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Granular flows are frequently observed in nature and appear in many industrial processes as well. In this numerical work the focus is mainly directed at the understanding of how the change of different grain properties, such as shape, friction and stiffness, influences the flow out of a silo. However, the heating dynamics of a granular gas of rods is also analyzed. In all these scenarios, the simulations are paired with experiments to calibrate and validate the results. The numerical analysis indicated that the discharge of soft, low-friction grains from a container exhibits a height-dependent flow rate, which is not usual for granular media. The systematic study mapped the parameter space of particle friction and stiffness, exploring the system’s macroscopic response in detail. Moreover, the examination of the coarse-graining fields helped us to explain when and why the flow rate depends on the column height. The answers include the material response to pressure gradients, but also the way stress is transmitted in the system. The outcomes allowed us to propose simple theoretical arguments, connecting the macroscopic flow rate with the pressure gradient at the orifice. As a result, we have come up with a well-reasoned explanation for the height-dependent discharge flow rate, shown experimentally and numerically by soft low-frictional grains. Our numerical investigation of a 2D silo flow of mixtures of soft and hard grains reproduced the high impact that even 5% of hard frictional grains have on the flow of an ensemble of low-friction, soft particles. Numerical results signaled the importance of the friction between the two types of grains. When the frictional hard grains are added to the soft grains, the flow gets slower, clogging becomes more frequent, and the force measured on the bottom plate decreases. Moreover, we obtained that these effects are enhanced when the interspecies friction is increased. The introduction of a rotational shear through the rotation of the flat silo bottom leads to a surprising effect on the discharge of rods: the flow rate is reduced significantly, by up to 70%. Our simulations and the application of the coarse-graining methods reveal the underlying reasons for this observation. The exit velocity of particles is the main contributing factor to this drop, which is in correlation with the vertical orientation of the grains. Our numerical tool allowed the exploration of the dependence of flow rate 𝑄 on the orifice size 𝐷. In the limit of large orifices, the classical power-law correlation 𝑄 ∼ 𝐷5/2 was reproduced. For small apertures, however, we obtained a power-law relation but with a notably larger exponent. Furthermore, the size of the so-called free fall arch region is also found to decrease due to the rotation. Finally, granular gas made up of rods and heated by the walls has been studied numerically. Our study provides additional insight into the process for instance by describing the system behavior in the non-symmetrically heated direction, which was not accessible experimentally. The velocity distributions of the particles are examined and found to be well-fitted by stretched exponential distributions, in agreement with previous experiments. Moreover, in the experimentally not accessible direction, we obtained asymmetrical distribution tails. Additionally, the collapsing of the velocity distributions lead us to conclude that the energy scales with the square of the characteristic velocity of the wall. Los flujos granulares se observan con frecuencia en procesos naturales e industriales. El enfoque de este trabajo se dirige a la comprensión de cómo el cambio de las diferentes propiedades de los granos (forma, fricción y rigidez) influye en el caudal de los silos. Complementariamente, se analiza la dinámica del calentamiento de un gas granular de partículas alargadas. En todos estos escenarios, las simulaciones se combinan con experimentos para calibrar y validar las herramientas numéricas empleadas. En primer lugar, el análisis numérico de la descarga de granos blandos-lisos de un contenedor indicó el desarrollo de un caudal másico dependiente de la altura, lo cual no es habitual en los medios granulares. Nuestro estudio sistemático examinó el espacio de parámetros de fricción y rigidez de las partículas, explorando detalladamente la respuesta macroscópica de este sistema. Complementariamente, el análisis de los campos medios nos ayudó a explicar cuándo y por qué el caudal depende de la altura de la columna. La explicación general incluye: la respuesta del material a los gradientes de presión en el orificio de salida, pero también la forma en que se transmiten los esfuerzos en el sistema. Los resultados nos permitieron proponer argumentos teóricos simples, conectando el caudal macroscópico con el gradiente de presión en el orificio. Como resultado, hemos encontrado una explicación bien razonada de los valores de caudal dependiente de la altura, lo cual ha sido encontrado, experimental y numéricamente, para granos blandos de baja fricción. En segundo lugar, realizamos una investigación numérica del flujo en un silo bidimensional, usando una de mezclas de granos blandos-lisos y duros-rugosos. Partiendo de un sistema homogéneo de granos blandos-lisos, nuestros resultados numéricos reproducen el alto impacto que produce la inclusión de solo un 5% de los granos duros, en el flujo del conjunto de partículas. Además, resaltaron la importancia de la fricción entre granos de diferente tipo, en le desarrollo de este proceso. Cuando los granos durosrugosos son agregados al sistema, el flujo se vuelve más lento, los atascos resultan más frecuentes y la fuerza medida sobre el fondo disminuye. Además, resulta que estos efectos se potencian cuando aumenta la fricción entre especies. También estudiamos, sistemáticamente, la introducción de esfuerzos cortantes, imponiendo la rotación del fondo de un silo plano. Estas condiciones de contorno producen un efecto sorprendente en la descarga de partículas alargadas: el caudal se reduce significativamente, hasta en un 70%. Nuestras simulaciones y la aplicación de los métodos de promediación espacio-temporales revelan las razones subyacentes de esta observación. La velocidad de salida de las partículas es el principal factor que contribuye a esta caída, lo cual correlaciona con la orientación vertical de los granos. Nuestra herramienta numérica permitió explorar la dependencia del caudal 𝑄 del tamaño del orificio 𝐷. En el límite de los orificios grandes, se reprodujo la clásica correlación de ley de potencia 𝑄 ∼ 𝐷5/2. Sin embargo, para aberturas pequeñas obtuvimos una ley de potencia pero con un exponente notablemente mayor. Además, también se encontró que el tamaño de la región denominada ”arco de caída libre” disminuye debido a la rotación. Finalmente, se ha estudiado numéricamente un gas granular agitado formado por partículas alargadas. Este sistema fue estudiado experimentalmente con anterioridad, y nuestro estudio proporciona información adicional sobre el proceso. Por ejemplo, describiendo el comportamiento del sistema en la dirección de calentamiento asimétrico, al que no se accedió experimentalmente. Se estudiaron las distribuciones de velocidad de las partículas, encontrando que ajustan muy bien con distribuciones exponenciales con colas largas, lo cual está en acuerdo con experimentos previos. Además, en la dirección no accesible experimentalmente, obtuvimos colas asimétricas. El colapso de las distribuciones de velocidad nos lleva a concluir que la energía media del sistema escala con el cuadrado de la velocidad característica de la pared.

