Particle Dynamics Simulation

Two of the most common classes of particle-dynamic simulations are termed hard-particle and soft-particle methods. Hard-particle methods calculate particle trajectories in response to instantaneous, binary collisions between particles and allow particles to travel ballistically between collisions. This class of... 

Fig. 7 Rapid, convective flow seen in particle-dynamic simulation of identical but colored spheres in V-blender. (A) view from front reveals that unlike in some designs, convection in this blender drives grains axially, alternately outward toward the tumbler arms and inward toward its center. This axial flow strongly influences mixing, as described in the section on Mixing Rates. (B) View from side indicates that transport is dominated by a spiraling flow, seen also in drums and other blenders (Fig. 4).

Fig. 8 Dispersive mixing is slow across the symmetry plane of a blender, here a tote design. After 10 revolutions, a front view reveals clear evidence of the initial left-right distribution of identical but colored spheres in this particle-dynamic simulation.

To examine the behavior of mixing measures, it is useful to begin by considering systems free of experimental uncertainties. Particle dynamic simulations such as those discussed in the sections Mixing mechanism in Three Dimensional Tumblers and Demixing, represent such ideal systems the presence and locations of all particles are known and are free of sampling errors (discussed in the section on Sampling Techniques ). 

Fig. 15 Variance of concentrations of identical color-coded grains from particle-dynamic simulations of (A) a doublecone and (B) a V-blender. Notice that the smooth flow in the double-cone is reflected in a smooth, asymptotically exponential, reduction in variance with time, while the sloshing flow in the V-blender (Fig. 7) produces periodic undulations in mixing response.

In practical blending processes, one cannot obtain arbitrary quantities of pristine data as one can using particle-dynamic simulations, and one must settle for sampling a static bed, as mentioned previously. In such a case, it is especially important to understand sampling limitations and systematic biases. A common means of obtaining samples in a tumbler is by the use of a scoop or thief sampler. These samplers are inserted into the bed and extract samples from its... 

Fig. 16 Evaluation of segregation between different size particles in particle dynamic simulations in (A) double-cone and (B) V-blender.

Figure 7.5. Representative results from dissipative particle dynamics simulations studying nonionic diblock surfactant adsorption onto oil-water interfaces [34], (a) A water film between two layers of oil, showing that the surfactant molecules have preferentially migrated to the interfaces and oriented themselves such that their hydrophilic portions are pointed towards the water layer while their hydrophobic portions are pointed towards the oil layers. See the insert showing the colored figures for a better view, (b) Final interfacial tension as a function of the bulk concentration of surfactant, (c) Evolution of the interfacial tension as a function of time (as represented by the simulation steps), for two different concentrations (5% and 15%) by volume of the surfactant. Dr. Brace Eichinger, from Accelrys, Inc., kindly provided this figure. Copyright (2001) Taylor Francis for Figure 7.5(c).

Density and solubility parameter as a function of chain length for (a) polyethylene oxide (PEO) and (b) polyvinyl chloride (PVC). (From Luo, Z. L., and Jiang, J. W. 2010. Molecular dynamics and dissipative particle dynamics simulations for the miscibility of poly(ethylene oxide)/ poly(vinyl chloride) blends. Polymer 51 291-299.)... 

Besold, G., Vattulainen, I., Karttunen, M., Poison, J.M. Towards better integrators for dissipative particle dynamics simulations. Phys. Rev. E 62(6), R7611 (2000). doi 10.1103/ PhysRevE.62.R7611... 

However, the dissipative particle dynamics simulation technique trys to avoid the major drawback of the classical MD method which often provides far more detail of the small-scale fluctuational motion of atoms than is necessary for an understanding of many physical processes of surfactants. With DPD, the mesoscopic length and time regimes in complex fluids are accessible... 

Vattulainen I, Karttunen M, Resold G, Poison JM (2002) Integration schemes for dissipative particle dynamics simulations from softly interacting systems towards hybrid models. J Chem Phys 116 3967-3979... 

Symenoidis V, Kamiadakis GE, Caswell B (2005) Dissipative particle dynamics simulations of polymer chains scaling laws and shearing response compared to DNA experiments. Phys Rev Lett 95 076001... 

Duong-Hong D, Wang J-S, Liu G, Chen Y, Han J, Hadjiconstantinou N (2008) Dissipative particle dynamics simulations of electroosmotic flow in nano-fluidic devices. Microfluid Nanofluid 4(3) 219-225... 

Atomistic computer simulation Particle dynamics simulation Molecular modeling... 

Irfachsyad, D., Tildesley, D., Malfreyt, P. Dissipative particle dynamics simulation of grafted polymer brushes under shear. Phys. Chem. Chem. Phys. 4, 3008-3015 (2002). doi 10.1039/ B110738k... 

Morgan, J.K. (2004) Particle dynamics simulations of rate- and state-dependent frictional sliding of granular fault gouge. Pure and Applied Geophysics 161,1877-1891. 

Soto-Figueroa C, del Rosario Rodriguez-Hidalgo M, Vicente L Dissipative particle dynamics simulation of the miceHization-demicellization process and micellar shuttle of a diblock copolymer in a biphasic system (water/ionic-liquid). Soft Matter 8 1871-1877, 2012. 

Tang Yuan-hui, He Yan-dong, and Wang Xiao-lin. Investigation on the membrane formation process of polymer-diluent system via thermally induced phase separation accompanied with mass transfer across the interface Dissipative particle dynamics simulation and its experimental verification. J. Membr. Sci. 474 (2015) 196—206. 

Groot, R. D. 2003. Electrostatic interactions in dissipative particle dynamics—Simulation of polyelectrolytes and anionic surfactants. 118, 11265. 

Figure 15-17 Axial segregation in top views of double-cone blender from (a) experiment and (b) particle-dynamic simulation using large, light and small, dark spherical grains. Similar patterns are seen in other tumbler designs for example, in the V-blender in (c) experiment and (d) simulation.

To model flow and blending in complicated geometries, particle-dynamic simulations have been applied. In these simulations, particles are treated as individual entities with physical properties (e.g size, static and dynamic friction coefficients, coefficient of restitution, etc.) appropriate to the problem of interest, and Newton s laws of motion are integrated for each particle. Particle-dynamic simulations are similar in concept to molecular-dynamic simulations but include... 

Two of the most common classes of particle-dynamic simulations are termed hard-particle and soft-particle methods. Hard-particle methods calculate particle trajectories in response to instantaneous, binary collisions between particles, and allow particles to follow ballistic trajectories between collisions. This class of simulation permits only instantaneous contacts and is consequently often used in rapid flow situations such as are found in chutes, fluidized beds, and energetically agitated systems. Soft-particle methods, on the other hand, allow each particle to deform elastoplastically and compute responses using standard models from elasticity and tribology theory. This approach permits enduring particle contacts and is therefore the method of choice for mmbler apphcations. The simulations described in this chapter use soft-particle methods and have been validated and found to agree in detail with experiments. 

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