, Gilmer MW, Sum AK, Sloan ED, Koh CA, Wu DT (2012) Jamming of particles in a two-dimensional fluid-driven flow. Phys Rev E 86:061311

    ADS  Google Scholar 

  • Guerrero BV, Pugnaloni LA, Lozano C, Zuriguel I, Garcimartín A (2018) Slow relaxation dynamics of clogs in a vibrated granular silo. Phys Rev E 97:042904

    ADS  Google Scholar 

  • Guerrero BV, Chakraborty B, Zuriguel I, Garcimartín A (2019) Nonergodicity in silo unclogging: broken and unbroken arches. Phys Rev E 100:032901

    ADS  Google Scholar 

  • Hadjigeorgiou J, Stacey T (2013) The absence of strategy in orepass planning, design, and management. J South Afr Inst Min Metall 113:795–801

    Google Scholar 

  • Helbing D, Johansson A, Mathiesen J, Jensen MH, Hansen A (2006) Analytical approach to continuous and intermittent bottleneck flows. Phys Rev Lett 97(16):168001

    ADS  Google Scholar 

  • Hidalgo RC, Lozano C, Zuriguel I, Garcimartín A (2013) Force analysis of clogging arches in a silo. Granul Matter 15(6):841–848

    Google Scholar 

  • Hong X, Kohne M, Morrell M, Wang H, Weeks ER (2017) Clogging of soft particles in two-dimensional hoppers. Phys Rev E 96:062605

    ADS  Google Scholar 

  • Hou M, Chen W, Zhang T, Lu K, Chan C (2003) Global nature of dilute-to-dense transition of granular flows in a 2d channel. Phys Rev Lett 91(20):204301

    ADS  Google Scholar 

  • Janda A, Zuriguel I, Garcimartín A, Pugnaloni LA, Maza D (2008) Jamming and critical outlet size in the discharge of a two-dimensional silo. EPL (Europhys Lett) 84(4):44002

    ADS  Google Scholar 

  • Janda A, Harich R, Zuriguel I, Maza D, Cixous P, Garcimartín A (2009a) Flow-rate fluctuations in the outpouring of grains from a twodimensional silo. Phys Rev E 79:031302

    ADS  Google Scholar 

  • Janda A, Maza D, Garcimartín A, Kolb E, Lanuza J, Clément E (2009b) Unjamming a granular hopper by vibration. EPL (Europhys Lett) 87(2):24002

    ADS  Google Scholar 

  • Janda A, Zuriguel I, Garcimartín A, Maza D (2015) Clogging of granular materials in narrow vertical pipes discharged at constant velocity. Granul Matter 17(5):545–551

    Google Scholar 

  • Janssen HA (1895) Versuche uber getreidedruck in silozellen. Z Ver Dtsch Ing 39(35):1045–1049

    Google Scholar 

  • Jenike AW (1964) Steady gravity flow of frictional-cohesive solids in converging channels. J Appl Mech 31(1):5–11

    Google Scholar 

  • Kamath S, Kunte A, Doshi P, Orpe AV (2014) Flow of granular matter in a silo with multiple exit orifices: jamming to mixing. Phys Rev E 90(6):062206

    ADS  Google Scholar 

  • Kohring G, Melin S, Puhl H, Tillemans H, Vermöhlen W (1995) Computer simulations of critical, non-stationary granular flow through a hopper. Comput Methods Appl Mech Eng 124(3):273–281

    ADS  Google Scholar 

  • Koivisto J, Durian DJ (2017) Effect of interstitial fluid on the fraction of flow microstates that precede clogging in granular hoppers. Phys Rev E 95:032904

    ADS  Google Scholar 

  • Kondic L (2014) Simulations of two dimensional hopper flow. Granul Matter 16(2):235–242

    Google Scholar 

  • Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7(4):284–304

    ADS  MathSciNet  MATH  Google Scholar 

  • Kunte A, Doshi P, Orpe AV (2014) Spontaneous jamming and unjamming in a hopper with multiple exit orifices. Phys Rev E 90:020201

