Phase separation simulation

Figures 1.5.1-1.5.3 show component frequency spectra for the reactive phase separation of the ternary system starting with 10wt% MAA and 90wt% water at a dimensionless reaction rate coefficient for the monomer, Da = 10.8. For comparison, the nonreactive phase separation simulation result is also shown in the...

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

The question of whether adsorption should be done ia the gas or Hquid phase is an interesting one. Often the choice is clear. Eor example, ia the separation of nitrogen from oxygen, Hquid-phase separation is not practical because of low temperature requirements. In C q—olefin separation, a gas-phase operation is not feasible because of reactivity of feed components at high temperatures. Also, ia the case of substituted aromatics separation, such as xylene from other Cg aromatics, the inherent selectivities of iadividual components are so close to one another that a simulated moving-bed operation ia hquid phase is the only practical choice. 

Another example of phase transitions in two-dimensional systems with purely repulsive interaction is a system of hard discs (of diameter d) with particles of type A and particles of type B in volume V and interaction potential U U ri2) = oo for < 4,51 and zero otherwise, is the distance of two particles, j l, A, B] are their species and = d B = d, AB = d A- A/2). The total number of particles N = N A- Nb and the total volume V is fixed and thus the average density p = p d = Nd /V. Due to the additional repulsion between A and B type particles one can expect a phase separation into an -rich and a 5-rich fluid phase for large values of A > Ac. In a Gibbs ensemble Monte Carlo (GEMC) [192] simulation a system is simulated in two boxes with periodic boundary conditions, particles can be exchanged between the boxes and the volume of both boxes can... 

L. M. Martiouchev, V. D. Seleznev, S. A. Skopinov. Computer simulation of nonequilibrium growth of crystals in a two-dimensional medium with a phase-separating impurity. J Stat Phys 90 1413, 1998. 

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... 

When the two phases separate the distribution of the solvent molecules is inhomogeneous at the interface this gives rise to an additional contribution to the free energy, which Henderson and Schmickler treated in the square gradient approximation [36]. Using simple trial functions, they calculated the density profiles at the interface for a number of system parameters. The results show the same qualitative behavior as those obtained by Monte Carlo simulations for the lattice gas the lower the interfacial tension, the wider is the interfacial region in which the two solvents mix (see Table 3). 

The basic model has already been extended to treat more complex phenomena such as phase separating and immiscible mixtures. These developments are still at an early stage, both in terms of the theoretical underpinnings of the models and the applications that can be considered. Further research along such lines will provide even more powerful mesoscopic simulation tools for the study of complex systems. 

In the perspective discussed in the present contribution, bundle formation occurs within the amorphous phase and in undercooled polymer solutions. It does not imply necessarily a phase separation process, which, however, may occur by bundle aggregation, typically at large undercoolings [mode (ii)]. In this case kinetic parameters relating to chain entanglements and to the viscous drag assume a paramount importance. Here again, molecular dynamics simulations can be expected to provide important parameters for theoretical developments in turn these could orient new simulations in a fruitful mutual interaction. 

Gelb, L. D. Gubbins, K. E., Studies of binary liquid mixtures in cylindrical pores phase separation, wetting and finite-size effects from Monte Carlo simulations, Physica A 1997, 244, 112-123... 

Figure 19. Double-phase-separated morphology reported from the 2D simulations of the phase separation in the hydrodynamic regime [158]. This figure has been kindly provided by Dr. T. Araki. 

Figure 41. The percolation threshold determination for polymer blends undergoing the phase separation. Minority phase volume fraction, fm, is plotted versus the Euler characteristic density for several simulation runs at different quench conditions, /meq- = 0.225,..., 0.5. The bicontinuous morphology (%Euier < 0) has not been observed for fm < 0.29, nor has the droplet morphology (/(Euler > 0) been observed for/m > 0.31. This observation suggests that the percolation occurs at fm = 0.3 0.01.

Obviously, these two items are not strictly separated in contrast, the most fruitful approach is when they are simultaneously followed, so that they can mutually benefit from each other. In this chapter, we want to focus on the use of simulation methods as a design tool for gas-fluidized bed reactors, for which we consider gas-solid flows at four distinctive levels of modeling. However, before discussing the multilevel scheme, it is useful to first briefly consider the numerical modeling of the gas and solid phase separately. 

Figure 8.2 Phase separation in binary mixtures of model spherical particles at a planar interface generated by Brownian dynamics simulation. The three 2-D images refer to systems in which (A) light particles form irreversible bonds, (B) light particles form reversible bonds, and (C) neither dark nor light particles form bonds, but they repel each other. Picture D shows a 3-D representation. Reproduced from Pugnaloni et al. (2003b) with permission.

---