Flow of granular materials with slip boundary condition: A continuum–kinetic theory approach

• Published in: Applied mathematics and computation Vol. 242; pp. 518 - 527
• Main Authors: Zhao, Xinran, Massoudi, Mehrdad
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.09.2014
• Subjects: Continuum mechanics; Granular materials; Kinetic theory; Shear flow; Slip boundary condition; Continuum mechanics; Kinetic theory; Granular materials; Shear flow; Slip boundary condition
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2014.05.093

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.