Scaled discrete particle model

Sutkar VS, Deen NG, Mohan M, et al Numerical investigations of a pseudo-2D spout fluidized bed with draft plates using a scaled discrete particle model, Chem Eng Sci 104 790-807, 2013. 

The methods used for modeling pure granular flow are essentially borrowed from that of a molecular gas. Similarly, there are two main types of models the continuous (Eulerian) models (Dufty, 2000) and discrete particle (Lagrangian) models (Herrmann and Luding, 1998 Luding, 1998 Walton, 2004). The continuum models are developed for large-scale simulations, where the controlling equations resemble the Navier-Stokes equations for an ordinary gas flow. The discrete particle models (DPMs) are typically used in small-scale simulations or... 

Consider an example from nucleation and growth of thin films. At least three length scales can be identified, namely, (a) the fluid phase where the continuum approximation is often valid (that may not be the case in micro- and nanodevices), (b) the intermediate scale of the fluid/film interface where a discrete, particle model may be needed, and (c) the atomistic/QM scale of relevance to surface processes. Surface processes may include adsorption, desorption, surface reaction, and surface diffusion. Aside from the disparity of length scales, the time scales of various processes differ dramatically, ranging from picosecond chemistry to seconds or hours for slow growth processes (Raimondeau and Vlachos, 2002a, b). 

This model is based on quasimolecular dynamics, in which the medium is assumed to be composed of an assembly of meso-scale discrete particles (i.e., finite elements). Tlie movement and deformation of the material system and its evolution are described by the aggregate movements of these elements. Two types of basic characteristics, geometrical and physical, are considered. In tlie geometrical aspect, sliapes and sizes of elements and tlie manner of their initial aggregation and arrangement are the important factors. In the physical aspect, mechanical, physical, and chemical characteristics, such as the interaction potential, phase transition, and chemical reactivity may be tlie important ones. To construct this model, many physical factors, including interaction potential, friction of particles, shear resistance force, energy dissipation and temperature increase, stress and strain at the meso- and macro-levels, phase transition, and chemical reaction are considered. In fact, simulation of chemical reactions is one of the most difficult tasks, but it is the most important aspect in shock-wave chemistiy. 

At a higher level, the flow field is modeled at a scale much larger than the size of the particles, and the fluid velocity and pressure are obtained by solving the volume-averaged Navier-Stokes equations. The particle particle interactions (particle wall as well) are formulated with the so-called discrete particle models (DPMs), which are based on the schemes that are traditionally used in molecular dynamics simulations, with the addition of dissipation of mechanical energy. 

Dzwinel, W., Alda, W., and Yuen, D.A., Cross-Scale numerical simulations using discrete particle models, Molecul. SimuL, 22, 397-418, 1999. 

Discrete particle model At one level smaller in detail (and thus larger in scale), the DPM model employs a Lagrangian description of the individual particles on a subgrid scale, while the gas flow field is continuous and solved by the compressible Navier-Stokes equations. The scale at which the gas flow field is described is an order of magnitude larger than the particles, (a CFD grid cell typically contains 0(10 )-0(10 ) particles). 

Kriebitzsch SHL, van der Hoef M A, Knipers JAM Drag force in discrete particle models— continuum scale or single particle scale AIChEJ 59 316—324, 2013b. 

These different casein monomers combine with calcium phosphate to form discrete particles on the nano-size scale. The phosphoserines of the caseins are seemingly clustered for the purpose of linking within the micelle to putative calcium phosphate microcrystallites, also known as nanoclusters (Holt, 1992 Home, 1998, 2002, 2003, 2006 Holt et al., 2003 Home et al., 2007). Structural evidence for the existence of such nanoclusters has come from neutron and X-ray scattering (de Kruif and Holt, 2003 Holt et al., 2003 Pignon et al., 2004 Marchin et al., 2007). The presence of nanoclusters allows native casein micelles to be effective natural suppliers of essential calcium salts in the human diet in a readily assimilated functional form. Protein-nanocluster interactions are the central concept of the cross-linking mechanism in Holt s model of casein micellar assembly (Holt et al., 2003 de Kruif and Holt, 2003). Any analogy with conventional soap-like micelles is considered to be... 

Certainly the most important models for the development of modem scaling theory of critical phenomena have been the discrete Ising model of ferromagnetism and its antipode - the continuum van der Waals model of fluid. The widespread belief is that real fluids and the lattice-gas 3D-model belong to the same universality class but the absence of any particle-hole-type symmetry in fluids requires the revised scaling EOS. The mixed variables were introduced to modify the original Widom EOS and account the possible singularity of the rectilinear diameter. 

The Discrete Element Model (DEM) (Bicanic 2004) is a numerical method on the micro scale. It is an explicit dynamic numerical method for the solution of interacting particle systems. Continuum properties are obtained by the cumulative behaviour of a large number of particles with short range interactions (Bicanic... 

In recent years, there has been great interest in developing physically inspired computational models based on the idea that the dynamics of the motion of fluid and interfaces can be represented in terms of the collective behavior of interactions of quasi-particle populations at scales smaller than macroscopic, but larger than molecular scales. These models fall in the class of mesoscopic methods - the LBM [6, 42, 45] being one. The LBM is generally based on minimal discrete kinetic models whose emergent behavior, under appropriate constraints, corresponds to the... 

Conversely, the modeling approach can be based on the microscopic description working from the smallest scales upward along the general hnes of the program for statistical mechanics. Discrete-particles techniques represent such an approach. 

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