Aggregation simulation

Most numerical techniques employed for aggregation simulation are based on the equilibrium growth assumption and on the Smoluchowski theory. As shown in Meakin (1988, 1998), analytical solutions for the Smoluchowski equation have been obtained for a variety of different reaction kernels these kernels represent the rate of aggregation of clusters of sizes x and y. In most cases, these reaction kernels are based on heuristics or semi-empirical rules. 

There are further application-dependent tools, either invented or developed within or outside of IMPROVE and used therein. In any case, they have been refined due to this use. One such example is the heterogeneous simulation of the chemical overall process (see Sect. 5.3) which unites different single simulations to one aggregated simulation for a whole chemical process. Another topic is a specific simulation approach for plastics processing (see Sect. 5.4) which especially helps to bridge the gap between chemical engineering and plastics processing. Both have been used and extended but not invented within IMPROVE. Other tools are specific for IMPROVE (see e.g. Sects. 5.1 and 5.2). 

MOSTAFAVI, M., MARIGNIER, J. L., AMBLARD, J., BELLONI, J., Size-Dependent Thermodynamic Properties of Silver Aggregates. Simulation of the Photographic Development Process , Z. Phys. D 1989,12, 31-35. 

Figure 3.9 Results from 2d random aggregation simulations in which the depth of the potential of interaction was either 7 kT (a) or 4 kT (h). At 4 kT the aggregates are roughly circular crystallites in equilibrium with a monomer phase, that is, a dissolved phase. At 7 kT the aggregates are fractal, with a fractal dimension of 1.4, the DLCA value, over large length scales, but they retain a dense crystal packing over small length scales. These are called fat fractals.

The second important aspect of the model [31] in reference to nanofiller particle aggregation simulation is a finite nonzero initial particle concentration c or (p effect, which takes place in any real systems. This effect is realized at the condition t R, which occurs at the critical value R (R), determined according to the relationship [31] ... 

Since this work deals with the aggregated simulation and planning of chemical production processes, the focus is laid upon methods to determine estimations of the process models. For process control this task is the crucial one as the estimations accuracy determines the accuracy of the whole control process. The task to find an accurate process model is often called process identification. To describe the input-output behaviour of (continuously operated) chemical production plants finite impulse response (FIR) models are widely used. These models can be seen as regression models where the historical records of input/control measures determine the output measure. The term "finite" indicates that a finite number of historical records is used to predict the process outputs. Often, chemical processes show a significant time-dynamic behaviour which is typically reflected in auto-correlated and cross-correlated process measures. However, classic regression models do not incorporate auto-correlation explicitly which in turn leads to a loss in estimation efficiency or, even worse, biased estimates. Therefore, time series methods can be applied to incorporate auto-correlation effects. According to the classification shown in Table 2.1 four basic types of FIR models can be distinguished. 

Liquid Distributions in a Drying Particle Aggregate Simulated by tbe Volume-of-Fluid Method... 

A multitude of different variants of this model has been investigated using Monte Carlo simulations (see, for example [M])- The studies aim at correlating the phase behaviour with the molecular architecture and revealing the local structure of the aggregates. This type of model has also proven useful for studying rather complex structures (e.g., vesicles or pores in bilayers). 

Gruen D W R 1984 A model for the ohains in amphiphilio aggregates I. Comparison with a moleoular dynamios simulation of a bilayer J. Phys. Chem. 89 645... 

Karaborni S and O Connell J P 1993 Moleoular dynamios simulations of model ohain moleoules and aggregates inoluding surfaotants and mioelles Tenside 30 235-42... 

Brown W D and Ball R C 1985 Computer simulation of chemically limited aggregation J. Phys. A Math. Gen. 18 L517-21... 

Conformational free energy simulations are being widely used in modeling of complex molecular systems [1]. Recent examples of applications include study of torsions in n-butane [2] and peptide sidechains [3, 4], as well as aggregation of methane [5] and a helix bundle protein in water [6]. Calculating free energy differences between molecular states is valuable because they are observable thermodynamic quantities, related to equilibrium constants and... 

Flollander etal. (2001) report numerieal simulations of orthokinetie aggregation in a turbulent ehannel flow and in a stirred tank, respeetively. Using a... 

Beyond the CMC, surfactants which are added to the solution thus form micelles which are in equilibrium with the free surfactants. This explains why Xi and level off at that concentration. Note that even though it is called critical, the CMC is not related to a phase transition. Therefore, it is not defined unambiguously. In the simulations, some authors identify it with the concentration where more than half of the surfactants are assembled into aggregates [114] others determine the intersection point of linear fits to the low concentration and the high concentration regime, either plotting the free surfactant concentration vs the total surfactant concentration [115], or plotting the surfactant chemical potential vs ln( ) [119]. 

Hence the sizes of spherical micelles are distributed around a most probable aggregation number M, which depends only on molecular details of the surfactants in this simplest approximation. Indeed, micelle size distributions at concentrations beyond the CMC have shown a marked peak at a given aggregation number in many simulations [37,111,112,117,119,138,144,154,157]. 

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