Flow of granular materials with slip boundary condition: A continuum–kinetic theory approach
We study the steady fully developed flow of granular materials between two horizontal flat plates, subject to slip at the walls. The constitutive model for the stress tensor is based on ideas in continuum mechanics and kinetic theory. The constitutive equation used in our study is a model proposed b...
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| Published in | Applied mathematics and computation Vol. 242; pp. 518 - 527 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Elsevier Inc
01.09.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2014.05.093 |
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| Abstract | We study the steady fully developed flow of granular materials between two horizontal flat plates, subject to slip at the walls. The constitutive model for the stress tensor is based on ideas in continuum mechanics and kinetic theory. The constitutive equation used in our study is a model proposed by Rajagopal et al. (1994) [24], and the material properties such as viscosity and the normal stress coefficients are derived using the kinetic theory approximation proposed by Boyle and Massoudi (1990) [2] which includes the effect of the gradient of volume fraction. The slip boundary condition is based on the particle dynamics simulation results of Rosato and Kim (1994) [30]. The governing equations are non-dimensionalized, and the resulting system of non-linear differential equations is solved numerically. The results for the velocity profiles and the volume fraction profiles are presented. |
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| AbstractList | We study the steady fully developed flow of granular materials between two horizontal flat plates, subject to slip at the walls. The constitutive model for the stress tensor is based on ideas in continuum mechanics and kinetic theory. The constitutive equation used in our study is a model proposed by Rajagopal et al. (1994) [24], and the material properties such as viscosity and the normal stress coefficients are derived using the kinetic theory approximation proposed by Boyle and Massoudi (1990) [2] which includes the effect of the gradient of volume fraction. The slip boundary condition is based on the particle dynamics simulation results of Rosato and Kim (1994) [30]. The governing equations are non-dimensionalized, and the resulting system of non-linear differential equations is solved numerically. The results for the velocity profiles and the volume fraction profiles are presented. |
| Author | Massoudi, Mehrdad Zhao, Xinran |
| Author_xml | – sequence: 1 givenname: Xinran surname: Zhao fullname: Zhao, Xinran organization: Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA – sequence: 2 givenname: Mehrdad surname: Massoudi fullname: Massoudi, Mehrdad email: mehrdad.massoudi@netl.doe.gov organization: US Department of Energy, National Energy Technology Laboratory (NETL), P.O. Box 10940, Pittsburgh, PA 15236, USA |
| BackLink | https://www.osti.gov/biblio/1165429$$D View this record in Osti.gov |
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| CitedBy_id | crossref_primary_10_1063_5_0018694 crossref_primary_10_1016_j_ijnonlinmec_2017_01_004 crossref_primary_10_1007_s11440_023_02115_9 crossref_primary_10_1016_j_ijnonlinmec_2021_103717 crossref_primary_10_3390_fluids3030055 |
| Cites_doi | 10.1007/s001610050089 10.1016/j.mechrescom.2011.05.002 10.1016/0093-6413(94)90027-2 10.1016/j.ijnonlinmec.2004.05.012 10.1017/S002211209600050X 10.1007/BF01182541 10.2307/2371950 10.1016/0167-6636(93)90047-U 10.1017/S0022112084002883 10.1146/annurev.fl.22.010190.000421 10.1080/14786448508627791 10.1007/BF01174637 10.1007/BF01182546 10.1007/BF01176949 10.1016/S0065-2156(08)70047-4 10.1146/annurev.fluid.35.101101.161114 10.1016/0020-7225(90)90074-S 10.1007/BF01138303 10.1115/1.2897623 10.1016/S0020-7462(00)00027-5 10.1007/BF01175958 10.1017/S0022112085000167 10.1122/1.549893 10.2172/7221796 10.1017/S0022112083001044 10.1017/S0022112087000570 10.1115/1.3261343 10.1007/BF01140894 |
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| Keywords | Continuum mechanics Kinetic theory Granular materials Shear flow Slip boundary condition |
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| Snippet | We study the steady fully developed flow of granular materials between two horizontal flat plates, subject to slip at the walls. The constitutive model for the... |
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| SubjectTerms | Continuum mechanics Granular materials Kinetic theory Shear flow Slip boundary condition |
| Title | Flow of granular materials with slip boundary condition: A continuum–kinetic theory approach |
| URI | https://dx.doi.org/10.1016/j.amc.2014.05.093 https://www.osti.gov/biblio/1165429 |
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