Article

Impact dynamics and power-law scaling behavior of wet agglomerates

Authors:
  • Danang Architecture University (DAU)
  • Hanoi University of Civil Engineering, Hanoi
  • The University of Science and Technology - University of Danang
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Abstract

We investigate the impact dynamics of a single wet agglomerate composed of primary spherical particles impacting a flat plane by using three-dimensional discrete element method simulations. The primary particle is assumed to be rigid and interacted with its near-neighboring particles by introducing approximate analytical expressions of capillary cohesion forces and lubrication forces induced from the liquid in addition to their elastic and frictional interactions. The paper analyzes the mechanical strength, the deformation, and the connectivity of wet particle agglomerate during the impact as well as in its early-stage impact and the final-stage deposition. We show that the mechanical strength, deformation, and connectivity of granule strongly depend on the key parameters (the liquid–vapor surface tension, the liquid viscosity, and the impact speed of agglomerate). In particular, the early-stage strength and the height of wet agglomerate at its final-stage deposition nicely behave as a function of the Capillary–Stokes inertial number that combines the Capillary number and Stokes number, and the macroscopic strength of the agglomerate at its early-stage impact has the microscopic origin from the normal compressive forces between primary particles. These observations are consistent that represent the relationship between the rheological properties and the liquid properties and the impact conditions of wet granular materials.

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... where k t and γ t denote the tangential elastic stiffness and tangential viscous damping parameter. δ t andδ t are the relative tangential displacement and the relative tangential velocity, respectively, between particle i and particle j, µ denotes the coefficient of friction between particles in contact [31][32][33]. n q T g x W M F + w F t K J v N p F 2 6 2 c T d i V B K / 4 Q X D 4 p 4 9 e 9 4 8 9 + 4 b X P Q 1 g c D j / d m m J k X Z l I Y 8 r x v Z 2 1 9 Y 3 N r u 7 R T 3 t 3 b P z i s H B 2 3 T J p r j k 2 e y l R 3 Q m Z Q C o V N E i S x k 2 l k S S i x H Y 5 u Z 3 7 7 C b U R q X q g c Y Z B w g Z K x I I z s l K n F 6 E k 1 l f 9 S t W r e X O 4 q 8 Q v S B U K N P q V r 1 6 U 8 j x B R V w y Y 7 q + l 1 E w Y Z o E l z g t 9 ...
... h a n g 2 r j u t 1 P a 2 N z a 3 i n v V v b 2 D w 6 P q s c n b Z 1 k i q H P E p G o b k g 1 C i 7 R N 9 w I 7 K Y K a R w K 7 I S T u 7 n f e U K l e S I f z D T In cohesive granular materials, besides the normal and tangential contact forces that appear in the solid interactions between particles, the interactions between grains are also enhanced by the capillary cohesion forces f c and viscous forces f v due to the presence of the capillary bonds of the liquid [33][34][35], as shown in Fig. 2. In these simulations, the capillary bridges are assumed to be reformed during the flows of granular materials. ...
... The viscous force f v depends on the particle size R, the liquid viscosity η of the capillary bridges, and the relative normal velocity v n between particles i and j [33,40], as given following ...
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... The macroscopic properties of such agglomerate are characterized by its mechanical strength, energy consumption, and deposition height. After constructing a spherical agglomerate composed of 31,500 wet primary particles in a cuboidal sample of 65,000 particles with a size ratio d max =d min ¼ 2, where d max and d min are the largest and smallest particle diameter [52], the impact test is generated by releasing such agglomerate from a height that equals to a half of its radius, measured from the lowest point of agglomerate, and setting an initial falling velocity v 0 for all primary particles. For all particles, gravity is set to g = 9.81 m/s 2 , and the coefficient of friction between primary spherical particles is set to 0.5. ...
... 6 Scaling behavior of macroscopic properties [8,51,52,54,59,60], the results obtained in this current work lead to raising the questions that whether all the data points of r p =r c , D stop =D 0 , and DE can collapse on a master curve as a function of a dimensionless scaling parameter for both cases of the capillary bonds considered in our simulations? and how do the roles of the reversibility and irreversibility of capillary contacts on these scalings? ...
... In this current work, the confining stress r n is absent. This leads to re-express Eq. 12 by considering two different dimensionless numbers: the Capillary number Ca ¼ r v =r c and the Stokes number St ¼ r i =r v [52,60], implying ...
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... In numerical simulations, it is well known that the interactions between grains, as a microscopic origin, strongly govern the rheological properties of granular materials in different configurations [34][35][36][37][38][39][40]. These interactions commonly involve elastic and frictional solid contact forces and liquid forces; all these forces exert on each particle. ...
... The scaling confirms that the rheology of wet granular flows is an extension of the dry granular flows. This concept was also further applied for the investigation of the physical and mechanical properties of wet granular materials in different models and configurations, including the rheological properties of inertial visco-cohesive granular flows in the steady state [42], the evolution of aggregates in the simple shear flow of dry granular materials [43], and the physical and mechanical properties of granules impacting a rigid surface [36,38]. However, the model of a dry spherical intruder vertically penetrating into both dry and wet granular packings is quite different as compared to the above-mentioned investigations. ...
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... In order to ligh-light the origins of the different contributions of the heavy-heavy, heavy-light, and light-light interactions to the strength of agglomerates presented above, the average normal compressive forces < f + n > of these interaction groups are considered [1,17]. Fig. 10 shows the average normal compressive forces of different couples of particles in contacts as a function of the lightweight particle content. ...
