Application of the Method of Generating Functions to the Derivation of Grad’s N-Moment Equations for a Granular Gas - Serero, Dan; Noskowicz, S. H. (Mathematical Modelling of Natural Phenomena, 2011)
A computer aided method using symbolic computations that enables the calculation of the source terms (Boltzmann) in Grad’s method of moments is presented. The method is extremely powerful, easy to program and allows the derivation of balance equations to very high moments (limited only by computer resources). For sake of demonstration the method is applied to a simple case: the one-dimensional stationary granular gas under gravity. The method should find applications in the field of rarefied gases, as well. Questions of convergence, closure are beyond the scope of this article.

Energy decay in a granular gas collapse - Almazan Torres, Lidia; Serero, Dan; Salueña, Clara; Pöschel, Thorsten (New Journal of Physics, 2017)
An inelastic hard ball bouncing repeatedly off the ground comes to rest in finite time by performing an infinite number of collisions. Similarly, a granular gas under the influence of external gravity, condenses at the bottom of the confinement due to inelastic collisions. By means of hydrodynamical simulations, we find that the condensation process of a granular gas reveals a similar dynamics as the bouncing ball. Our result is in agreement with both experiments and particle simulations, but disagrees with earlier simplified hydrodynamical description. Analyzing the result in detail, we find that the adequate modeling of pressure plays a key role in continuum modeling of granular matter.

Homogeneous cooling of mixtures of particle shapes - Hidalgo, Raúl Cruz; Serero, Dan; Pöschel, Thorsten (Physics of Fluids, 2016)
In this work, we examine theoretically the cooling dynamics of binary mixtures of spheres and rods. To this end, we introduce a generalized mean field analytical theory, which describes the free cooling behavior of the mixture. The relevant characteristic time scale for the cooling process is derived, depending on the mixture composition and the aspect ratio of the rods. We simulate mixtures of spherocylinders and spheres using a molecular dynamics algorithm implemented on graphics processing unit (GPU) architecture. We systematically study mixtures composed of spheres and rods with several aspect ratios and varying the mixture composition. A homogeneous cooling state, where the time dependence of the system’s intensive variables occurs only through a global granular temperature, is identified. We find cooling dynamics in excellent agreement with Haff’s law, when using an adequate time scale. Using the scaling properties of the homogeneous cooling dynamics, we estimated numerically the efficiency of the energy interchange between rotational and translational degrees of freedom for collisions between spheres and rods.

Homogeneous cooling state of dilute granular gases of charged particles - Takada, Satoshi; Serero, Dan; Pöschel, Thorsten (Physics of Fluids, 2017)
We describe the velocity distribution function of a granular gas of electrically charged particles by means of a Sonine polynomial expansion and study the decay of its granular temperature. We find a dependence of the first non trivial Sonine coefficient, a2 , on time through the value of temperature. In particular, we find a sudden drop of a2 when temperature approaches a characteristic value, T∗ , describing the electrostatic interaction. For lower values of T , the velocity distribution function becomes Maxwellian. The theoretical calculations agree well with numerical Direct Simulation Monte Carlo, to validate our theory.

Homogeneous cooling state of dilute granular gases of charged particles - Takada, Satoshi; Serero, Dan; Pöschel, Thorsten (Physics of Fluids, 2017)
We describe the velocity distribution function of a granular gas of electrically charged particles by means of a Sonine polynomial expansion and study the decay of its granular temperature. We find a dependence of the first non trivial Sonine coefficient, a2 , on time through the value of temperature. In particular, we find a sudden drop of a2 when temperature approaches a characteristic value, T∗, describing the electrostatic interaction. For lower values of T , the velocity distribution function becomes Maxwellian. The theoretical calculations agree well with numerical Direct Simulation Monte Carlo, to validate our theory.

Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution - Pöschel, Thorsten; Serero, Dan; Gunkelmann, Nina (Journal of Fluid Mechanics, 2015)
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.
Keywords: granular media; granular mixing; kinetic theory

Self-organized shocks in the sedimentation of a granular gas - Almazan Torres, Lidia; Serero, Dan; Salueña, Clara; Pöschel, Thorsten (Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2015)
A granular gas in gravity heated from below develops a certain stationary density profile. When the heating is switched off, the granular gas collapses. We investigate the process of sedimentation using computational hydrodynamics, based on the Jenkins-Richman theory, and find that the process is significantly more complex than generally acknowledged. In particular, during its evolution, the system passes several stages which reveal distinct spatial regions of inertial (supersonic) and diffusive (subsonic) dynamics. During the supersonic stages, characterized by Mach>1, the system develops supersonic shocks which are followed by a steep front of the hydrodynamic fields of temperature and density, traveling upward.
Keywords: granular gas

Stochastic Nature of Particle Collisions and its Impact on Granular Material Properties - Gunkelmann, Nina; Serero, Dan; Glielmo, Aldo; Montaine, Marina; Heckel, Michael; Pöschel, Thorsten (Particles in Contact: Micro Mechanics, Micro Process Dynamics and Particle Collective, 2019)
The dynamics of rapid granular flows is governed by dissipative interactions of particles with each other and with the system walls. To adequately describe these interactions, roughness and particle shape must be taken into account. The coefficient of restitution for arbitrary particles thus depends not only on material properties and impact velocity but also on the angular orientation at the instant of the collision. By measurements of the coefficient of restitution from the sound signal emitted by a sphere bouncing repeatedly off the ground, it was found that small deviations from the perfect shape of the sphere lead to large measurement errors. Using stochastic methods, the effective coefficient of restitution for the collision of a rough sphere with a plane was described as a fluctuating quantity, characterized by a rather uncommon probability density function. It was shown that modelling the coefficient of restitution as a stochastic variable significantly affects the dynamics of particles under rapid granular flows. The decay of temperature of rapid granular flows in the homogeneous cooling state deviates from Haff's law for gases of particles interacting via a constant coefficient of restitution also from the scaling law for gases of viscoelastic particles.<br

Temperature of a granular gas with regard to the stochastic nature of particle interactions - Gunkelmann, Nina; Serero, Dan; Pöschel, Thorsten (New Journal of Physics, 2013)
The decay of temperature of a force-free granular gas in the homogeneous cooling state depends on the specific model for particle interaction. For the case of rough spheres, in recent experimental and theoretical work, the coefficient of restitution was characterized as a fluctuating quantity. We show that for such particles, the decay of temperature with time follows the law which deviates from Haff's law, T ∼ t, obtained for gases of particles interacting via a constant coefficient of restitution also from obtained for gases of viscoelastic particles. Our results are obtained from kinetic theory and are in very good agreement with Monte Carlo simulations. © IOP Publishing and Deutsche Physikalische Gesellschaft.

Transport coefficients for granular gases of electrically charged particles - Takada, Satoshi; Serero, Dan; Pöschel, Thorsten (Journal of Fluid Mechanics, 2022)
We consider a dilute gas of electrically charged granular particles in the homogeneous cooling state. We derive the energy dissipation rate and the transport coefficients from the inelastic Boltzmann equation. We find that the deviation of the velocity distribution function from the Maxwellian yields overshoots of the transport coefficients, and especially, the negative peak of the Dufour-like coefficient, mu, in the intermediate granular temperature regime. We perform the linear stability analysis and investigate the granular temperature dependence of each mode, where the instability mode is found to change against the granular temperature. The molecular dynamics simulations are also performed to compare the result with that from the kinetic theory.
CRIS-Team WoS Importer:2022-02-11