CFD (Computational Fluid Dynamics) methods and are based on continuous models (Massoudi, 2006) includ- ing finite element/finite volume methods (FEM/FVM), lattice Boltzmann techniques (LBM) or fractional calculus (Szymanek et al., 2014). Vargas and McCarthy (Vargas and McCarthy, 2001) have developed a TPD (thermal particle dynamics) method based on the Discrete Element Method (DEM) allowing analysis of grain-grain inter- actions. This approach was also used to describe the heat and mass flow in granular beds by Ferrez and Liebling (Ferrez and Liebling, 2001). In their work the granular beds were treated as systems consisting of solid bodies and a system of different pore sizes filled with liquid, gas or a mixture of them. A similar approach to the problem was presented in (Tian and Shu, 2009), where the granularmaterial was described as a homogeneous bed consisting of elements of irregular structure (porous, granular). Ordonez and Alvarado (Ordonez and Alvarado, 2010) proposed a model of heat transfer through a granular bed taking into account the temperature of the solid and gaseous phase separately.
Hollow glass beads were used as the granularmaterial in the measurements. Table 1 shows the basic properties of the hollow glass beads. These beads were filled in cylindrical containers made of polylactic acid resin, and no additional force was applied as the material was constrained by the container walls. The surface of the material in the container was leveled smoothly by light tapping after pouring. Figure 1 shows the material used in the measurements.
The constitutive model ( 3 ) captures the salient solid-like behaviours of granularmaterial, such as nonlinearity in stress-strain relation, loading path dependence, stress level dependence of friction angle and dilatancy and critical state behaviour [ 51 ]. It covers the whole spectrum of granular from loose to dense packing. Unlike elastoplastic models, the employed model makes no distinction between the elastic and plastic ranges. The strain decomposition and complex stress integration algorithms are unnecessary when using the hypoplastic model. Therefore, numerical implementation can be greatly simplified. It is noteworthy that although the hypoplastic model is developed without recourse to plasticity theory, some widely-accepted con- cepts, such as failure surface and flow rule, may be obtained as natural outcomes [ 52 – 54 ]. Figure 1 shows the failure surface and flow rule derived from the hypoplastic model. The failure surface in 3-D principal stress space is a conical surface, close to the failure surface of Mohr– Coulomb plastic criterion but without singularities. The plastic flow directions in Fig. 1 b indicate that the flow rule of the employed hypoplastic model is non-associative. 2.3 Extended 3-D Bagnold-type rheology
About the understanding of the dynamic of granularmaterial, significant progress has been made on the study of granular flows down a slope using depth averaged continuum equations with various different ways of reproducing the effect of friction (Savage & Hutter 1989, Pouliquen 1999). Regarding transient situations, some experiments have been conducted considering the instantane- ous release of a stationary cylindrical column of dry granularmaterial on a horizontal plane (Lube et al. 2004, Lajeunesse et al. 2004). Despite the complexity of the dynamics, simple scaling laws have been found for describing the final deposit
However, the averaging methods above are very compli- cated and depend highly on the shape, position and scale of the averaging volumes [ 7 , 10 ]. Some methods do not take the positions of particles into account, which is not correct since particles in different positions (center or boundary of the averaging volume) have different contributions on the over- all rotation. A new method of rotation averaging for granularmaterial is proposed here. This averaging method is simple yet works for both 2D and 3D cases. It is not restricted by the size or position of the averaging volume. The method is shown for granularmaterial with circular shaped particles (discs in 2D and spheres in 3D). However, it can be easily applied to arbitrary shaped particles.
As mentioned before, stresses lie only on the yield surface (in other words, the yield criterion is fulfilled f T ( ) = 0 ), if the respective mate- rial is flowing. Otherwise (e.g. in stable zones of the slide, levees and deposition) the stress has to lie within the yield surface. However, this is not included in the presented relations and the viscosity will reach a singularity in stationary zones where D = 0 . To allow deviatoric stresses lower than the deviatoric stresses at yield, we can limit the viscosity to a predefined upper threshold. This way we can simulate quasi-stationary zones - zones with very high viscosity, that will deform very slowly. The viscosity threshold should be chosen high enough such that the deformation is negligible, but low enough to circumvent nu- merical problems. However, we want to emphasize that this approach is an extreme simplification of quasi-static granularmaterial behaviour and results (e.g. stresses) in static zones are questionable. An elasto- plastic model is more appropriate than the simple visco-plastic model applied in here. The time step in numerical simulations is chosen fol- lowing the stability criterion (CFL condition) as given by Moukalled et al. [47, pp. 497] . Note that the viscosity has to be taken into account in the calculation of the CFL number and that without a limitation of the viscosity, the time step would be very small. This method has been found to be sufficient for the here presented cases.