    ADS  Google Scholar 

  • Lafond PG, Gilmer MW, Koh CA, Sloan ED, Wu DT, Sum AK (2013) Orifice jamming of fluid-driven granular flow. Phys Rev E 87:042204

    ADS  Google Scholar 

  • Liu AJ, Nagel SR (1998) Nonlinear dynamics: jamming is not just cool any more. Nature 396(6706):21

    ADS  Google Scholar 

  • Longhi E, Easwar N, Menon N (2002) Large force fluctuations in a flowing granular medium. Phys Rev Lett 89:045501

    ADS  Google Scholar 

  • Longjas A, Monterola C, Saloma C (2009) Force analysis of jamming with disks of different sizes in a two-dimensional hopper. J Stat Mech: Theory Exp 2009(05):P05006

    MATH  Google Scholar 

  • López-Rodríguez D, Gella D, To, K, Maza D, Garcimartín A, Zuriguel I (2019) Effect of hopper angle on granular clogging. Phys Rev E 99:032901

    ADS  Google Scholar 

  • Lozano C, Janda A, Garcimartín A, Maza D, Zuriguel I (2012a) Flow and clogging in a silo with an obstacle above the orifice. Phys Rev E 86:031306

    ADS  Google Scholar 

  • Lozano C, Lumay G, Zuriguel I, Hidalgo RC, Garcimartín A (2012b) Breaking arches with vibrations: the role of defects. Phys Rev Lett 109:068001

    ADS  Google Scholar 

  • Lozano C, Zuriguel I, Garcimartín A (2015) Stability of clogging arches in a silo submitted to vertical vibrations. Phys Rev E 91:062203

    ADS  Google Scholar 

  • Mankoc C, Garcimartín A, Zuriguel I, Maza D, Pugnaloni LA (2009) Role of vibrations in the jamming and unjamming of grains discharging from a silo. Phys Rev E 80:011309

    ADS  Google Scholar 

  • Marin A, Lhuissier H, Rossi M, Kähler CJ (2018) Clogging in constricted suspension flows. Phys Rev E 97:021102

    ADS  Google Scholar 

  • Masuda T, Nishinari K, Schadschneider A (2014) Critical bottleneck size for jamless particle flows in two dimensions. Phys Rev Lett 112:138701

    ADS  Google Scholar 

  • Merrigan C, Birwa SK, Tewari S, Chakraborty B (2018) Ergodicity breaking dynamics of arch collapse. Phys Rev E 97:040901

    ADS  Google Scholar 

  • Mondal S, Sharma MM (2014) Role of flying buttresses in the jamming of granular matter through multiple rectangular outlets. Granul Matter 16(1):125–132

    Google Scholar 

  • Mueth DM, Jaeger HM, Nagel SR (1998) Force distribution in a granular medium. Phys Rev E 57:3164–3169

    ADS  Google Scholar 

  • Nguyen HT, Reichhardt C, Reichhardt CJO (2017) Clogging and jamming transitions in periodic obstacle arrays. Phys Rev E 95:030902

    ADS  Google Scholar 

  • Nicodemi M, Coniglio A (1999) Aging in out-of-equilibrium dynamics of models for granular media. Phys Rev Lett 82(5):916

    ADS  Google Scholar 

  • Nicolas A, Garcimartín Á, Zuriguel I (2018) Trap model for clogging and unclogging in granular hopper flows. Phys Rev Lett 120(19):198002

    ADS  Google Scholar 

  • Pacheco-Martinez H, Van Gerner HJ, Ruiz-Suárez J (2008) Storage and discharge of a granular fluid. Phys Rev E 77(2):021303

    ADS  Google Scholar 

  • Parretta A, Grillo P (2019) Flow dynamics of spherical grains through conical cardboard hoppers. Granul Matter 21(2):31

