Hard-particle methods

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... 

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. 

Case Hardening by Surface Deformation. When a metaUic material is plastically deformed at sufficiently low temperature, eg, room temperature for most metals and alloys, it becomes harder. Thus one method to produce a hard case on a metallic component is to plastically deform the surface region. This can be accomplished by a number of methods, such as by forcing a hardened rounded point onto the surface as it is moved. A common method is to impinge upon the surface fine hard particles such as hardened steel spheres (shot) at high velocity. This process is called shot... 

The results for the chemical potential determination are collected in Table 1 [172]. The nonreactive parts of the system contain a single-component hard-sphere fluid and the excess chemical potential is evaluated by using the test particle method. Evidently, the quantity should agree well with the value from the Carnahan-Starling equation of state [113]... 

At high-particle number densities or low coefficients of normal restitution e, the collisions will lead to a dramatical decrease in kinetic energy. This is the so-called inelastic collapse (McNamara and Young, 1992), in which regime the collision frequencies diverge as relative velocities vanish. Clearly in that case, the hard-sphere method becomes useless. 

Before applying the ideas summarised in the first section to polymer latices it is appropriate to consider the nature of polymer latex particles. We know, for example, that each particle is composed of a large number of polymer chains, with the chains having molecular weights in the range of about 105 to 107. Moreover, the particles themselves can be amorphous, crystalline, rubbery, glassy or monomer swollen, either extensively or minutely. It follows, therefore, that the properties of the system on drying depends directly on the physical state of the particles, for example, if the particles are soft, coalescence can occur to form a continuous film, whereas with hard particles their individuality is retained. The nature of the particle obtained is directly related to the preparative method employed and the surface properties are often determined by s-... 

Due to the variety in porous structure, particle size and surface area, pure silica gels and powders find a very wide range of applications. Variation in preparation methods and parameters allows the tailoring of the substrate properties for specific application needs. The main features in the silica applications are its porosity, active surface, hardness, particle size and the viscous and thixotropic properties. Although most applications are based on a combination of those, a classification according to the main properties of interest may be set up. For references, the reader is referred to the works of Iler6 and Unger7 and to the references cited in chapter 8. 

Here, we report some basic results that are necessary for further developments in this presentation. The merging process of a test particle is based on the concept of cavity function (first adopted to interpret the pair correlation function of a hard-sphere system [75]), and on the potential distribution theorem (PDT) used to determine the excess chemical potential of uniform and nonuniform fluids [73, 74]. The obtaining of the PDT is done with the test-particle method for nonuniform systems assuming that the presence of a test particle is equivalent to placing the fluid in an external field [36]. 

There are two main approaches for the numerical simulation of the gas-solid flow 1) Eulerian framework for the gas phase and Lagrangian framework for the dispersed phase (E-L) and 2) Eulerian framework for all phases (E-E). In the E-L approach, trajectories of dispersed phase particles are calculated by solving Newton s second law of motion for each dispersed particle, and the motion of the continuous phase (gas phase) is modeled using an Eulerian framework with the coupling of the particle-gas interaction force. This approach is also referred to as the distinct element method or discrete particle method when applied to a granular system. The fluid forces acting upon particles would include the drag force, lift force, virtual mass force, and Basset history force.Moreover, particle-wall and particle-particle collision models (such as hard sphere model, soft sphere model, or Monte Carlo techniques) are commonly employed for this approach. In the E-E approach, the particle cloud is treated as a continuum. Local mean... 

Figure 11.10 A schematic representation of the hard-template method used to prepare CPCs (a) porous membrane, (b) colloidal particles, (c) nanowires...

The wear resistance of a material can also be improved by adding particles of a second phase. If the particles are hard, the softer matrix material will wear off first, resulting in the hard particles sticking out of the surface and then determining the wear properties. This method is used, for example, in aluminium cylinder liners in combustion engines whose wear resistance is improved by silicon precipitates, or in cast iron (figure 6.42). 

In Section 1.4.4, the erosion test was outlined in the list of hardness determination methods and it was concluded that it was of minimal practical importance. However, solid particle erosion is a serious problem in gas turbine operations and in plants where powders are handled and it is of course used as a secondary shaping method in ceramic technology. Therefore it is more useful to consider how a knowledge of ceramic hardness contributes to an assessment of erosion. Figure 5.19 outlines how a knowledge of the process has developed through models taken from the types of indentation test damage already discussed in this chapter. 

Note that since the hard point has no soft interaction, the average binding energy Bs s is zero (as for any hard particle of any size see section 7.11). Therefore all of AH must be due to structural changes induced in the solvent. This can be interpreted in terms of a relaxation term using any method for classifying the solvent molecules into... 

The presence of other materials in primary explosives (additives) also influences the resulting sensitivity values. In some cases, hard particles (e.g., glass dust) are added to increase the sensitivity of a primary explosive which would otherwise be too insensitive for the desired method of initiation. A typical example is addition of glass dust to the LA which increases the sensitivity of the mixture to a level desired for application in stab and ftictiOTi detonators. The opposite effect is observed after addition of waxes or oils which lubricate the resulting mixture. This desensitizing effect is often utilized when it would be too risky to transport the substance in its pure form. 

Another complication associated with determination is of a more fundamental nature. One should remember that, unlike for hard particles, which has a unique value, in the case of interacting particles, is dependent not only on electrostatic interactions but also on the transport mechanism and particle distribution over an interface. Also, the polydispersity of the colloid suspension affects (cf Fig. 29). All of these effects lead to the deviation of the 0 versus x dependencies from linearity hence, a direct extrapolation of the kinetic data to infinite time may not be accurate enough. Even with these limitations, which are expected to be of the order of percents [12], the extrapolation procedure is more accurate than the usually adopted method of treating the coverage attained after a long (but undefined) time as the true 0, value. 

The dissipative particle dynamics (DPD) method is a recent variation of the molecular dynamics technique. Here, in addition to Newtonian forces between hard particles, soft forces between particles are also introduced. These pairwise damping and noise forces model slower molecular motions. The dissipative forces also reduce the drift in kinetic energy that occurs in molecular dynamics simulations. These two reasons mean that DPD can be used to model longer time-scale processes, such as hydrodynamic flows or phase separation processes. 

---