Abstract
Granular materials may readily segregate due to differences in particle properties such as size, shape, and density. Segregation is common in industrial processes involving granular materials and can occur even after a material has been uniformly blended. The specific objective of this work is to investigate via simulation the effect of particle cohesion due to liquid bridging on particle segregation. Specifically, a bi-disperse granular material flowing from a 3-D hopper is simulated using the discrete element method (DEM) for cohesive particles and the extent of discharge segregation is characterized over time. The cohesion between the particles is described by a pendular liquid bridge force model and the strength of the cohesive bond is characterized by the Bond number determined with respect to the smaller particle species. As the Bond number of the system increases, the extent of discharge segregation in the system decreases. A critical value of Bo = 1 is identified as the condition where the primary mechanism of segregation in the cohesionless hopper system, i.e. gravity-induced percolation, is essentially eliminated due to the liquid bridges between particles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A :
-
Hopper aspect ratio, A = H / W [–]
- d L :
-
Larger particle diameter [L]
- d S :
-
Smaller particle diameter [L]
- e :
-
Coefficient of restitution in the normal direction [–]
- F lb :
-
Liquid bridge force [M · L · t −2]
- F vf :
-
Viscous force due to the liquid bridge in the normal direction [M · L · t −2]
- F N :
-
Collisional normal force [M · L · t − 2]
- F S :
-
Collisional tangential force [M · L · t −2]
- g :
-
Acceleration due to gravity [L · t −2]
- h :
-
Separation distance [L]
- h rupture :
-
Rupture separation distance [L]
- H :
-
Hopper fill height [L]
- k L :
-
Loading spring stiffness [M · t −2]
- k T :
-
Tangential spring stiffness [M · t −2]
- k U :
-
Unloading spring stiffness [M · t −2]
- M R :
-
Moment due to rolling friction [M · L 2 · t − 2]
- m :
-
Particle mass [M]
- N :
-
Total number of discharge samples
- n :
-
Number of particles in the system [–]
- \({\hat{n}}\) :
-
Unit normal vector [–]
- R 1 :
-
Radius of particle 1 [L]
- R 2 :
-
Radius of particle 2 [L]
- \({\hat{s}}\) :
-
Unit tangential vector [–]
- V :
-
Volume of liquid bridge
- v n :
-
Relative speed between particles forming a liquid bridge bond [Lt −1]
- W :
-
Hopper width [L]
- W 0 :
-
Hopper outlet width [L]
- \({\Delta{x}^\cdot}\) :
-
Relative velocity at contact [L · t −1]
- z depth :
-
Hopper depth in the z-direction [L]
- β :
-
Contact angle of liquid with the particle
- γ :
-
Surface tension of the liquid [M · L 2 · t −2]
- η :
-
Viscosity of the liquid [M · L −1 · t −1]
- θ :
-
Hopper half-angle with respect to vertical [–]
- μ :
-
Coefficient of sliding friction [–]
- μ R :
-
Coefficient of rolling friction [L]
- δ :
-
Normal overlap [L]
- δ 0 :
-
Normal overlap such that the unloading curve goes to zero [L]
- ξ :
-
Tangential displacement [L]
- ξ max :
-
Limiting tangential displacement before sliding occurs [L]
- ρ :
-
Density [M · L −3]
- ω i :
-
Angular velocity of particle i [t −1]
References
Cundall P.A., Strack O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979)
Hsiau S.S., Yang S.C.: Numerical simulation of self-diffusion and mixing in a vibrated granular bed with the cohesive effect of liquid bridges. Chem. Eng. Sci. 58, 339–351 (2003)
Ketterhagen W.R., Curtis J.S., Wassgren C.R., Hancock B.C.: Modeling granular segregation in flow from quasi-three-dimensional, wedge-shaped hoppers. Powder Technol. 179(3), 126–143 (2008)
Lian G., Thornton C., Adams M.J.: A theoretical study of the liquid bridge forces between two rigid spherical bodies. J. Colloid Interface Sci. 161, 138–147 (1993)
Lian G., Thornton C., Adams M.J.: Discrete particle simulation of agglomerate impact coalescence. Chem. Eng. Sci. 53(19), 3381–3391 (1998)
Mason G., Clark W.C.: Liquid bridges between spheres. Chem. Eng. Sci. 20, 859–866 (1965)
McCarthy J.J.: Micro-modeling of cohesive mixing processes. Powder Technol. 138, 63–67 (2003)
Mehrotra V.P., Sastry K.V.S.: Pendular bond strength between unequal sized spherical particles. Powder Technol. 25, 203–214 (1980)
Mikami T., Kamiya H., Horio M.: Numerical simulation of cohesive powder behavior in a fluidized bed. Chem. Eng. Sci. 53, 1927–1940 (1998)
Nase S.T., Vargas W.L., Abatan A.A., McCarthy J.J.: Discrete characterization tools for cohesive granular material. Powder Technol. 116, 214–223 (2001)
Seville J.P.K., Willett C.D., Knight P.C.: Interparticle forces in fluidisation: a review. Powder Technol. 113, 261–268 (2000)
Shi D., McCarthy J.J.: Numerical simulation of liquid transfer between particles. Powder Technol. 184, 64–75 (2008)
Soulié F., Cherblanc F., El Youssoufi M.S., Saix C.: Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials. Int. J. Numer. Anal. Meth. Geomech. 30, 213–228 (2006)
Walton O.R., Braun R.L.: Viscosity, granular temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30, 949–980 (1986)
Willett C.D., Adams M.J., Johnson S.A., Seville J.P.K.: Capillary bridges between two spherical bodies. Langmuir 16, 9396–9405 (2000)
Yang R.Y., Zou R.P., Yu A.B.: Numerical study of the packing of wet coarse uniform Spheres. AIChE J. 49(7), 1656–1666 (2003)
Zhou Z., Zhu H., Yu A., Wright B., Pinson D., Zulli P.: Discrete particle simulation of solid flow in a model blast furnace. ISIJ Int. 45, 1828–1837 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Anand, A., Curtis, J.S., Wassgren, C.R. et al. Segregation of cohesive granular materials during discharge from a rectangular hopper. Granular Matter 12, 193–200 (2010). https://doi.org/10.1007/s10035-010-0168-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-010-0168-9