Free energy of the Lennard-Jones solid

We have determined a simple expression for the absolute Helmholtz free energy of the fcc Lennard-Jones solid from molecular dynamics simulations. The pressure and energy data from these simulations have been fitted to a simple functional form (18 parameters) for densities ranging from around 0.94–1.20, and temperatures ranging from 0.1 to 2.0 (values in reduced Lennard-Jones units). The absolute free energy at an arbitrary state point in this range is obtained by integrating over density and temperature from the triple-point. Our result for the free energy is in very good agreement with the values reported in literature previously. Also the melting line obtained from our free energy expression, in combination with an equation of state for the liquid phase, is in excellent agreement with results by Agrawal and Kofke [Mol. Phys. 85, 43 (1995)] obtained via the Gibbs–Duhem integration method

Effects of heterogeneity on the drag force in random arrays of spheres

The modelling of the gas-solid interaction is a prerequisite in order\ud to accurately predict fluidized bed behaviour using models\ud such as the Discrete Particle Model (DPM) or the Two Fluid\ud Model (TFM). Currently, the drag force is usually modelled\ud purely based on porosity and slip velocity, which are averaged\ud with respect to the grid size used to solve the model equations.\ud Interfaces at heterogenous structures such as bubbles or free\ud board are not accounted for. As recently pointed out by Xu\ud et al. (2007), sub-grid information for the particle position is\ud available in DPM simulations, thus the local porosity is known\ud and can be used when calculating the drag.\ud Direct Numerical Simulation of flow in particulate systems\ud were done using the lattice Boltzmann method. These simulations\ud were carried out with random arrays of spheres which\ud only have a slight degree of heterogeneity and the gas-solid interaction\ud force on each particle was measured. First we compared\ud these results, which can be considered as the “true drag\ud force, with the drag force one would predict from a correlation\ud typically used in larger scale models (such as the relation of\ud van der Hoef et al. (2005)). Even for the random arrays, the\ud drag on some individual particles differed considerably (up to\ud 40%) from the predicted drag. Then we evaluate the effectiveness\ud of improved drag models, that use information on local\ud porosit

Simulation of density segregation in vibrated beds

We have investigated by numerical simulation the density segregation of fine equal-sized bronze and glass particles subject to vertical vibrations. The model was found to be capable of predicting the two main segregation forms (“bronze on top” and “sandwich”) in roughly the same regions of the phase diagram as was found experimentally by Burtally et al. We investigated the effects of pressure air forcing, friction and restitution of kinetic energy in collisions, and box size on the segregation behavior. We find that next to the interstitial air friction also has a large influence on the formation of the sandwich structure

Fluid-particle interaction force for polydisperse systems from lattice boltzmann simulations

Gas-solid fluidized beds are almost always polydisperse in industrial\ud application. However, to describe the fluid-particle interaction\ud force in models for large-scale gas-solid flow, relations\ud are used which have been derived for monodisperse system, for\ud which ad-hoc modifications are made to account for polydispersity.\ud Recently it was shown, on the basis of detailed lattice\ud Boltzmann simulations, that for bidisperse systems these\ud modifications predict a drag force which can be factors different\ud from the true drag force. In this work fluid-particle interaction\ud forces for polydisperse system are studied by means of\ud lattice Boltzmann simulation, using a grid that is typically an\ud order of magnitude smaller than the sphere diameter. Two different\ud lognormal size distributions are considered for this study.\ud The systems consist of polydisperse random arrays of spheres\ud in the diameter range of 8-24 grid spacing and 8-40 grid spacing,\ud a solid volume fraction of 0.5 and 0.3 and Reynolds number\ud 0.1 to 500. The data confirms the observations made for bidisperse\ud systems, namely that an extra correction factor for the\ud drag force is required to adequately capture the effect of polydispersity.\ud It was found that the correction factor derived by van\ud der Hoef et al (J. Fluid Mech. 528 (2005) 233) on the basis of\ud bidisperse simulation data, applies also to general polydisperse\ud system

Discrete particle simulation of the homogeneous fluidization of Geldart A particles

The homogeneous fluidization of Geldart A particles has been studied with a 2D soft-sphere discrete particle model. We find that the homogeneous fluidization regime represents a quasi-equilibrium state where the force balance exists at the macroscopic-level, but not at the level of individual particles. The velocity fluctuation of particles is an exponential function of the squared superficial gas velocity in the homogeneous fluidization regime, not a linear function as found by\ud Cody et al

