Non-monotonic Mpemba effect in binary molecular suspensions

United States

The Mpemba effect is a phenomenon in which an initially hotter sample cools sooner. In this paper, we show the emergence of a non-monotonic Mpemba-like effect in a molecular binary mixture immersed in a viscous gas. Namely, a crossover in the temperature evolution when at least one of the samples presents non-monotonic relaxation. The influence of the bath on the dynamics of the particles is modeled via a viscous drag force plus a stochastic Langevin-like term. Each component of the mixture interchanges energy with the bath depending on the mechanical properties of its particles. This discrimination causes the coupling between the time evolution of temperature with that of the partial temperatures of each component. The non-monotonic Mpemba effect—and its inverse and mixed counterparts—stems from this coupling. In order to obtain analytical results, the velocity distribution functions of each component are approximated by considering multitemperature Maxwellian distributions. The theoretical results derived from the Enskog kinetic theory show an excellent agreement with direct simulation Monte Carlo (DMSC) data.

Powders &amp; Grains 2021

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Powders & Grains 2021

Powders & Grains 2021 will be held in Buenos Aires (Argentina, VIRTUAL) July 5, 13, 21, 29 and Aug 6, 2021. The aim of the conference is to give an up-to-date picture of the broad research field of granular media, powders and grains. Contributions from experts around the world will focus on research topics that cover a wide range of open problems in the field.

technical paper

Flowing grains can clog an orifice by developing arches, an undesirable event in many cases. Several strategies have been put forward to avoid this. One of them is to vibrate the system in order to undo the clogging. Nevertheless, the time taken to break an arch under a constant vibration has a distribution displaying a heavy tail. This can lead to a situation where the average breaking time is not well defined. Moreover, it has been observed in some experiments that these tails tend to flatten for very long times, exacerbating the problem. Here we will review two conceptual frameworks that have been proposed to understand the phenomenon and discuss their physical implications.

On the broad tails in breaking time distributions of vibrated clogging arches

The aim of this work is to explore the capability of the μ(I)-rheology model and its numerical implementation in addressing a silo discharge problem by computational simulation. In order to do so, the model was implemented in the general structure of an Eulerian multiphase solver based on the Volume-Of-Fluid (VOF) method of the
OpenFOAM(R) suite. First, the implementation is validated against the results of another Lagrangian and Eulerian codes in a two-dimensional discharge problem. After that, the model is tested against the experimental results of a lab-scale and industrial-scale discharge problem. While the results of the first one were satisfactory in terms of discharge rate, for the latter one, the model exhibits disagreements in the flow patterns inside the silo. The study shows the limits of applicability of the standard formulation of the model for real scale silos and sets the ground for further discussion and improvements.

The performance of the μ(I)-rheology model on flat bottom silos discharge

Granular dilatancy has been previously characterised through a simple linear relationship between the packing fraction and dimensionless shear rate. However, this relationship was developed for granular flows in a simple shear cell geometry. Here we examine volume changes in a shear cell with gravity and a vertical chute. In so doing, we show that the packing fraction displays both a local and non-local response, analogous to what is typically observed for the stress ratio μ. We then extend this analysis, looking at the direct connection between the packing fraction and the stress ratio, as well as how these variables behave in a more complex system, specifically a pseudo 2D hopper.

Evidence of a non-local φ(I) response

Particle size segregation is ubiquitous in granular systems with differently sized constituents but is found to diminish in the presence of viscous ambient fluids. We study this inhibiting effect through coupled fluid-particle numerical 
simulations. It is found that size segregation is indeed slower in the presence 
of fluid and this effect becomes more significant as fluid viscosity is increased. Direct calculation of segregation forcing terms reveal that the ambient fluids affect segregation in two major ways: buoyant forces reduce contact pressures, while viscous dissipation diminish particle-fluctuation driven kinetic pressures, 
both of which are necessary in driving large particles up. Surprisingly, the fluid drag in the normal direction is negligible regardless of the fluid viscosity and does not directly affect segregation.