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... ISSN 1859-2996 has been increasingly developed over four decades and has been applied for almost all kinds of geomaterials such as sand, concrete, and rock [16]- [19]. The DEM allows modeling the geomaterial at a small scale by considering the interaction between its particles. ...
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... The physics of the nucleation, growth and breakage of wet aggregates underlies also wet granulation (agglomeration), which is a widespread process in industry. Capillary forces have been extensively studied in this context (Ennis, Tardos & Pfeffer 1991;Bocquet et al. 1998;D'Anna 2000;Geromichalos et al. 2003;Liu, Yang & Yu 2013b;Raux & Biance 2018;Vo et al. 2022;Walls, Thompson & Brown 2022). The nucleation stage is governed by wetting thermodynamics during the first contact between powder and binder. ...
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... Remarkably, the intensity of the strong compressive forces is about four times higher as compared to the strong tensile forces. This finding of the normal forces may be explained as the microscopic origins for the high observations of the compressive strength as compared to the tensile strength due to the crucial contribution of the strong normal forces on the mechanical strength of granular materials [44]. By making the normalization between f n and σ c d 2 , there are only small differences of the density and intensity of the normal forces when using different values of the cohesive stress σ c . ...
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... The simulations are performed by using an in-house 3D molecular dynamics DEM program, namely cFGd-3D++code, originally developed by Mutabaruka [27]. This coding program is then improved by the author in order to apply to previous works and also for this current simulation [28][29][30]. The primary particles are modeled by using spheres as rigid bodies and interacting with others by considering the contact forces law based on a linear spring-dashpot model. ...
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... where k t and δ t are the tangential elastic stiffness and the relative tangential displacement, respectively. The tangential contact force f t has the direction opposite to the relative tangential displacement between two particles in contact [41,42]. In this work, the presence of the liquid in the granular bed as the liquid clusters is assumed to be naturally formed due to the condensation from the liquid-vapor. ...
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Using particle dynamics simulations, we investigate the strength and microstructure of agglomerates of wet frictional particles subjected to axial compression. The numerical model accounts for the cohesive and viscous effects of the binding liquid up to a debonding distance with the liquid assumed to be distributed homogeneously inside the agglomerate. We show that wet agglomerates undergo plastic deformation due to the rearrangements of primary particles during compression. The compressive strength is thus characterized by the plastic threshold before the onset of failure by the irreversible loss of wet contacts between primary particles. We find that the agglomerate plastic threshold is proportional to the characteristic cohesive stress defined from the liquid-vapor surface tension and the mean diameter of primary particles, with a prefactor that is a nearly linear function of the debonding distance and increases with size span. We analyze the agglomerate microstructure and, considering only the cohesive capillary forces at all bonds between primary particles, we propose an expression of the plastic strength as a function of the texture parameters such as the wet coordination number and packing fraction. This expression is shown to be consistent with our simulations up to a multiplicative factor reflecting the distribution of the capillary bridges.
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When dealing with unsaturated wet granular materials, a fundamental question is: what is the effect of capillary cohesion on the bulk flow and yield behavior? We inwestigate the dense flow rheology of unsaturated granular materials through experiments and discrete element simulations of homogeneous, simple annular shear flows of frictional, cohesive, spherical particles.
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By means of extensive contact dynamics simulations, we analyzed the effect of particle size distribution (PSD) on the strength and microstructure of sheared granular materials composed of frictional disks. The PSDs are built by means of a normalized β function, which allows the systematic investigation of the effects of both, the size span (from almost monodisperse to highly polydisperse) and the shape of the PSD (from linear to pronouncedly curved). We show that the shear strength is independent of the size span, which substantiates previous results obtained for uniform distributions by packing fraction. Notably, the shear strength is also independent of the shape of the PSD, as shown previously for systems composed of frictionless disks. In contrast, the packing fraction increases with the size span, but decreases with more pronounced PSD curvature. At the microscale, we analyzed the connectivity and anisotropies of the contacts and forces networks. We show that the invariance of the shear strength with the PSD is due to a compensation mechanism which involves both geometrical sources of anisotropy. In particular, contact orientation anisotropy decreases with the size span and increases with PSD curvature, while the branch length anisotropy behaves inversely.
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We analyze inertial granular flows and show that, for all values of the inertial number I, the effective friction coefficient μ arises from three different parameters pertaining to the contact network and force transmission: (1) contact anisotropy, (2) force chain anisotropy, and (3) friction mobilization. Our extensive 3D numerical simulations reveal that μ increases with I mainly due to an increasing contact anisotropy and partially by friction mobilization whereas the anisotropy of force chains declines as a result of the destabilizing effect of particle inertia. The contact network undergoes topological transitions, and beyond I≃0.1 the force chains break into clusters immersed in a background "soup" of floating particles. We show that this transition coincides with the divergence of the size of fluidized zones characterized from the local environments of floating particles and a slower increase of μ with I.