Next, experimental results and numerical results are compared for the accelerance when applying granularmaterial and applying each excitation force (20N, 50N, 80N, 120N, 200N). The experimental results are shown in Fig. 12 and the numerical results are shown in Fig. 6. As can be seen from these results, it was confirmed that the following tendencies were seen in the numerical results. The excitation force dependency and the decrease of each bending mode frequency in the state where the granularmaterial is applied, even in the experimental results. In addition, in the experimental results, the frequency characteristics around the (3, 3) bending mode under the condition of the excitation force of 20 N are different from other excitation forces, however the same tendency is also seen in the analysis results. On the other hand, in the experimental results of the excitation force of 80 N, unl ike the analysis results, no sharp peak was found at the (1, 1) bending mode frequency.
So far this section concentrated on introducing non-uniform material behavior for single objects. The approach can however also be used by introducing drastically varying parameters across multiple objects, as was shown in . Some constitutive models are capable of expressing distinctly different materials. For example, if µ = 0 for the fixed corotated model, then it depends only on the determinant. This is similar to the model for fluids (Section 5.1.5) and is also how the model behaves in this case . The snow model is based on the fixed corotated model and it is possible to opt-out of the plasticity by setting θc = 1 and θs to some very large value. This means that the same model can be used to simulate fluids, hyperelastic materials as well as snow and many other elasto-plastic materials at the same time in the same scene. This is demonstrated by Stomakhin et al. , although their work uses a variation of the original model and further augments MPM to be able to handle a wider range of stiffness and degrees of incompressibility. A similar case can be made for the sand model. If hardening is not used and the friction angle is set to zero, it can be used to model a fluid. Varying levels of cohesion can be used to model dry or wet sand, while very high cohesion levels behave less and less like sand and eventually become hyperelastic. 6.1.2 Multiple Constitutive Models
tungsten as an anode, penetrates through the shear cell, placed in the beam path and subse- quently, the attenuated X-rays are collected with a detector panel, mounted behind the shear cell. The best material contrast with sufficiently large photon flux is achieved for an accelerating voltage ≈ 160 kV and the tube current ≈ 139 mA. The detector panel is a 12-bit CMOS camera (Model: C7942SK − 25, Hamamatsu Photonics Corporation, Japan) combined with an efficient scintillator screen (gadolinium oxysulfide). The scintillating material converts the attenuated X- rays into visible light before it reaches to the camera. Due to conical shape of the beam profile, the geometric magnification of the shear cell can be adjusted. Following the same operating principle as explained in section 4.1.2 , an initial pressure (P int ) is externally applied to the test granulates filled into the shear cell (r = 15 mm, H = 10 mm) and we thereafter capture a radiograph with an exposure time t = 1000 ms. The spatial resolution of the radiograph is about 14 µm/pixel. Thus, we have acquired the radiographic images of dry and wet glass granulates at different initial pressures; bead-sizes, wetting fluid and liquid content are the same as in fig. 4.12 . A few selective rediographs are displayed in fig. 4.13 earlier.
By employing a large-diameter constant-head seepage test apparatus, internal instability in sand and gravel by upward water flow was investigated. Reconstituted granular soils having various particle gradations, densities and particle roundness were tested. It was found that the maximum critical hydraulic gradient for seepage failure drastically increases with increasing uniformity coefficient and becomes more than 3 times higher than the theoretical value. A mode of seepage failure is different due to different particle gradations such that poorly-graded sand or gravel (C u <4) shows global boiling failure while well-graded gravelly sand (C u >4) undertakes local boiling and eventual separation between coarser and finer grains. Among well-graded soils, some tends to exhibit a local piping failure of finer particles at hydraulic gradient much lower than the theoretical value, which may be predicted based on particle gradation curves.