Mechanisms of size segregation in granular flows with different ambient fluids

Granular dampers are passive devices used to attenuate mechanical vibrations. The most common configuration consists in an enclosure, partially filled with particles, attached to the vibrating structure that needs to be damped. The energy is dissipated due to inelastic collisions and friction between the grains and between the grains and the inner walls of the container as the structure vibrates. As a result of the collisions, the mechanical response of the system often results in chaotic motion even if the driving is harmonic. Despite the vibration attenuation achieved, this chaotic response may render the granular damper unsuitable for a range of applications. In this work, we showcase two simple modifications of the enclosure design that are able to mitigate the chaotic response of the granular damper. To this end we use Discrete Element Method simulations of: (a) a granular damper with a conical base, and (b) a granular damper with obstacles fixed inside the enclosure. We compare results against a standard flat-base enclosure damper. The basic mechanical response of the dampers is characterized by measuring the apparent mass and the loss factor. The suppression of the chaotic response is assessed qualitatively via the phase space diagram.

Avoiding chaos in granular dampers

Rock particle shape plays a crucial role in influencing shear resistance and energy consumption during transient loads. The dynamics of such granular materials are complex and cannot be properly described using closed-form solutions when the problem involves more than a few particles. Thus, for the sake of computational efficiency, it is common practice to implement simplified numerical models that involve a limited number of particle interactions. In this study, a novel approach is used to capture realistic particle shapes while maintaining a relatively high simulation efficiency. The geometry of the particles is determined by a Delaunay triangulation which operates on a set of vertices and returns the corresponding network of facets and grid connections. Inertial and material properties are assigned to the rock prototype which are representative of realistic gravel particles. The algorithm is validated by performing a series of numerical simulations for various particle configurations, demonstrating that mass and momentum are conserved. A potential application of this work is related to rockfall barriers and their response to rigid boulder impacts. This innovative model, based on the discrete element method (DEM), is shown to be capable of simulating rock particles with realistic shapes and complex physical interactions.

DEM modelling of 3D polyhedra with applications to gabion rockfall barriers

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.

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

I am interested in the evaluation of debris flow impact on structures. I developed a discrete numerical model able to simulate such impacts at the scale of the close surrounding of the structure. The largest particles carried by the flow are modelled explicitly using Distinct Element Method and the finer solid particles are integrated in a fluid phase, which induces two interactions on the largest particles, i.e. buoyancy and drag. The fields of fluid velocity and of fluid free surface are obtained from Computational Fluid Dynamics code then imported in the DEM simulation in a one way coupling scheme. For the results, the influence of particle shape on the impact forces generated on the obstacle is investigated: spherical particles and polygonal rigid blocks (r-blocks) are considered. The shape of the particle influences the contact surface and therefore the impact pressure. With an angular shape and several facets like r-blocks, the impact pressure on an obstacle is more important for a flow with the same characteristics.

Influence of the particle shape on the impact force of lahar on an obstacle

We study the influence of particle shape on the evolution of particle breakage process taking place inside rotating cylinders. Extensive particle dynamics simulations taking into account the dynamics of the granular flow, particle breakage, and polygonal particle shapes were carried out. We find that the rate of particle breakage is faster in samples composed of initially rounder particles. The analysis of the active flowing layer thickness suggests that for samples composed of rounder particles a relatively lower dilatancy and higher connectivity lead to a less curved free surface profile. As a result, rounder particles rolling down the free surface have a higher mobility and thus higher velocities. In consequence, the faster breakage observed for rounder initial particles is due to the larger particles kinetic energy at the toe of the flow.

Effect of particle shape on particle breakage inside rotating cylinders

Size limitations of geotechnical testing equipment often require that samples of coarse granular materials have to be scaled in order to be tested in the laboratory. Scaling implies a convenient modification of the particle size distribution (PSD) to reduce particle sizes. However, it is well known that particle size and shape may be correlated in nature, due to geological factors (as an example). By means of two-dimensional contact dynamics simulations, we analyzed the e↵ect of altering the size span on the shear strength of granular materials when particle size and shape are correlated. Two di↵erent systems were considered: one made of only circular particles, and the second made of size-shape correlated particles. By varying systematically the size span we observed that the resulting alteration of material strength is not due to the change in particle sizes. It results instead from the variation of the particle shapes induced by the modification of the PSD, when particle size and particle shape are correlated. This finding suggests that particle shape distribution is a higher order factor than PSD for the shear strength of granular materials. It also highlights the importance of particle shape quantification in soil classification and the case for its consideration in activities such as sampling, sub- sampling, and scaling of coarse materials for geotechnical testing

Non-monotonic Mpemba effect in binary molecular suspensions

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Non-monotonic Mpemba effect in binary molecular suspensions

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On the broad tails in breaking time distributions of vibrated clogging arches

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DEM examination of SPT correction factors

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