Transition models from the quenched to ignited states for flows of inertial particles suspended in a simple sheared viscous fluid

Parmentier, Jean-François; Simonin, Olivier

doi:10.1017/jfm.2012.381

Cited by 10 publications

(6 citation statements)

References 7 publications

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“…39, and later extended by Ref. 31. In the KTGF formulation, granular viscosity is due to particle agitation and can be calculated with collision integrals.…”

Section: B Agitation Of the Particulate Phasementioning

confidence: 99%

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Inertia-driven particle migration and mixing in a wall-bounded laminar suspension flow

et al. 2015

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International audienceLaminar pressure-driven suspensionflows are studied in the situation of neutrally buoyant particles at finite Reynolds number. The numerical method is validated for homogeneous particle distribution (no lateral migration across the channel): the increase of particle slip velocities and particle stress with inertia and concentration is in agreement with former works in the literature. In the case of a two-phase channel flow with freely moving particles, migration towards the channel walls due to the Segré-Silberberg effect is observed, leading to the development of a non-uniform concentration profile in the wall-normal direction (the concentration peaks in the wall region and tends towards zero in the channel core). The particle accumulation in the region of highest shear favors the shear-induced particle interactions and agitation, the profile of which appears to be correlated to the concentration profile. A 1D model predicting particle agitation, based on the kinetic theory of granular flows in the quenched state regime when Stokes number St = O(1) and from numerical simulations when St < 1, fails to reproduce the agitation profile in the wall normal direction. Instead, the existence of secondary flows is clearly evidenced by long time simulations. These are composed of a succession of contra-rotating structures, correlated with the development of concentration waves in the transverse direction. The mechanism proposed to explain the onset of this transverse instability is based on the development of a lift force induced by spanwise gradient of the axial velocity fluctuations. The establishment of the concentration profile in the wall-normal direction therefore results from the combination of the mean flow Segré-Silberberg induced migration, which tends to stratify the suspension and secondary flows which tend to mix the particles over the channel cross section

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“…39, and later extended by Ref. 31. In the KTGF formulation, granular viscosity is due to particle agitation and can be calculated with collision integrals.…”

Section: B Agitation Of the Particulate Phasementioning

confidence: 99%

“…In homogeneous shear flow, λ(St) can be calculated from the equilibrium between the production (second term of Eq. 14) and dissipation (third term), the granular temperature given from the quenched state theory, 31,39 T * = T (γa)…”

Section: B Agitation Of the Particulate Phasementioning

confidence: 99%

Inertia-driven particle migration and mixing in a wall-bounded laminar suspension flow

et al. 2015

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“…1996; Wylie et al. 2009; Parmentier & Simonin 2012; Heussinger 2013; Wang et al. 2014; Saha & Alam 2017; Alam, Saha & Gupta 2019; Saha & Alam 2020) only consider the Stokes linear drag law for gas–solid interactions.…”

Section: Introductionmentioning

confidence: 99%

“…Tsao & Koch 1995; Sangani et al. 1996; Parmentier & Simonin 2012; Heussinger 2013; Seto et al. 2013; Kawasaki, Ikeda & Berthier 2014; Chamorro, Vega Reyes & Garzó 2015; Hayakawa, Takada & Garzó 2017; Saha & Alam 2017; Alam et al.…”

Section: Introductionmentioning

confidence: 99%

“…In this context and assuming nearly instantaneous collisions, the influence of gas-phase effects on the dynamics of solid particles is usually incorporated in the starting kinetic equation in an effective way via a fluid-solid interaction force (Koch 1990;Gidaspow 1994;Jackson 2000). Some models for granular suspensions (Louge, Mastorakos & Jenkins 1991;Tsao & Koch 1995;Sangani et al 1996;Wylie et al 2009;Parmentier & Simonin 2012;Heussinger 2013;Wang et al 2014;Saha & Alam 2017;Alam, Saha & Gupta 2019;Saha & Alam 2020) only consider the Stokes linear drag law for gas-solid interactions. Other models (Garzó et al 2012) include also an additional Langevin-type stochastic term.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic theory of granular particles immersed in a molecular gas

González

Garzó

2022

J. Fluid Mech.

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The transport coefficients of a dilute gas of inelastic hard spheres immersed in a gas of elastic hard spheres (molecular gas) are determined. We assume that the number density of the granular gas is much smaller than that of the surrounding molecular gas, so that the latter is not affected by the presence of the granular particles. In this situation, the molecular gas may be treated as a thermostat (or bath) of elastic hard spheres at a fixed temperature. The Boltzmann kinetic equation is the starting point of the present work. The first step is to characterise the reference state in the perturbation scheme, namely the homogeneous state. Theoretical results for the granular temperature and kurtosis obtained in the homogeneous steady state are compared against Monte Carlo simulations showing a good agreement. Then, the Chapman–Enskog method is employed to solve the Boltzmann equation to first order in spatial gradients. In dimensionless form, the Navier–Stokes–Fourier transport coefficients of the granular gas are given in terms of the mass ratio $m/m_g$ ( $m$ and $m_g$ being the masses of a granular and a gas particle, respectively), the (reduced) bath temperature and the coefficient of restitution. Interestingly, previous results derived from a suspension model based on an effective fluid–solid interaction force are recovered in the Brownian limit ( $m/m_g \to \infty$ ). Finally, as an application of the theory, a linear stability analysis of the homogeneous steady state is performed showing that this state is always linearly stable.

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Revisiting ignited–quenched transition and the non-Newtonian rheology of a sheared dilute gas–solid suspension

Saha

Alam

2017

J. Fluid Mech.

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The hydrodynamics and rheology of a sheared dilute gas-solid suspension, consisting of inelastic hard-spheres suspended in a gas, are analysed using anisotropic Maxwellian as the single particle distribution function. The closed-form solutions for granular temperature (T ) and three invariants of the second-moment tensor are obtained as functions of the Stokes number (St), the mean density (ν) and the restitution coefficient (e). Multiple states of high and low temperatures are found when the Stokes number is small, thus recovering the "ignited" and "quenched" states, respectively, of Tsao & Koch (J. Fluid Mech.,1995, vol. 296, pp. 211-246). The phase diagram is constructed in the three-dimensional (ν, St, e)-space that delineates the regions of ignited and quenched states and their coexistence. Analytical expressions for the particle-phase shear viscosity and the normal stress differences are obtained, along with related scaling relations on the quenched and ignited states. At any e, the shear-viscosity undergoes a discontinuous jump with increasing shear rate (i.e. discontinuous shear-thickening) at the "quenchedignited" transition. The first (N 1 ) and second (N 2 ) normal-stress differences also undergo similar first-order transitions: (i) N 1 jumps from large to small positive values and (ii) N 2 from positive to negative values with increasing St, with the sign-change of N 2 identified with the system making a transition from the quenched to ignited states. The superior prediction of the present theory over the standard Grad's method and the Chapman-Enskog solution is demonstrated via comparisons of transport coefficients with simulation data for a range of Stokes number and restitution coefficient.

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Transition models from the quenched to ignited states for flows of inertial particles suspended in a simple sheared viscous fluid

Cited by 10 publications

References 7 publications

Inertia-driven particle migration and mixing in a wall-bounded laminar suspension flow

Inertia-driven particle migration and mixing in a wall-bounded laminar suspension flow

Kinetic theory of granular particles immersed in a molecular gas

Revisiting ignited–quenched transition and the non-Newtonian rheology of a sheared dilute gas–solid suspension

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