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We use numerical simulations to investigate force and stress transmission in cohesive granular media covering a wide class of materials encountered in nature and industrial processing. The cohesion results either from capillary bridges between particles or from the presence of a solid binding matrix filling fully or partially the interstitial space. The liquid bonding is treated by implementing a capillary force law within a debonding distance between particles and simulated by the discrete element method. The solid binding matrix is treated by means of the Lattice Element Method (LEM) based on a lattice-type discretization of the particles and matrix. Our data indicate that the exponential fall-off of strong compressive forces is a generic feature of both cohesive and noncohesive granular media both for liquid and solid bonding. The tensile forces exhibit a similar decreasing exponential distribution, suggesting that this form basically reflects granular disorder. This is consistent with the finding that not only the contact forces but also the stress components in the bulk of the particles and matrix, accessible from LEM simulations in the case of solid bonding, show an exponential fall-off. We also find that the distribution of weak compressive forces is sensitive to packing anisotropy, particle shape and particle size distribution. In the case of wet packings, we analyze the self-equilibrated forces induced by liquid bonds and show that the positive and negative particle pressures form a bi-percolating structure.
Chapter
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We investigate shear strength properties of wet granular materials as a function of water content in the pendular state. Sand and glass beads were wetted and tested in a direct shear cell. In parallel, we carried out molecular dynamics simulations by using an explicit expression of capillary force as a function of interparticle distance, water bridge volume and surface tension. Experiments and numerical simulations are in good agreement. We show that the shear strength is mostly controlled by the distribution of liquid bonds. This property results leads to the saturation of shear strength as a function of water content. We arrive at the same conclusion by analyzing the shear strength from the microstructure and by accounting for particle polydispersity. Finally, we discuss the potentialities of the discrete element approach as applied to unsaturated soils.
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Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behaviour at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This set-up is conceptually identical to the recent experiments of Boyer and co-workers [Phys. Rev. Lett. 107,188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.
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We numerically analyze the tensile strength of a single wet agglomerate modeled as a viscocohesive aggregate impacting a flat surface by using the discrete-element simulations. The viscocohesive agglomerate composed of primary spherical particles with the inclusion of the interstitial liquid in the form of the capillary bridges characterized by the cohesive and viscous forces between particles is extracted from a cuboidal sample of granular materials by applying a spherical probe. The tensile strength is measured from the impact test of a wet agglomerate by systematically varying different values of the surface tension of the interstitial liquid, the liquid viscosity, and the impact speed. We show that the tensile stress increases immediately when the collision occurs between the agglomerate and the flat surface. The peak of the tensile stress obtained after the collision, then decreases smoothly with increasing the particle movement. The maximum tensile stress is defined to be the tensile strength of such agglomerate. It is remarkable that the normalized tensile strength of such agglomerate can be well described as a function of a dimensionless impact number that incorporates the capillary number and Stokes number (calculated from the surface tension and the viscosity of the liquid and the impact rate of the agglomerate), thus providing the confirmation for the unified representation of the liquid properties and the impact rate of wet granular media.
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The impact of agglomerates on solid surfaces occurs inevitably during the processing of granular materials. In this work, numerical simulations of the surface impact of wet agglomerates are carried out by introducing liquid bridge interactions into a soft-sphere DEM model, and the instantaneous impact behaviors are discussed quantitatively at the single particle scale. Results indicate that the impact process usually includes four stages, i.e., compression, expansion, fragmentation, and re-agglomeration. The expanding radius is found to follow an exponential-law with time, and the number of fragments follows a power-law with impact velocity. Due to liquid bridge interactions, chain-like structures are observed beyond the impact, similar to those formed during the impact of dense suspension droplets. Moreover, the impact behaviors can be generally classified into four groups with respect to impact velocity, i.e., minor compression without splashing, severe compression with minor splashing, severe splashing with minor fragmentation, and severe fragmentation.
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The presence of liquids in particulate materials can have a significant effect on their bulk behaviour during processing and handling. It is well recognised that the bulk behaviour of particulate materials is dominated by the interactions between particles. Therefore, a thorough understanding of particle-particle interaction with the presence of liquids is critical in unravelling complex mechanics and physics of wet particulate materials. In the current study, a discrete element method for wet particulate systems was developed, in which a contact model for interactions with pendular liquid bridges between particles of different sizes was implemented. In order to evaluate the accuracy and robustness of the developed DEM, normal elastic impacts of wet particles with a wall were systematically analysed. It was shown that the DEM simulations can accurately reproduce the experimental observations reported in the literature. In addition, the DEM analysis was also in good agreement with the elastohydrodynamic model. It was further demonstrated that the rebound behaviour of wet particles is dominated by the Stokes number. There was a critical Stokes number, below which the particle will stick with the wall. For impacts with a Stokes number higher than the critical Stokes number, the coefficient of restitution increases as the stokes number increases for elastic particles. It was also found that the contact angle and surface tension played an insignificant role in the normal impact of wet particles, while the viscosity of the liquid has a dominant effect on the rebound behaviour.
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By means of extensive particle dynamics simulations in a three-dimensional model, we analyze the rheology and granular texture in the steady-state of the viscoinertial granular flow. The interactions between dry particles are added by the theoretical description of the capillary cohesion forces and viscous forces due to the presence of the viscous liquid bridge. We show that the rheology of such flow characterized by the apparent friction coefficient and packing fraction can be nicely described as a function of the viscoinertial number combining the particle inertia and viscous stress of the liquid bridge by keeping the constant value of the liquid-vapor surface tension. Furthermore, the flow behavior can alternatively be described by the effective viscosities (normal and shear components) as a function of the imposed volume fraction, which is in good agreement with previous numerical simulations of particles immersed in a viscous fluid and experiments in dense suspensions. Interestingly, the granular texture characterized by the fabric and force anisotropies and the bond coordination number is also well-described by this modified inertial number. Remarkably, the stress transmission ratio reflects the intermediate relationship between microstructure and mechanical behavior of wet granular flow, expressed as a function of the viscoinertial number. We also find that shearing leads to variations of the compressive and tensile interactions between neighboring particles.