    Google Scholar 

  • Pastor JM, Garcimartín A, Gago PA, Peralta JP, MartínGómez C, Ferrer LM, Maza D, Parisi DR, Pugnaloni LA, Zuriguel I (2015) Experimental proof of faster-is-slower in systems of frictional particles flowing through constrictions. Phys Rev E 92(6):062817

    ADS  Google Scholar 

  • Patterson GA, Fierens PI, Sangiuliano Jimka F, König PG, Garcimartín A, Zuriguel I, Pugnaloni LA, Parisi DR (2017) Clogging transition of vibration-driven vehicles passing through constrictions. Phys Rev Lett 119:248301

    ADS  Google Scholar 

  • Pérez G (2008) Numerical simulations in granular matter: the discharge of a 2d silo. Pramana 70(6):989–1007

    ADS  Google Scholar 

  • Péter H, Libál A, Reichhardt C, Reichhardt CJ (2018) Crossover from jamming to clogging behaviours in heterogeneous environments. Sci Rep 8(1):10252

    ADS  Google Scholar 

  • Pournin L, Ramaioli M, Folly P, Liebling TM (2007) About the influence of friction and polydispersityon the jamming behavior of bead assemblies. Eur Phys J E 23(2):229

    Google Scholar 

  • Pugnaloni LA, Valluzzi MG, Valluzzi LG (2006) Arching in tapped deposits of hard disks. Phys Rev E 73:051302

    ADS  Google Scholar 

  • Roussel N, Nguyen TLH, Coussot P (2007) General probabilistic approach to the filtration process. Phys Rev Lett 98(11):114502

    ADS  Google Scholar 

  • Sakaguohi H, Ozaki E, Igarashi T (1993) Plugging of the flow of granular materials during the discharge from a silo. Int J Mod Phys B 07(09n10):1949–1963

    ADS  Google Scholar 

  • Saraf S, Franklin SV (2011) Power-law flow statistics in anisometric (wedge) hoppers. Phys Rev E 83:030301

    ADS  Google Scholar 

  • Serrano DA, Cabrera D, Gutiérrez GJ, Medina A (2014) Experimental study of mass flow rate in a Silo under the wall width influence. Springer International Publishing, Cham, pp 207–217

    Google Scholar 

  • Sheldon HG, Durian DJ (Dec 2010) Granular discharge and clogging for tilted hoppers. Granul Matter 12(6):579–585

    Google Scholar 

  • Stoop RL, Tierno P (2018) Clogging and jamming of colloidal monolayers driven across disordered landscapes. Commun Phys 1(1):68

    Google Scholar 

  • Suzuki A, Takahashi H, Tanaka T (1968) Behaviour of a particle bed in the field of vibration ii flow of particles through slits in the bottom of a vibrating vessel. Powder Technol 2(2):72–77

    Google Scholar 

  • Tang J, Behringer RP (2016) Orientation, flow, and clogging in a two-dimensional hopper: Ellipses vs. disks. EPL (Europhys Lett) 114(3):34002

    ADS  Google Scholar 

  • Tejada I, Sibille L, Chareyre B (2016) Role of blockages in particle transport through homogeneous granular assemblies. EPL (Europhys Lett) 115(5):54005

    ADS  Google Scholar 

  • Tewari S, Dichter M, Chakraborty B (2013) Signatures of incipient jamming in collisional hopper flows. Soft Matter 9:5016–5024

    ADS  Google Scholar 

  • Thomas CC, Durian DJ (2013) Geometry dependence of the clogging transition in tilted hoppers. Phys Rev E 87:052201

    ADS  Google Scholar 

  • Thomas CC, Durian DJ (Apr 2015) Fraction of clogging configurations sampled by granular hopper flow. Phys Rev Lett 114:178001

    ADS  Google Scholar 

  • Thomas CC, Durian DJ (2016) Intermittency and velocity fluctuations in hopper flows prone to clogging. Phys Rev E 94:022901

    ADS  Google Scholar 

  • To K (2005) Jamming transition in two-dimensional hoppers and silos. Phys Rev E 71:060301

