Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution

2015 ◽  
Vol 781 ◽  
pp. 595-621 ◽  
Author(s):  
D. Serero ◽  
N. Gunkelmann ◽  
T. Pöschel
Keyword(s):  
Constitutive Relations ◽  
Transport Coefficients ◽  
Coefficient Of Restitution ◽  
Granular Gases ◽  
Hydrodynamic Description ◽  
Perturbative Method ◽  
Binary Collisions ◽  
Computer Aided ◽  
Stochastic Coefficient ◽  
Polynomial Expansions

A hydrodynamic description of dilute binary gas mixtures comprising smooth inelastic spheres interacting by binary collisions with a random coefficient of restitution is presented. Constitutive relations are derived using the Chapman–Enskog perturbative method, associated with a computer-aided method to allow high-order Sonine polynomial expansions. The transport coefficients obtained are checked against DSMC simulations. The resulting equations are applied to the analysis of a vertically vibrated system. It is shown that differences in the shape of the distributions of the coefficient of restitution are sufficient to produce partial segregation.

scholarly journals A panoply of Schwinger-Keldysh transport

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Kristan Jensen ◽  
Raja Marjieh ◽  
Natalia Pinzani-Fokeeva ◽  
Amos Yarom
Keyword(s):  
Effective Action ◽  
Constitutive Relations ◽  
Transport Coefficients ◽  
Second Law ◽  
Relativistic Fluids ◽  
Hydrodynamic Description ◽  
Onsager Relations ◽  
Statistical Mechanical ◽  
Classical Hydrodynamic

We classify all possible allowed constitutive relations of relativistic fluids in a statistical mechanical limit using the Schwinger-Keldysh effective action for hydrodynamics. We find that microscopic unitarity enforces genuinely new constraints on the allowed transport coefficients that are invisible in the classical hydrodynamic description; they are not implied by the second law or the Onsager relations. We term these conditions Schwinger-Keldysh positivity and provide explicit examples of the various allowed terms.

scholarly journals Hydrodynamic magneto-transport in holographic charge density wave states

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Andrea Amoretti ◽  
Daniel Areán ◽  
Daniel K. Brattan ◽  
Luca Martinoia
Keyword(s):  
Black Hole ◽  
Transport Coefficients ◽  
Density Wave ◽  
Thermo Electric ◽  
Hydrodynamic Description ◽  
Dc Conductivities ◽  
Analytic Expressions ◽  
Wave States ◽  
Hole Geometry ◽  
Gauge Gravity

Abstract We employ hydrodynamics and gauge/gravity to study magneto-transport in phases of matter where translations are broken (pseudo-)spontaneously. First we provide a hydrodynamic description of systems where translations are broken homogeneously at nonzero lattice pressure and magnetic field. This allows us to determine analytic expressions for all the relevant transport coefficients. Next we construct holographic models of those phases and determine all the DC conductivities in terms of the dual black hole geometry. Combining the hydrodynamic and holographic descriptions we obtain analytic expression for the AC thermo-electric correlators. These are fixed in terms of the black hole geometry and a pinning frequency we determine numerically. We find an excellent agreement between our hydrodynamic and holographic descriptions and show that the holographic models are good avatars for the study of magneto-phonons.

scholarly journals Dissipation in holographic superfluids

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Aristomenis Donos ◽  
Polydoros Kailidis ◽  
Christiana Pantelidou
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Chemical Potential ◽  
Constitutive Relations ◽  
Transport Coefficients ◽  
Heat Current ◽  
Goldstone Mode ◽  
Thermodynamic Quantities ◽  
Conserved Current ◽  
Dissipative Terms

Abstract We study dissipation in holographic superfluids at finite temperature and zero chemical potential. The zero overlap with the heat current allows us to isolate the physics of the conserved current corresponding to the broken global U(1). By using analytic techniques we write constitutive relations including the first non-trivial dissipative terms. The corresponding transport coefficients are determined in terms of thermodynamic quantities and the black hole horizon data. By analysing their behaviour close to the phase transition we show explicitly the breakdown of the hydrodynamic expansion. Finally, we study the pseudo-Goldstone mode that emerges upon introducing a perturbative symmetry breaking source and we determine its resonant frequency and decay rate.

scholarly journals Universality of shear-banding instability and crystallization in sheared granular fluid

2008 ◽  
Vol 615 ◽  
pp. 293-321 ◽  
Author(s):  
MEHEBOOB ALAM ◽  
PRIYANKA SHUKLA ◽  
STEFAN LUDING
Keyword(s):  
Constitutive Model ◽  
Constitutive Relations ◽  
Shear Banding ◽  
Transport Coefficients ◽  
Navier Stokes ◽  
Dynamic Friction ◽  
Homogeneous State ◽  
Band Formation ◽  
Uniform Shear ◽  
Uniform Shear Flow

The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier–Stokes-level constitutive model in which we incorporate the global equation of states for pressure and thermal conductivity (which are accurate up to the maximum packing density νm) and the shear viscosity is allowed to diverge at a density νμ (<νm), with all other transport coefficients diverging at νm. It is shown that the emergence of shear-banding instabilities (for perturbations having no variation along the streamwise direction), that lead to shear-band formation along the gradient direction, depends crucially on the choice of the constitutive model. In the framework of a dense constitutive model that incorporates only collisional transport mechanism, it is shown that an accurate global equation of state for pressure or a viscosity divergence at a lower density or a stronger viscosity divergence (with other transport coefficients being given by respective Enskog values that diverge at νm) can induce shear-banding instabilities, even though the original dense Enskog model is stable to such shear-banding instabilities. For any constitutive model, the onset of this shear-banding instability is tied to a universal criterion in terms of constitutive relations for viscosity and pressure, and the sheared granular flow evolves toward a state of lower ‘dynamic’ friction, leading to the shear-induced band formation, as it cannot sustain increasing dynamic friction with increasing density to stay in the homogeneous state. A similar criterion of a lower viscosity or a lower viscous-dissipation is responsible for the shear-banding state in many complex fluids.

scholarly journals Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

2021 ◽  
Vol 249 ◽  
pp. 04005
Author(s):  
Vicente Garzó ◽  
Ricardo Brito ◽  
Rodrigo Soto
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Transport Coefficients ◽  
Nonlinear Dependence ◽  
Granular Gases ◽  
Two Dimensional ◽  
Hydrodynamic Equations ◽  
Homogeneous Steady State ◽  
Granular Fluid ◽  
The Stability

A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the system after a transient regime. In contrast to previous studies (which considered dilute or quasielastic systems), our analysis is based on the results obtained from the inelastic Enskog kinetic equation, which takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on dissipation and applies to moderate densities. As in earlier studies, the analysis shows that the HSS is linearly stable with respect to long enough wavelength excitations.

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