In the present work, we investigate experimentally and numerically the motion of solid macroscopic spheres (Brownian and colloidal effects are negligible) when settling from rest in a quiescent fluid toward a solid wall under confined and unconfined configurations. Particle trajectories for spheres of two types of materials are measured using a high-speed digital camera. For unconfined configurations, our experimental findings are in excellent agreement with well-established analytical frameworks, used to describe the forces acting on the sphere. Besides, the experimental values of the terminal velocity obtained for different confinements are also in very good agreement with previous theoretical formulations. Similar conditions are simulated using a resolved CFD-DEM approach. After adjusting the parameters of the numerical model, we analyze the particle dynamic under several confinement conditions. The simulations results are contrasted with the experimental findings, obtaining a good agreement. We analyze several systems varying the radius of the bead and show the excellent agreement of our results with previous analytical approaches. However, the results indicate that confined particles have a distinct dynamics response when approaching the wall. Consequently, their motion cannot be described by the analytical framework introduced for the infinite system. Indeed, the confinement strongly affects the spatial scale where the particle is affected by the bottom wall and, accordingly, the dimensionless results can not be collapsed in a single master curve, using the particle size as a characteristic length. Alternatively, we rationalize our findings using a kinematic approximation to highlight the relevant scale of the problem. Our outcomes suggest it is possible to determine a new spatial scale to describe the collisional process, depending on the specific confining conditions.

We present a critical comparative analysis between numerical and experimental results of quasi-two-dimensional silo and hopper flows. In our approach, the Discrete Element Method was employed to describe a single-layer mono-disperse sphere confined by two parallel walls with an orifice at the bottom. As a first step, we examined the discharge process, varying the size of the outlet and the hopper angle. Next, we set the simulation parameters fitting the experimental flow rate values obtained experimentally. Remarkably, the numerical model captured the slight non-monotonic dependence of the flow rate with the hopper angle, which was detected experimentally. Additionally, we analyzed the vertical velocity and solid fractions profiles at the outlet numerically and experimentally. Although numerical results also agreed with the experimental observations, a slight deviation appeared systematically between both approaches. Finally, we explored the impact of the system’s confinement on this process, examining the consequences of particle-particle and particle-wall friction on the system macroscopic response. We mainly found that the degree of confinement and particle-wall friction have a relevant impact on the outflow dynamics. Our analysis demonstrated that the naive 2D approximation of this 3D flow process fails to describe it accurately.