    ADS  Google Scholar 

  • To K, Tai H-T (2017) Flow and clog in a silo with oscillating exit. Phys Rev E 96(3):032906

    ADS  Google Scholar 

  • To K, Lai P-Y, Pak HK (2001) Jamming of granular flow in a two dimensional hopper. Phys Rev Lett 86:71–74

    ADS  Google Scholar 

  • To K, Yen Y, Mo Y-K, Huang J-R (2019) Granular flow from silos with rotating orifice. Phys Rev E 100(1):012906

    ADS  Google Scholar 

  • Uñac RO, Vidales AM, Pugnaloni LA (2012) The effect of the packing fraction on the jamming of granular flow through small apertures. J Stat Mech: Theory Exp 2012(04):P04008

    MATH  Google Scholar 

  • Valdes JR, Santamarina JC (2008) Clogging: bridge formation and vibration-based destabilization. Can Geotech J 45(2):177–184

    Google Scholar 

  • Vamsi Krishna Reddy A, Kumar S, Anki Reddy K, Talbot J (2018) Granular silo flow of inelastic dumbbells: clogging and its reduction. Phys Rev E 98:022904

    ADS  Google Scholar 

  • Verbücheln F, Parteli EJR, Pösohel T (2015) Helical inner-wall texture prevents jamming in granular pipe flows. Soft Matter 11:4295–4305

    ADS  Google Scholar 

  • Walker D (1966) An approximate theory for pressures and arching in hoppers. Chem Eng Sci 21(11):975–997

    Google Scholar 

  • Wassgren CR, Hunt ML, Freese P, Palamara J, Brennen C (2002) Effects of vertical vibration on hopper flows of granular material. Phys Fluids 14(10):3439–3448

    ADS  MATH  Google Scholar 

  • Wes G, Stemerding S, van Zuiliohem D (1990) Control of flow of cohesive powders by means of simultaneous aeration, and vibration. Powder Technol 61(1):39–49

    Google Scholar 

  • Zhao Y, Cocco RA, Yang S, Chew JW (2019) Dem study on the effect of particle-size distribution on jamming in a 3d conical hopper. AICHE J 65(2):512–519

    Google Scholar 

  • Zhou Y, Lagrée P-Y, Popinet S, Ruyer P, Aussillous P (2017) Experiments on, and discrete and continuum simulations of, the discharge of granular media from silos with a lateral orifice. J Fluid Mech 829:459–485

    ADS  MATH  Google Scholar 

  • Zuriguel I, Pugnaloni LA, Garcimartín A, Maza D (2003) Jamming during the discharge of grains from a silo described as a percolating transition. Phys Rev E 68:030301

    ADS  Google Scholar 

  • Zuriguel I, Garcimartín A, Maza D, Pugnaloni LA, Pastor JM (2005) Jamming during the discharge of granular matter from a silo. Phys Rev E 71:051303

    ADS  Google Scholar 

  • Zuriguel I, Janda A, Garcimartín A, Lozano C, Arévalo R, Maza D (2011) Silo clogging reduction by the presence of an obstacle. Phys Rev Lett 107:278001

    ADS  Google Scholar 

  • Zuriguel I, Parisi DR, Hidalgo RC, Lozano C, Janda A, Gago PA, Peralta JP, Ferrer LM, Pugnaloni LA, Clément E, Maza D, Pagonabarraga I, Garcimartín A (2014) Clogging transition of many-particle systems flowing through bottlenecks. Sci Rep 4:7324

    Google Scholar 

  • Zuriguel I, Janda A, Arévalo R, Maza D, Garcimartín A (2017) Clogging and unclogging of many-particle systems passing through a bottleneck. EPJ Web Conf 140:01002

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. Zuriguel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Science+Business Media LLC

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Zuriguel, I., Garcimartín, A. (2020). Statistical Mechanics of Clogging. In: Meyers, R.A. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_746-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27737-5_746-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27737-5

  • Online ISBN: 978-3-642-27737-5

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

Publish with us

Policies and ethics