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We experimentally and computationally study the early-stage forces during intruder impacts with granular beds in the regime where the impact velocity approaches the granular force propagation speed. Experiments use 2D assemblies of photoelastic disks of varying stiffness, and complimentary discrete-element simulations are performed in 2D and 3D. The peak force during the initial stages of impact and the time at which it occurs depend only on the impact speed, the intruder diameter, the stiffness of the grains, and the mass density of the grains according to power-law scaling forms that are not consistent with Poncelet models, granular shock theory, or added-mass models. The insensitivity of our results to many system details suggests that they may also apply to impacts into similar materials like foams and emulsions.
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In order to get insight into the wet agglomeration process, we numerically investigate the growth of a single granule inside a dense flow of an initially homogeneous distribution of wet and dry particles. The simulations are performed by means of the discrete element method and the binding liquid is assumed to be transported by the wet particles, which interact via capillary and viscous force laws. The granule size is found to be an exponential function of time, reflecting the conservation of the amount of liquid and the decrease of the number of available wet particles inside the flow during agglomeration. We analyze this behavior in terms of the accretion and erosion rates of wet particles for a range of different values of material parameters such as mean particle size, size polydispersity, friction coefficient and liquid viscosity. In particular, we propose a phase diagram of the granule growth as a function of the mean primary particle diameter and particle size span, which separates the parametric domain in which the granule grows from the domain in which the granule does not survive. Graphical abstract Open image in new window
Article
Through discrete element modeling, we investigate the breakage, deposition and attachment of wet dust agglomerates during normal surface impacts. The morphology and structure of the deposited dirt layer is studied through statistical analysis of the height profiles. It is found that the deposited layer is influenced by both the structural properties of the primary agglomerates and the impact conditions. The roughness of the deposited dirt layer shows a positive correlation to impact velocity and a negative correlation to the agglomerate moisture content. Within the pendular liquid regime the structural strength of the agglomerates shows a strong correlation to the moisture content while at higher moisture content the correlation becomes weaker. It is also observed that for a given impact velocity agglomerates of various sizes show similar deposition patterns. To unify the results for different agglomerate sizes, a dimensionless surface density is introduced.
Article
We use three-dimensional contact dynamics simulations to analyze the rheology of polydisperse packings of spherical particles subjected to simple shear. The macroscopic and microstructural properties of several packings are analyzed as a function of their size span (from nearly monodisperse to highly polydisperse). Consistently with previous two-dimensional simulations, we find that the shear strength is independent of the size span despite the increase of packing fraction with size polydispersity. At the grain scale, we analyze the particle connectivity, force transmission, and the corresponding anisotropies of the contact and force networks. We show that force distributions become increasingly broader as the size span increases. In particular, stronger forces are captured by large particles, which are also better connected creating the so-called granular backbone. Throughout this backbone friction mobilization is rare and compressive forces control the stability of such structure. In return, small particles create an important population of rattlers discarded of the strength and granular structure analysis. As a consequence, the contact anisotropy declines with size span, whereas the force and branch anisotropies increase. These microstructural compensations allow us to explain the independence of the shear strength from particle size polydispersity.
Article
By means of extensive three-dimensional contact dynamics simulations, we analyze the strength properties and microstructure of a granular asteroid, modeled as a self-gravitating cohesive granular aggregate composed of spherical particles, and subjected to diametrical compression tests. We show that, for a broad range of system parameters (shear rate, cohesive forces, asteroid diameter), the behavior can be described by a modified inertial number that incorporates interparticle cohesion and gravitational forces. At low inertial numbers, the behavior is ductile with a well-defined stress peak that scales with internal pressure with a prefactor ≃0.9. As the inertial number increases, both the prefactor and fluctuations around the mean increase, evidencing a dynamical crisis resulting from the destabilizing effect of particle inertia. From a micromechanical description of the contact and force networks, we propose a model that accounts for solid fraction, local stress, particle connectivity, and granular texture. In the limit of small inertial numbers, we find a very good agreement of the theoretical estimate of compressive strength, evidencing the major role of these structural parameters for the modeled aggregates.
Article
The normal surface impacts of wet and dry agglomerates are simulated in a DEM framework. While the impact behavior of dry agglomerates has been addressed previously, similar studies on wet agglomerate impact are missing. We show that by adding a small amount of liquid the impact behavior changes significantly. The impact behavior of the agglomerates at different moisture contents and impact energies are analyzed through post-impact parameters and coupled to their microscopic and macroscopic properties. While increasing the impact energy breaks more inter-particle bonds and intensifies damage and fragmentation, increasing the moisture content is found to provide the agglomerates with higher deformability and resistance against breakage. It is shown that the interplay of the two latter parameters together with the agglomerate structural strength creates various impact scenarios, which are classified into different regimes and addressed with a regime map. This article is protected by copyright. All rights reserved.
