544
G. Kotalczyk and F. E. Kruis
reproduced by the merging as well as the random removal approach. The random
removal approach leads to larger noise levels, which can be seen in slight deviations
of the PSD in the mixer unit in Fig. 15. The addition of a tear stream leads to an
increase of these noise levels, as can be seen Fig. 16—the approximations based on
the random removal technique become less accurate but can be still considered to be
in accordance with the results obtained by the fixed pivot method.
The replacement of the mixer with a sieve unit (or replacing flowsheet 1 with
flowsheet 3) leads also to a system, which can be well simulated by the random
removal technique (see Fig. 17). The addition of a tear stream to flowsheet 3 (resulting in flowsheet 4) leads—however—to such a complex system, that the random
removal method is not applicable. Figure 18 shows the striking deviations of the
PSDs obtained with the random removal method—which predict a wrong particlenumber concentration in the screen and filter 2 by a factor of nearly 10. The suggested
merging techniques—on the other hand—are able to reproduce the benchmark results
with a very high accuracy. This allows to say, that the specific combination of tearstream and screen leads to a simulation scenario, which cannot be addressed with
conventional MC simulation techniques—as the random removal technique. This
finding also explains the failure of the random removal techniques to describe an
even more complex simulation scenario, reported in [57].
4 Conclusions
The application of weighted MC particles for the solution of a compartmental
network in the framework of an operator splitting approach (the single processes
like coagulation and nucleation are separated for short periods of time) has been
discussed.
First, the solution of a one-compartmental system has been discussed, it has been
found that:
• the application of the stochastic resolution allows to describe the coagulation
between weighted simulation particles (like already discussed in [23]).
• merging techniques allow to simulate the combined nucleation and coagulation with a lower amount of statistical noise than conventional MC simulation
techniques (like already discussed in [23]).
• the parallel simulation of evaporation and condensational growth allows to simulate particles formation processes and investigate the role of different nucleation
theories (this has been already discussed for metallic [26] and atmospheric systems [27], but the here presented case-study of Ag-particle synthesis has not been
published prior to this work).
• novel selection and weighting techniques of the MC fragment population resulting
from particle breakage lead to simulation techniques which are able to render the
full particle size spectrum completely (these simulation techniques and findings
have already been presented in [43]).
G. Kotalczyk and F. E. Kruis
reproduced by the merging as well as the random removal approach. The random
removal approach leads to larger noise levels, which can be seen in slight deviations
of the PSD in the mixer unit in Fig. 15. The addition of a tear stream leads to an
increase of these noise levels, as can be seen Fig. 16—the approximations based on
the random removal technique become less accurate but can be still considered to be
in accordance with the results obtained by the fixed pivot method.
The replacement of the mixer with a sieve unit (or replacing flowsheet 1 with
flowsheet 3) leads also to a system, which can be well simulated by the random
removal technique (see Fig. 17). The addition of a tear stream to flowsheet 3 (resulting in flowsheet 4) leads—however—to such a complex system, that the random
removal method is not applicable. Figure 18 shows the striking deviations of the
PSDs obtained with the random removal method—which predict a wrong particlenumber concentration in the screen and filter 2 by a factor of nearly 10. The suggested
merging techniques—on the other hand—are able to reproduce the benchmark results
with a very high accuracy. This allows to say, that the specific combination of tearstream and screen leads to a simulation scenario, which cannot be addressed with
conventional MC simulation techniques—as the random removal technique. This
finding also explains the failure of the random removal techniques to describe an
even more complex simulation scenario, reported in [57].
4 Conclusions
The application of weighted MC particles for the solution of a compartmental
network in the framework of an operator splitting approach (the single processes
like coagulation and nucleation are separated for short periods of time) has been
discussed.
First, the solution of a one-compartmental system has been discussed, it has been
found that:
• the application of the stochastic resolution allows to describe the coagulation
between weighted simulation particles (like already discussed in [23]).
• merging techniques allow to simulate the combined nucleation and coagulation with a lower amount of statistical noise than conventional MC simulation
techniques (like already discussed in [23]).
• the parallel simulation of evaporation and condensational growth allows to simulate particles formation processes and investigate the role of different nucleation
theories (this has been already discussed for metallic [26] and atmospheric systems [27], but the here presented case-study of Ag-particle synthesis has not been
published prior to this work).
• novel selection and weighting techniques of the MC fragment population resulting
from particle breakage lead to simulation techniques which are able to render the
full particle size spectrum completely (these simulation techniques and findings
have already been presented in [43]).