Clustering and melting in a wet granular monolayer Philipp Ramming 1 and Kai Huang 1 ,
1 Experimentalphysik V, Universität Bayreuth, 95440 Bayreuth, Germany
Abstract. We investigate experimentally the collective behavior of a wet granular monolayer under vertical vibrations. The spherical particles are partially wet such that there are short-ranged attractive interactions between adjacent particles. As the vibration strength increases, clustering, reorganizing and melting regimes are identiﬁed subsequently through a characterization with the bond-orientational order parameters and the mean kinetic energy of the particles. The melting transition is found to be a continuous process starting from the defects inside the crystal.
Eine andere Möglichkeit, um die ganz eigenen Wahrnehmungen, Empfindungen und Fragen gestalterisch zur Sprache zu bringen, ergibt sich aus den vielfältigen Eigenschaften und Möglichkeiten des Materials und den sich daraus ergebenden Bearbeitungsweisen. So wird es nicht immer möglich sein, dass die Schüler mit verschiedenartigen Materialien arbeiten. In diesem Fall gilt es, trotz des gleichen Ausgangsmaterials einen persönlichen Zugriff darauf zu entwickeln. Erinnert sei wieder an das Beispiel mit dem Ton und dessen vielseitigen Verwendungen: Man kann den Ton kneten, ausrollen, kneifen, ritzen, platt klopfen, durchbohren, auseinanderzupfen und erneut zusammenfügen, werfen, verflüssigen, trocknen und pulverisieren etc. und bei jeder dieser Zugriffsweisen lassen sich undenkbar viele Formen erfinden. Eine derart vielfältige Annäherung an das Material ist möglich, weil die charakteristische Beschaffenheit des jeweiligen Materials dazu auffordert und weil die individuellen Zugriffsweisen vor dem Hintergrund der persönlichen Erfahrungen betrachtet werden müssen. „Wahrgenommenes wird nicht unabhängig von
MSD is shown to be a decaying function of the length of the measured trajectory (ageing). (iii) We study an eﬀective single particle mean field approach to the granular gas dynamics. This underdamped scaled Brownian motion (SBM) demon- strates how non-ergodicity and ageing emerge from the non- stationarity invoked by the time dependence of the granular temperature, which translates into the power-law time depen- dence of the diﬀusion coeﬃcient of SBM. We note that systems with time dependent diﬀusion coeﬃcients are in fact common in nature, ranging from mobility of proteins in cell mem- branes, 17 motion of molecules in porous environments, 18 water diﬀusion in brain as measured by magnetic resonance ima- ging, 19 to snow-melt dynamics. 20,21
Identifying aggregate shocks that drive business cycles might be difficult (Cochrane (1994)). A recent literature advances the possibility that shocks at the firm or sector level may be the origin of aggregate fluctuations. This view stands in contrast to the “diversification argument” of Lucas (1977), which conjectures idiosyncratic shocks at a highly disaggregated level average out. 1 In contrast, Gabaix (2011) argues the diversification argument does not readily apply when the firm-size distribution is fat-tailed, which is the empirically relevant case for the United States. Intuitively, shocks to disproportionately large firms matter for aggregate fluctuations, known as the “granular” effect. In a similar vein, Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2012) focus on sectoral shocks and show that input-output relationships across sectors can mute the diversification argument if measures of sector centrality follow a fat-tailed distribution. They label this channel the “network” channel. Thus, either through a granular or network channel, microeconomic shocks to small numbers of firms or sectors may drive aggregate fluctuations. 2
§ In der aktivitätsbezogenen Rechnung wird das Aufkommen und die Verwendung von Material und Energie dargestellt, die von den Aktivitäten der 58 Produktionsbereiche der inländischen Wirtschaft sowie der Haushalte ausgehen. Unter einem Produktionsbereich ist dabei die Gesamt- heit aller wirtschaftlichen Aktivitäten, die ausschließlich und vollständig die Güter einer Güter- gruppe erzeugen, zu verstehen. Durch die Verwendung der Gliederung nach homogenen Produk- tionsbereichen können die Daten zu umweltrelevanten Material- und Energieströmen sowie zu Umweltbelastungen direkt in Beziehung zu ökonomischen Kennziffern aus der Volkswirtschaft- lichen Gesamtrechnung gesetzt werden. Produktionsbereiche stellen somit das Bindeglied zwischen Wirtschafts- und Umweltdaten dar.