Article
Wet granulation is a very vital process in material science that finds applications in various industries like food, pharma, agriculture etc. There has been lot of research done in this area in batch and continuous modes. In this review, various granulators working in batch and continuous modes have been discussed and compared with reference to their design, performance, operating parameters, scale and application, merits and demerits. Process control and optimization of the process parameters viz., mode of operation, type of granulator, feed properties, binder type and flow rate, moisture content in feed, fluidizing medium, temperature and time etc to achieve the desired granule attributes viz., size distribution, granule strength and flowability, attrition resistance etc have been thoroughly discussed, Developmental trends in characterization of these granules for various attributes have been given with the modelling and simulation studies done to understand the phenomenon better under different process conditions. Kinetic and scale up strategies adopted in the process and the challenges in its translation to commercial scale also have been discussed. The paper presents a comprehensive and contemporary review on the very important unit process of wet granulation.
Article
By means of extensive coupled molecular dynamics–lattice Boltzmann simulations, accounting for grain dynamics and subparticle resolution of the fluid phase, we analyze steady inertial granular flows sheared by a viscous fluid. We show that, for a broad range of system parameters (shear rate, confining stress, fluid viscosity, and relative fluid-grain density), the frictional strength and packing fraction can be described by a modified inertial number incorporating the fluid effect. In a dual viscous description, the effective viscosity diverges as the inverse square of the difference between the packing fraction and its jamming value, as observed in experiments. We also find that the fabric and force anisotropies extracted from the contact network are well described by the modified inertial number, thus providing clear evidence for the role of these key structural parameters in dense suspensions.
Article
The behaviour of a single cluster aggregate made up of sticky wet granulates inside a Couette cell under constant shear has been numerically studied with the help of a Lattice Boltzmann model. Cluster composition and ratio of shear to capillary force present in the clusters have been found to be the two important factors in determining cluster behaviour. Clusters having size below a critical value are found to exhibit rigid translational and rotational movement; above this critical value the cluster breaks. Two broad failure regimes have been identified based on the relative magnitude of shear and capillary forces. For low values of the ratio the clusters are seen to undergo ductile failure either by thinning at the middle or due to severe coiling-recoiling action. At very high force ratios the clusters cannot withstand any shear and almost immediately breaks to form debri-like structures. Failure in these clusters is found to bring down the stress levels in the fluid. Increase in mass, less hysteresis in capillary forces, shear thinning base fluid and intrinsic voidage present in the clusters are found to make cluster-aggregates more susceptible to breakage.
Article
In this study, the impact of agglomerates composed of autoadhesive, elastic-plastic primary particles are simulated using the discrete element method. Results obtained are compared to the impact breakage of an agglomerate of autoadhesive elastic particles. It is found that, for the same impact velocity, the elastic agglomerate fractures but the elastic-plastic agglomerate disintegrates adjacent to the impact site. For the elastic-plastic agglomerate, the impact damage increases with increase in material yield stress. It is also found that the particle size distribution of the debris is more accurately defined by a logarithmic function rather than the power law function commonly obtained for impacts of agglomerates composed of elastic particles.
Chapter
The alternative to a continuum model of granular media (see other chapters in this book) is to view the material as a collection of discrete particles. In order to simplify the description, we assume the particles to be spheres in the following. For the characterization of a system with many particles we specify only two-particle interactions, assuming many-body interactions to result from the sum of the two-particle forces. The scope of this chapter is to give a summary of frequently used approaches and to compare them. The applicability of any two-particle interaction model will depend on the properties of the system that are to be described. In static, rather dense, systems frictional interactions are most important, whereas in dynamic, dilute, systems collisional properties dominate. Furthermore, the existence of only binary contacts vs. the possibility of multi-particle contacts influences the response of the system and also the choice of the interaction model.
Article
DEM-based analysis is conducted to investigate the effects of interface energy between particles on the breakage and adhesion of loose agglomerates upon impact with a spherical target. A mechanistic approach is tested to find a relationship between particle properties and the agglomerate structure after the impact, which resulted in a new dimensionless number, i.e. the ratio of the two interface energies. In combination with Δ - a dimensionless number relating incident kinetic energy to agglomerate strength 1, a good description of the agglomerate impact is obtained. The agglomerate structure after impact is mapped using the two dimensionless numbers and is in good agreement with experimental observations. The constructed regime map can serve as a guide for selecting preliminary process parameters in adhesive particle mixing. This article is protected by copyright. All rights reserved.
Article
Séminaire invité à l'Université Los Andes, Bogota
Article
By means of extensive lattice Boltzmann simulations, we investigate the process of growth and coalescence of liquid clusters in a granular material as the amount of liquid increases. A homogeneous grain-liquid mixture is obtained by means of capillary condensation, thus providing meaningful statistics on the liquid distribution inside the granular material. The tensile stress carried by the grains as a function of the amount of condensed liquid reveals four distinct states, with a peak stress occurring at the transition from a primary coalescence process, where the cohesive strength is carried mostly by the grains, to a secondary process governed by the increase of the liquid cluster volumes. We show that the evolution of capillary states is correctly captured by a simple model accounting for the competing effects of the Laplace pressure and grain-liquid interface.
Article
The combination of physical, chemical, and biological influences active in soil gives rise to aggregates, groups of soil particles that cohere more closely to each other than to other soil particles. The size, shape, and cohesive stability of soil aggregates are vital controls on soil function and development as well as on the transport of water and other substances. Numerous techniques are available for evaluating aggregate properties and their distribution, as essential for the characterization and understanding of soil.