Este proyecto consiste en el análisis de la dinámica de un proyectil en un medio granular denso para su puesta en práctica en un contexto de Bachillerato Internacional (BI). El punto de partida del proyecto son unos datos que se obtienen mediante simulación software facilitados por el Departamento de Física y Matemática Aplicada de la Universidad de Navarra y que otorgan información sobre el movimiento de un cuerpo esférico en un medio granular denso a lo largo de la dirección de la gravedad. En este Trabajo Final de Máster se analizan estos datos para el caso de gravedad cero y se lleva a cabo un estudio crítico apoyándonos en la ecuación de movimiento que define la dinámica del proyectil en el medio dado. También se desarrolla el código que mejor defina el comportamiento de un proyectil a lo largo del medio granular, el cual se valida con los datos proporcionados. Al mismo tiempo, se va a desarrollar una propuesta didáctica a través del Proyecto del Grupo 4 enfocándonos exclusivamente en la disciplina de la Física, en donde el alumnado es capaz de analizar esos datos haciendo uso del código para llegar a unas conclusiones pertinentes. Este tipo de proyectos es idóneo para que los alumnos tomen conciencia de la forma en que los científicos profesionales trabajan y se comunican entre ellos a nivel internacional. This project consists of the analysis of the dynamics of a projectile in a dense granular medium for its implementation in an International Baccalaureate (IB) context. The starting point of the project is data obtained through software simulation, which gives information about the movement of a spherical body in a dense granular medium along the direction of gravity. It is provided by the Department of Physics and Applied Mathematics of the University of Navarra. In this master’s thesis, these data are analysed for the case of zero gravity and a critical study is conducted, which is based on the equation of motion that defines the dynamics of the projectile in the given medium. We develop the code that best defines the behaviour of a projectile along the granular medium, which is validated by the data provided. In parallel with that, a didactic proposal is developed through the Group 4 Project focusing exclusively on the discipline of Physics, where students can analyse these data using the code to reach pertinent conclusions. This type of project is ideal for students to become aware of the way in which professional scientists work and communicate with each other on an international level.

Very recently, To et al. have experimentally explored granular flow in a cylindrical silo, with a bottom wall that rotates horizontally with respect to the lateral wall [Phys. Rev. E 100, 012906 (2019)]. Here we numerically reproduce their experimental findings, in particular, the peculiar behavior of the mass flow rate Q as a function of the frequency of rotation f . Namely, we find that for small outlet diameters D the flow rate increased with f , while for larger D a nonmonotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, and the stress tensor fields. These results show conclusively that changes in the discharge process are directly related to changes in the flow pattern from funnel flow to mass flow. Moreover, by decomposing the mass flux (linear momentum field) at the orifice into two main factors, macroscopic velocity and density fields, we obtain that the nonmonotonic behavior of the linear momentum is caused by density changes rather than by changes in the macroscopic velocity. In addition, by analyzing the spatial distribution of the kinetic stress, we find that for small orifices increasing rotational shear enhances the mean kinetic pressure (pk) and the system dilatancy. This reduces the stability of the arches, and, consequently, the volumetric flow rate increases monotonically. For large orifices, however, we detected that (pk) changes nonmonotonically, which might explain the nonmonotonic behavior of Q when varying the rotational shear.

We report extensive numerical simulations of the fow of anisotropic self-propelled particles through a constriction. In particular, we explore the role of the particles’ desired orientation with respect to the moving direction on the system fowability. We observe that when particles propel along the direction of their long axis (longitudinal orientation) the fow-rate notably reduces compared with the case of propulsion along the short axis (transversal orientation). And this is so even when the efective section (measured as the number of particles that are necessary to span the whole outlet) is larger for the case of longitudinal propulsion. This counterintuitive result is explained in terms of the formation of clogging structures at the outlet, which are revealed to have higher stability when the particles align along the long axis. This generic result might be applied to many diferent systems fowing through bottlenecks such as microbial populations or diferent kind of cells. Indeed, it has already a straightforward connection with recent results of pedestrian (which self-propel transversally oriented) and mice or sheep (which self-propel longitudinally oriented).

We present a numerical framework to simulate pedestrian dynamics in highly competitive conditions by means of a force-based model implemented with spherocylindrical particles instead of the traditional, symmetric disks. This modification of the individuals' shape allows one to naturally reproduce recent experimental findings of room evacuations through narrow doors in situations where the contact pressure among the pedestrians was rather large. In particular, we obtain a power-law tail distribution of the time lapses between the passage of consecutive individuals. In addition, we show that this improvement leads to new features where the particles' rotation acquires great significance.