Calculated and measured Auger lineshapes in clean Si(100)2×1, SiOx and Si-NO

The measurements were performed on the clean 2*1 reconstructed Si(100) surface and this surface exposed to molecular oxygen (O2) or nitric oxide (NO) at room temperature. The data were corrected for electron loss and spectrometer distortions using the authors' newly developed deconvolution method. This method which uses global approximation and spline functions can overcome several difficulties with respect to deconvolution and allows them to derive high-quality auger lineshapes from the SiL2.3 VV Auger electron spectra. The authors experimentally obtained Auger lineshapes were compared with theoretical lineshapes utilising quantum chemical cluster calculations. They used this type of calculation for the interpretation of the Auger lineshape in the actual p-like and s-like partial local density of states for different types of silicon atom. The observed intensities of the major features are in reasonable agreement with the authors' calculations

Transition density of states (TDOS) of the Si(100)2 × 1 surface derived from the L2,3VV Auger lineshape compared with cluster calculations

The termination of a silicon crystal along the (100) orientation resulting in a 2 × 1 reconstructed surface induces relatively large variations in the local density of states (LDOS) of the different types of surface atoms, such as the up and down dimer atom and the backbond atom. Auger electron spectroscopy (AES) is able to probe the LDOS of the silicon atom in which the L2,3 core hole has been created and is therefore a candidate to analyze the LDOS of the surface atoms. A detailed analysis of the SiL2,3VV Auger electron spectrum allows us to determine a high quality transition density of state (TDOS) of the Si(100)2 × 1 reconstructed surface. The resolved peaks in the TDOS were compared with previous AES, UPS and EELS measurements reported by other investigators. Quantum chemical cluster calculations were used for the interpretation of the TDOS in the actual p-like and s-like partial local density of states for different types of silicon atoms. These quantum chemical cluster calculations of the partial LDOS localized at atoms of the Si(100)2 × 1 surface were found to be in agreement with other types of calculations. Comparing the experimental and the calculated DOS we were able to distinguish several new peaks in the TDOS obtained with AES and to discriminate features in the experimentally obtained TDOS into local electron distributions localized at different surface atoms

The influence of the (2 × 1) reconstruction of the Si(1 0 0) surface on the Si---L2,3 VV Auger lineshape

The extreme surface sensitiveness of the Si---L2,3 VV Auger process and its ability to probe the atomic electron distribution in the direct neighbourhood of the L2,3-core-hold makes this electron spectroscopic technique a candidate for investigations of the local changes in the electron distribution due to surface reconstruction. In this paper we show, explicitly, the influence of the (2 × 1) reconstruction of the Si(1 0 0) surface on the Si---L2,3 VV Auger lineshape. Furthermore, the calculated Auger lineshape will be compared with an experimentally obtained line profile

Modeling of tribo-electrification of a pneumatically conveyed powder in a squared duct using DEM-CFD

Dry separation technology is a sustainable alternative to conventional wet separation technology for production of food ingredients. This paper is concerned with the exploration of a new driving force for dry separation, i.e. triboelectrification. To investigate the possibilities of this driving force, we modified our in-house DEM-CFD code to model a learning system where powder is tribo-electrically charged by conveying it pneumatically through a squared tube. The charged particles will electrostatically interact with both other charged particles, as well as their induced charges on the conducting walls. We show that the amount of acquired charge depends on the electrostatic interaction between particles and walls and show the corresponding spatial distribution of the particles. They depend both highly on the (mean) charge of the particles. We observed a critical charge per particle after which particles charged rapidly to their saturation charge. This critical charge is delicate and lower than expected from first order derivations

Numerical investigation of the vertical plunging force of a spherical intruder into a granular bed

The plunging of a large sphere into a prefluidized granular bed with various constant velocities is investigated using a state-of-theart hybrid Discrete Particle and Immersed Boundary Method (DPIBM), with which both the gas-induced drag force and the contact force exerted on the intruder can be investigated separately. Our simulation method has been validated by comparison with the existing experimental results. Current simulation results show a concave-to-convex plunging force as a function of depth and in the concave region the force fits to a power-law with exponent around 1.3, which is in good agreement with existing experimental observations