Article
Heap leaching is a promising, economically viable processing pathway for extracting nickel (Ni) and cobalt (Co) from complex, low grade laterite ores. Producing a stable heap with high permeability and sustainable lixiviant percolation rate is a key requirement to ensure efficient leaching operation for maximum value metal recovery. Agglomeration of fine ore particles to produce robust granules with desirable attributes (e.g., size distribution and strength and porosity) is a critically important precursor to the heap leaching process. In this study, the effect of binder type/composition and dosage, drum speed, temperature and batch time on drum agglomeration behavior of siliceous goethite (SG) Ni laterite ore was investigated. Isothermal, batch agglomeration performed with tap water and 30, 44 and 98%w/w H2SO4 solutions as binders revealed the key role of binder dosage and acidity in controlling ore particle wettability, granule nucleation and growth behavior. Increasing the binder acidity from zero (tap water) to 30, 44 and 98%w/w H2SO4 led to a higher binder dosage to initiate and maintain a moderate rate of agglomeration. This accordingly reflected decreasing growth rates with increasing binder acidity where 98%w/w H2SO4 resulted in complete suppression of granule growth. At a fixed binder acidity and dosage, both higher temperature and drum speeds led to faster agglomeration rates. The impact of binder acidity and dosage on agglomerates' wet strength appeared to be insignificant. Acid-bound, wet agglomerates' integrity/stability in solution was, however, greater at lower binder dosage and/or binder acidity. The findings foster our understanding of how various, primary process variables may be prudently controlled to produce Ni laterite agglomerates with desirable properties and behavior, as a key step to enhance heap leaching.
Article
Wet agglomeration mechanisms developing in low shear mixers have been described considering a fractal morphogenesis process that links the median size of the agglomerates with their solid volume fraction via a fractal dimension. It appears fundamental to integrate the polydispersity of the generated structures (nuclei, agglomerates, dough pieces) in the analysis of the agglomeration process in order to approach the industrial problems. The objective of this study is to correlate the influence of the physicochemical characteristics of several liquid binders, on the fractal agglomeration mechanisms. To do so, we considered the values of the fractal model parameters. The obtained results confirmed that semolina wet agglomeration follows a fractal morphogenesis for the different applied liquid binders. Our results also showed a marked influence of the studied physicochemical properties of the liquid binder on the value of the fractal model parameters. During wet agglomeration in low shear mixers, the mechanisms implied during agglomeration (wetting, nucleation and growth) do not occur consecutively, but they coexist throughout at each water contents.
Article
The effect of the operating conditions of three continuous high shear granulators on the internal structure and strength of granules has been investigated and the possibility of seeded granulation has been explored. In a recently concluded programme of research on the scale-up of a high shear granulator, Cyclomix (manufactured by Hosokawa Micron B.V., The Netherlands), a novel method of granulation called seeded granulation was introduced, where each granule contained, at its core, a large particle from the upper tail end of the feed particle size distribution. Seeded granulation is particularly useful for process control of continuous granulators as there is the potential to control granulation by the flow rate of the seed particles. Hence, the performance of three different types of continuous granulators in terms of granule strength and structure has been evaluated here; these are Extrudomix, Modulomix (manufactured by Hosokawa Micron, UK and The Netherlands, respectively) and the Nica M6 Turbine continuous granulator (manufactured by GEA, UK). Calcium carbonate (Durcal 65) powder was granulated using an aqueous solution of polyethylene glycol (PEG) as binder in the same ratio as used previously in our batch granulation, to allow comparison between the continuous and batch processes. The crushing strength was characterised by quasi-static side crushing between two platens using a mechanical testing machine. The internal structure and morphology were evaluated by scanning electron microscopy and the extent of seeding quantified. Granules produced in all the three continuous granulators were significantly weaker than those of the batch granulator tested previously. Among the continuous granulators only the Modulomix granulator produced some seeded granules. It is considered that longer residence time is necessary to produce seeded granules.
Article
Dispersions of solid spherical grains of diameter D = 0\cdot 13 cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums. The density sigma of the grains was balanced against the density rho of the fluid, giving a condition of no differential forces due to radial acceleration. The volume concentration C of the grains was varied between 62 and 13%. A substantial radial dispersive pressure was found to be exerted between the grains. This was measured as an increase of static pressure in the inner stationary drum which had a deformable periphery. The torque on the inner drum was also measured. The dispersive pressure P was found to be proportional to a shear stress T attributable to the presence of the grains. The linear grain concentration lambda is defined as the ratio grain diameter/mean free dispersion distance and is related to C by lambda =1/(C0/C)1/3-1, where C0 is the maximum possible static volume concentration. Both the stresses T and P, as dimensionless groups Tsigma D2/lambda eta 2 and Psigma D2/lambda eta 2, were found to bear single-valued empirical relations to a dimensionless shear strain group lambda 1/2sigma D2(dU/dy)/eta for all the values of lambda < 12 (C = 57% approx.) where dU/dy is the rate of shearing of the grains over one another, and eta the fluid viscosity. This relation gives T propto \ sigma (lambda D)2 (dU/dy)2 and T propto \ lambda 3/2eta dU/dy, according as dU/dy is large or small, i.e. according to whether grain inertia or fluid viscosity dominate. An alternative semi-empirical relation T = (1 + lambda ) (1 + 1/2lambda ) eta dU/dy was found for the viscous case, when T is the whole shear stress. The ratio T/P was constant at 0\cdot 3 approx. in the inertia region, and at 0\cdot 75 approx. in the viscous region. The results are applied to a few hitherto unexplained natural phenomena.