In this work, we numerically examine the steady-state granular flow of 3D non-spherical particles down an inclined plane. We use a hybrid CPU/GPU implementation of the discrete element method of nonspherical elongated particles. Thus, a systematic study of the system response is performed varying the particle aspect ratio and the plane inclination. Similarly to the case of spheres, we observe three well-defined regimes: arresting flows, steady uniform flows and accelerating flows. Both steady and dynamic macroscopic fields are derived from microscopic data, by time-averaging and spatial smoothing (coarse-graining), including density, velocity, as well as the kinetic and contact stress tensors. The internal morphology of the flow was quantified exploring the solid fraction profiles and the particle orientation distribution. Furthermore, the system¿s characteristic time and length scales are investigated in detail. Our aim is to achieve a continuum mechanical description of granular flows composed of non-spherical particles based on the micromechanical details. Thus, to evaluate the influence of particle shape on the constitutive response in granular of those systems. However, to meet the proceeding¿s page restrictions here we will only discuss the dependence of some terms of the continuum averaged equations on the coarse-graining scale, specifically the case of the kinetic part of the stress tensor.

El objetivo de esta tesis doctoral se basa en describir numéricamente el comportamiento de sistemas granulares compuestos por partículas de diferente geometría, desde el caso esférico hasta otras formas m´as complejas. Se ha llevado a cabo la implementación de un algoritmo híbrido CPU-GPU del método de elementos discretos para el caso de medios granulares. Se han tenido en cuenta todos los grados de libertad presentes en el problema, incluyendo la implementación de un formalismo de quaterniones que permite modelar de forma eficiente las rotaciones en 3D. La interacción entre partículas se ha definido a partir de fuerzas de contacto constituidas por un término elástico y otro disipativo. La forma geométrica de las partículas juega un papel fundamental en la definición de la fuerza interacción entre dos granos. La implementación CPU-GPU incluye el modelado de partículas esféricas y no esféricas, tales como granos alargados o elipsoidales. Entre otras aplicaciones, este algoritmo ha permitido examinar flujos granulares de partículas esféricas, y se ha podido establecer la existencia de un estado de enfriamiento homogéneo para gases granulares constituidos por partículas no esféricas sin fricción. Por otro lado, observando muestras granulares fluyendo, se ha podido examinar tanto experimental como numéricamente las propiedades micro-mecánicas de ese flujo de partículas a través del orificio situado en la base de un silo. Este estudio ha permitido clarificar por qué, pese a las inconsistencias que supone, el tradicional concepto de arco de caída libre permite describir la forma funcional de la velocidad media de las partículas en las proximidades del orificio de salida.

Several theoretical predictions of the mass flow rate of granular flows through outlets are based on the existence of a free fall arch region covering the silo outlet. Early in the nineteenth century, it was suggested that the particles crossing this region lose their kinetic energy and start to fall freely under their own weight. However, there is not conclusive evidence of this hypothetical region. We examined experimentally and numerically the micro-mechanical details of the particle flow through an orifice placed at the bottom of a silo. Remarkably, the contact stress monotonously decreases when the particles approach to the exit and it only vanishes just at the outlet. The behavior of this magnitude was practically independent of the size of orifice indicating that particle deformation, is insensible to the size of the aperture. Contrary, the behavior of the kinetic stress puts on evidence that the outlet size controls the propagation of the velocity fluctuations inside the silo. Examining this magnitude, we conclusively argue that indeed there is a well-defined transition region where the particle flow changes its nature. Above this region, the particle motion is completely correlated with the macroscopic flow. Our outcomes clarifies why the free fall arch picture has served as an approximation to describe the flow rate in the discharge of silos.

In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ.

We report experimental and theoretical results of the effect that particle shape has on the packing properties of granular materials. We have systematically measured the particle angular distribution, the cluster size distribution and the stress profiles of ensembles of faceted elongated particles deposited in a bidimensional box. Stress transmission through this granular system has been numerically simulated using a two-dimensional model of irregular particles. For grains of maximum symmetry (squares), the stress propagation localizes and forms chain-like forces analogous to those observed for granular materials composed of spheres. For thick layers of grains, a pressure saturation is observed for deposit depths beyond a characteristic length. This scenario correlates with packing morphology and can be understood in terms of stochastic models of aggregation and random multiplicative processes. As grains elongate and lose their symmetry, stress propagation is strongly affected. Lateral force transmission becomes less favored than vertical transfer, and hence, an increase in the pressure develops with depth, hindering force saturation.