Model of a gas of solid particles with allowance for inelastic collisions

Matveev, S. K.

doi:10.1007/bf01090735

Cited by 4 publications

(10 citation statements)

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“…The formation of such a layer, which has a finite density which is the maximal possible that may be achieved within granular media, constitutes a specific feature distinguishing non-conservative systems from molecular gases. This phenomenon was disregarded by Matveev (1983) who treated a related problem of sedimentation of a granular gas on a solid plate, where infinite gas density was obtained.…”

Section: Introductionmentioning

confidence: 99%

Mechanics of collisional motion of granular materials. Part 3. Self-similar shock wave propagation

1996

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Shock wave propagation arising from steady one-dimensional motion of a piston in a granular gas composed of inelastically colliding particles is treated theoretically. A self-similar long-time solution is obtained in the strong shock wave approximation for all values of the upstream gas volumetric concentration v0. Closed form expressions for the long-time shock wave speed and the granular pressure on the piston are obtained. These quantities are shown to be independent of the particle collisional properties, provided their impacts are accompanied by kinetic energy losses. The shock wave speed of such non-conservative gases is shown to be less than that for molecular gases by a factor of about 2.The effect of particle kinetic energy dissipation is to form a stagnant layer (solid block), on the surface of the moving piston, with density equal to the maximal packing density, vM. The thickness of this densely packed layer increases indefinitely with time. The layer is separated from the shock front by a fluidized region of agitated (chaotically moving) particles. The (long-time, constant) thickness of this layer, as well as the kinetic energy (granular temperature) distribution within it are calculated for various values of particle restitution and surface roughness coefficients. The asymptotic cases of dilute (v0 [Lt ] 1) and dense (v0 ∼ vM) granular gases are treated analytically, using the corresponding expressions for the equilibrium radial distribution functions and the pertinent equations of state. The thickness of the fluidized region is shown to be independent of the piston velocity.The calculated results are discussed in relation to the problem of vibrofluidized granular layers, wherein shock and expansion waves were registered. The average granular kinetic energy in the fluidized region behind the shock front calculated here compared favourably with that measured and calculated (Goldshtein et al. 1995) for vibrofluidized layers of spherical granules.

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Section: Introductionmentioning

confidence: 99%

Mechanics of collisional motion of granular materials. Part 3. Self-similar shock wave propagation

1996

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“…Shock waves in fluidised granular flows have been noticed in canonical compressible flow configurations using both molecular dynamics (Rericha et al. 2001; Padgett, Mazzoleni & Faw 2015; Sirmas & Radulescu 2015) and hydrodynamic (Matveev 1983; Goldshtein, Shapiro & Gutfinger 1996 a ; Kamenetsky et al. 2000; Rericha et al.…”

Section: Introductionmentioning

confidence: 99%

“…2004; Khan et al. 2020), in both one-dimensional (Matveev 1983; Goldshtein et al. 1996 a ; Kamenetsky et al.…”

Section: Introductionmentioning

confidence: 99%

“…2000; Sirmas & Radulescu 2015, 2019). In the moving-piston frame of reference, this problem is identical to a granular gas colliding with a fixed wall, a configuration that was studied by Matveev (1983) assuming zero granular temperature for the oncoming flow in front of the shock and steady-state conditions. Similar to molecular gas, the jump relations across the shock showed that both pressure and density increase while the absolute velocity decreases.…”

Section: Introductionmentioning

confidence: 99%

“…In the region behind the shock, the analytical solution showed that both pressure and density increase monotonically whereas the absolute velocity decreases to become zero at the wall. Matveev (1983) allowed the density behind the shock to become infinite at the wall because the used equation of state does not take into account the volumetric effects due to the size of the particles. This shortcoming was later avoided in a study of the moving-piston problem where Goldshtein et al.…”

Section: Introductionmentioning

confidence: 99%

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