Article
Agglomeration of fine particles in wet granulation is achieved by introducing a binder fluid onto a shearing mass of powder. Owing to the viscosity and the surface tension of the fluid, powder particles are bound together to form larger aggregates. Despite its widespread use in the chemical, pharmaceutical and food industries, little effort has gone into comprehensive modeling of the overall process from first principles. Modeling is important however, if one needs to estimate a-priori agglomerated granule characteristics such as size, shape and density, from knowledge of operating conditions and powder and binder physical and chemical properties.
Article
This work presents the results of the computational analysis of the influence of interparticle cohesion on the energy propagated and dissipated in agglomerates during impact against a rigid target. Agglomerate impact was simulated using Discrete Element Method (DEM). The cohesion between particles was simulated using the Johnson, Kendall and Roberts model. Four different regimes of breakage have been identified and the energy dissipated by the agglomerate upon impact has been determined for each regime of breakage. A comparison between the energy dissipated by the breakage of individual interparticle contacts and the net loss of kinetic energy has shown that the rupture of interparticle bonds utilises less than 10% of the total kinetic energy dissipated during agglomerate impact for all cases analysed here. In contrast, most of the incident kinetic energy is dissipated by contact damping and tangential deformation between the individual particles forming the agglomerates.
Article
The distinct element method is a numerical model capable of describing the mechanical behavior of assemblies of discs and spheres. The method is based on the use of an explicit numerical scheme in which the interaction of the particles monitored contact by contact and the motion of the particles modelled particle by particle. The main features of the distinct element method are described. The method is validated by comparing force vector plots obtained from the computer program BALL with the corresponding plots obtained from a photoelastic analysis.
Article
Traditional theoretical and experimental investigations of the mechanical behavior of particulate solids are restricted by the limited quantitative information about what actually happens inside particulate assemblies. This paper presents computer simulation results of the breakage of lactose agglomerates due to impact on a target plate using distinct element analysis. The agglomerates of interest here are generally weak and easy to disintegrate as no binder other than weak surface forces is holding the primary particles together. Particle interaction laws in the simulation code are based on theoretical contact mechanics, where adhesive interface energy determines the bond strength between individual particles of the assembly. Experimental investigations have been conducted to validate the computer simulation results, using a simple air-eductor where particles are accelerated to the required velocity by an air flow and impacted against a rigid target plate. Computer graphics of the simulation results of agglomerate breakdown are compared with the images obtained by high speed video recording of the impact events. A good agreement has been found between the simulation results and experimental measurements. Dynamic features and loading compliance of weak agglomerates are found to be distinctly different from those of high strength agglomerates and solid particles.
Article
A method was developed for measuring the capillary forces arising from microscopic pendular liquid bridges. Results are described for perfectly wetting bridges between spheres of equal and unequal radii. A comparison with the theoretical values calculated from a numerical integration of the Laplace−Young equation demonstrated the accuracy of the method. It also showed that existing criteria for gravitational distortion are too restrictive and that the influence of the disjoining pressure is negligible. The Derjaguin approximation for spheres of unequal size was shown to be relatively accurate for small bridge volumes and for separation distances excluding those at close-contact and near-rupture, which correspond to maxima in the filling angle. Closed-form approximations were developed in order to conveniently calculate the capillary forces between equal and unequal spheres as a function of the separation distance and for a given bridge volume and contact angle. A closed-form approximation was also developed to calculate the rupture distance for liquid bridges between spheres of unequal sizes.
Article
Dry sand turns into a stiff and moldable material as soon as it is mixed with some liquid. This is a direct consequence of the internal liquid–air interfaces spanning between the grains which causes capillary cohesion by virtue of the surface tension of the liquid. As a model for wet granulates we investigated random packings of submillimeter spherical beads mixed with water. Measurements of the tensile strength and the fluidization threshold demonstrate that the mechanical stiffness is rather insensitive to the liquid content over a wide range. Only for a high liquid content, when more than half of the available pore space is filled with liquid, does the capillary cohesion weaken. In order to understand the interplay between the mechanical properties and the liquid content, we investigated the liquid distribution in random packings of glass spheres by means of x-ray microtomography. The three-dimensional images reveal that the liquid forms a network of capillary bridges fused at local triangular bead configurations. The spontaneous organization of the liquid into these ramified structures, which exhibit a large liquid–air interface, is responsible for the constancy of the cohesive forces in a wide range of liquid contents beyond the onset of capillary bridge coalescence.
Article
Three raw granular materials: kaolin, microcrystalline cellulose, and calcium phosphate, usually used in various industrial areas, are wetted and mixed independently with distilled water. Agglomeration in a low shear mixer is then analyzed. The measurements of agglomerates granulometric (d25, d50 and d75) and hydro-textural (solid volume fraction, saturation degree and water content) parameters resulting from the wetting/mixing process are carried out. The later are plotted on a phase diagram, called the hydro-textural diagram. This study brings complementary information about the traditional description of agglomeration: (i) the first stage of nucleation represents that during which the fractal growth patterns (the nuclei) are built, (ii) the second stage of growth by coalescence was proven to conform to a fractal structuring behaviour. In low shear conditions, this experimental observation contradicts the classical description of agglomeration insofar as no consolidation phenomena are observed during coalescence.