The notion that we might recruit nature to surpass nature is not new. It has a long history, at least in alchemy and other magical sciences, in romantic philosophy of nature (Naturphilosophie), but also in theories of self-organization and, not least, in biomimetics or bionics. If there is anything new about it in the context of nanotechnologies, then it is its innocuous appearance and the way in which it is taken for granted. In fact, it assumes a kind of spectacular prominence only in the debates about so-called transhumanism and its goal of technologically enhancing human nature, which is to be enabled, somehow, by nanotechnologies and their convergence with other emerging technologies. In contrast, the idea of mobilizing nature to go beyond nature goes just about unnoticed where it proves to be fundamental, namely with regard to the project of technologically enhancing or surpassing material nature. This basic idea therefore needs to be brought to light before it can be properly contextualized historically and appreciated philosophically.
Mechanism of solubility, D-mannose differs from D-glucose only in the stereochemistry at C-2. Therefore, it can fine that D-mannan is an insoluble fibrous material similar to its D-glucose analogue, cellulose. This behavior is attributed to the formation of stable crystalline regions in the solid in which the linear chains lie in close proximity. The inclusion of side chains spoils this crystallinity and thereby promotes the penetration of water and enhances solubility. Thus, commercial gums showing high substitution ratio, such as guar, tend to hydrate fully in cold water, while gums with limited substitution, such as locust bean gum, hydrate completely only in hot water. Commercial gums exhibiting high substitution ratio (i.e. guar gum) are better hydrated in cold water than gums with limited substitution (i.e. LBG), because the presence of side chain interferes with the formation of stable crystalline regions and promotes water penetration, thereby enhance solubility. This behavior is reflected in the viscosity of the hot- and cold-prepared solution. Galactomannans don’t hydrate instantaneously in water. At 25 o C, guar gum may require up to 120 min hydrate fully and yield its maximum potential viscosity. This time can be shortened by using a high-shear mixer, a fine powder or by increasing the temperature. However, at temperatures above 80 o C, thermal degration become significant and the maximum potential viscosity will not achieve. The rate and degree of hydration may be dramatically reduced by the presence of other solutes. When using galactomannans in formulated food, it is good practice, therefore, to hydrate these first in any free water present in recipe before adding the remaining ingredients.
From an engineering point of view, a reliable prediction of operation time and thus breakthrough of GFH adsorbers based on easily accessible data is needed to design GFH fixed-bed columns. In figure 41, a general procedure for breakthrough prediction is shown. The traditional approach is a sequence of laboratory-scale experiments to determine the adsorption equilibrium (isotherm experiments) and mass transfer coefficients (DCBR/SFBR/CMBR experiments). Ultimately, the breakthrough of a GFH fixed-bed column can be predicted using mass transfer models, such as the homogeneous surface diffusion model (HSDM). In this study, breakthrough of arsenate, phosphate, salicylic acid and groundwater DOC could be predicted using models which already have been established for trace organic adsorption onto granular activated carbon. Breakthrough curves were experimen- tally determined and modeled using the HSDM and two of its derivatives, the constant pattern homogeneous surface diffusion model (CPHSDM) and the linear driving force model (LDF). Input parameters, the Freundlich isotherm constants, and mass transfer coefficients for liquid- and solid-phase diffusion were deter- mined and analized for their influence on the shape of the breakthrough curve. HSDM simulation results predict the breakthrough of all investigated substances satisfactorily, but LDF and CPHSDM could not describe arsenate breakthrough correctly. This is due to a very slow intraparticle diffusion and hence higher Biot numbers. Based on this observation, limits of applicability were defined for LDF and CPHSDM. When designing fixed-bed adsorbers, model selection based on known or estimated Biot and Stanton numbers is possible. In addition, the deter- mined isotherm data and mass transfer coefficients form the basis of a data base which can be used in future model simulations.