Abstract
Constitutive relations are derived for a gas-particle suspension in which the particles are subject to a fluid velocity field, and experience inter-particle collisions. The flow is driven by two types of energy sources, an imposed mean shear and fluid velocity fluctuations, in the limit where the time between collisions τc is small compared to the viscous relaxation time τv, so that the dissipation of energy between collisions is small compared to the energy of a particle. Constitutive relations from the kinetic theory of dense gases are used when the flow is driven by the mean shear. The effect of fluid velocity fluctuations is incorporated using an additional diffusive term in the Boltzmann equation for the particle velocity distribution, and this leads to an additional ‘diffusino’ stress.
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References
S.B. Savage and D.J. Jeffrey, 1981, The stress tensor in a granular flow at high shear rates, J. Fluid Mech., 110, 255–272.
J.T. Jenkins and S.B. Savage, 1983, A theory for the rapid flow of identical, smooth, nearly elastic particles, J. Fluid Mech., 130, 186–202.
C.K.K. Lun, S.B. Savage, D.J. Jeffrey and N. Chepurnity, 1984, Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field, J. Fluid Mech., 140, 223–256.
J.T. Jenkins and M.W. Richman, 1985, Grad’s 13 — Moment system for a dense gas of inelastic spheres, Arch. Rat. Mech. Anal., 87, 355–377.
N. Sela, I. Goldhirsch and S. H. Noskowicz, 1996, Kinetic theoretical study of a simply sheared two dimensional granular gas to Burnett order, Phys. Fluids, 8, 2337.
N. Sela and I. Goldhirsch, 1998, Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order, J. Fluid Mech., 361, 41–74.
V. Kumaran, 2004, Constitutive relations and linear stability of a sheared granular flow, J. Fluid Mech., 506, 1.
D.L. Koch, 1990, Kinetic theory for a monodisperse gas-solid suspension, Phys. Fluids A, 6, 2894–2899.
V. Kumaran and D.L. Koch, 1993, Properties of a bidisperse particle-gas suspension. Part 1. Collision time small compared to viscous relaxation time, J. Fluid Mech., 247, 623–642.
V. Kumaran and D.L. Koch, 1993, Properties of a bidisperse particle-gas suspension. Part 2. Viscous relaxation time small compared to collision relaxation time, J. Fluid Mech., 247, 643–660.
H.-K. Tsao and D.L. Koch, 1995, Shear flows of a dilute gas-solid suspension, J. Fluid Mech., 296, 211–245.
A.S. Sangani, G. Mo, H.-K. Tsao and D.L. Koch, 1996, Simple shear flows of dense gas-solid suspensions at finite Stokes numbers, J. Fluid Mech., 313, 309–341.
S. Chapman and T.G. Cowling, 1970, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, London.
V. Kumaran, 2003, Stability of a sheared particle suspension, Phys. Fluids, 15, 3625.
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Kumaran, V. (2006). Effect of Fluid Velocity Fluctuations on the Dynamics of a Sheared Gas-Particle Suspension. In: Balachandar, S., Prosperetti, A. (eds) IUTAM Symposium on Computational Approaches to Multiphase Flow. Fluid Mechanics and Its Applications, vol 81. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4977-3_41
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DOI: https://doi.org/10.1007/1-4020-4977-3_41
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