Article
This paper is concerned with liquid bridges between two spherical rigid bodies of equal radii under conditions where the effects of gravity are negligible. Previous work on the necessary condition for the stability of such bridges is examined and the minimum free-energy formulation applicable to any contact angle is proven. It is shown that this formulation is a more fundamental criterion for specifying the stable numerical solutions of the Laplace-Young equation, although equivalent to previous conjectures based on the liquid bridge neck diameter and filling angle. At relatively low contact angles, say <40°, the critical separation for rupture is given by the cube root of the liquid bridge volume to a good approximation. The toroidal approximation provides a simple method of estimating the total liquid bridge force. The "gorge method" of evaluation leads to errors of <10% for all stable separations and a wide range of bridge volumes. The accuracy is independent of contact angle because of geometrical self-similarity. Simple scaling coefficients can be introduced into the toroidal approximation to allow force estimations to be made with relatively high accuracy.
Article
A numerical study of the micro-mechanics of breakage of agglomerates impacting with a target wall has been carried out using discrete element simulations. Three agglomerates of different shapes are examined, namely spherical, cuboidal and cylindrical. Each agglomerate consists of 10,000 polydisperse auto-adhesive elastic spheres with a normal size distribution. The effect of agglomerate shape and impact site on the damage of the agglomerates under an impact velocity of 1.0 m/s for an interface energy of 1.0 J/m 2 is reported. It is found from the simulations that cuboidal edge, cylindrical rim and cuboidal corner impacts generate less damage than spherical agglomerate impacts. The cuboidal face, cylindrical side and cylindrical end impacts fracture the agglomerates into several fragments. Detailed examinations of the evolutions of damage ratio, number of wall contacts and total wall force indicate that the size of the contact area and the rate of change of the contact area play important roles in agglomerate breakage behaviour. Internal damage to the agglomerate is closely related to the particle deceleration adjacent to the impact site. However, the local microstructure may not be a decisive factor in terms of the breakage mode for non-spherical agglomerates.
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This paper presents a numerical study of the breakage of loose agglomerates based on the discrete element method. Agglomerates of fine mannitol particles were impacted with a target wall at different velocities and angles. It was observed that the agglomerates on impact experienced large plastic deformation before disintegrating into small fragments. The velocity field of the agglomerates showed a clear shear zone during the impacts. The final breakage pattern was characterised by the damage ratio of agglomerates and the size distribution of fragments. While increasing impact velocity improves agglomerate breakage, a 45-degree impact angle provides the maximum breakage for a given velocity. The analysis of impact energy exerted from the wall indicated that impact energy in both normal and tangential directions should be considered to characterise the effects of impact velocity and angle.
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Past granulation research has been essentially restricted to a macroscopic study of the impact of operating variables on granule morphology. While fundamental groundwork regarding agglomeration forces has been laid by pioneers such as Rumpf, little progress towards ana priori characterization of microlevel phenomena in terms of macroscopic process variables has been achieved. The present work centers on this microscale and introduces a classification of granulation mechanisms based on the collisional dissipation of relative particle kinetic energy.The mechanism of granule coalescence is, in part, a function of a dimensionless binder Stokes' numberStv, which is a measure of the ratio of granule collisional kinetic energy to the viscous dissipation brought about by interstitial binder. The Stokes' number provides a convenient classification of granulation regimes. For smallStv, coalescence hinges on the presence and distribution of binder and is independent of particle kinetic energy and binder viscosity. In this regime, binder viscosity controls the rate of granule consolidation and ultimate granule voidage. For the case where the maximumStv is of the order ofSt*v, increases in binder viscosity increase coalescence rate as traditionally expected. HereSt*v is a critical Stokes' number, being a known function of the volume of binder deposited on the bed. Finally, for largeStv, only granule coating is possible. Fluid-bed granulation and defluidization experiments supporting this simple classification of granulation regimes is presented. Implications regarding successful granulation operation are drawn.
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The paper reports granular dynamics simulations of a dense spherical agglomerate consisting of a random polydisperse system of autoadhesive particles impacting orthogonally with a target wall. A range of impact velocities has been examined which resulted in rebound, fracture or shattering depending on the magnitude of the impact velocity specified. Visualisations of agglomerate breakage are presented together with data on the evolution of the target wall force, the kinetic energy of the agglomerate, the number of bonds broken and the amount of debris detached during a collision. The evolution of the processes preceding agglomerate breakage is also discussed.RésuméCet article présente les résultats de simulations numérique du choc contre une paroi d'un agglomérat sphérique et compact, composé d'un ensemble polydisperse de particules autoadhésives. Différentes vitesses d'impact ont été examinées, qui produisent des phénoménes de ricochet, de fracture et d'écrasement suivant la vitesse. Des images de la fragmentation de l'agglomérat sont présentées de même que des informations sur les évolutions de la force de la cible, de l'énergie cinétique de l'agglomérat, du nombre de liaisons brisées et de la quantité de débris. On s'intéresse aussi á l'évolution des processus qui précédent la fragmentation de l'agglomérat.
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The paper examines the various factors that influence the breakage of particle agglomerates resulting from impact. Numerical simulations of polydisperse spherical agglomerates impacting orthogonally on a target wall have been performed to study the effects of impact velocity, solid fraction, contact density, and the local arrangement of particles near the impact zone. Results of simulations show distinct fracture patterns for dense agglomerates above a critical impact velocity whereas for loose agglomerates disintegration occurs under identical testing conditions. Either fracture or disintegration may occur for agglomerates with an intermediate packing density. It is also demonstrated that, for agglomerates with intermediate packing densities, the mode of failure can change from disintegration to fracture by either increasing the contact density or changing the location on the agglomerate surface, which is used as the impact site.