Fuentes, Andrés

Liu, Fengshan

Morán, José

Poux, Alexandre

Yon, Jérôme

English

HAL - Normandie Université

Improving Monte Carlo simulations for an accurate modeling of nanoparticles coagulation

Archive Ouverte en Sciences de l'Information et de la Communication

  
Improving Monte Carlo simulations for an accurate  
modeling of nanoparticles coagulation 
 
José Morán1, Jérôme Yon1, Alexandre Poux1, Fengshan Liu2, Andrés Fuentes3 
 
1Normandie Université, INSA Rouen, UNIROUEN, CNRS, CORIA, Rouen, 76000, France 
2Measurement Science and Standards, National Research Council of Canada, Ontario, Ottawa, Canada 
3Dep. de Industrias, Univ. Técnica Federico Santa María, Av. España 1680, Casilla 110-V, Valparaíso, Chile 
 
Keywords: Monte Carlo, Langevin Dynamics, coagulation, aggregation 
Contact: morancoj@coria.fr 
 
 
Introduction 
 The growth of suspended nanoparticles by 
coagulation (aggregation and/or coalescence) is 
found in many industrial, combustion and 
environmental processes (Friedlander, 2000). In this 
context particles naturally evolve into polydisperse 
sizes. These particles experience a movement 
characterized by very different momentum relaxation 
times. Thus, accurate numerical methods, such as 
Langevin Dynamics, become computationally 
expensive to simulate the coagulation of a large 
population of particles (Buesser et al., 2009). On the 
other hand, the Monte Carlo (MC) method (simply 
consisting in selecting a particle at time and moving 
it in a random orientation), is a very computationally 
efficient alternative to overcome this issue. However, 
it is usually regarded as a technique that relies on an 
artificial description of time making it difficult to 
study coagulation (Lazzari et al., 2016). Despite this, 
some efforts have been made to obtain a more 
physical description of time (Hasmy & Jullien, 1995; 
Lazzari & Lattuada, 2017). Unfortunately, as we will 
show, they usually lead to incoherent time progress 
for the ensemble of polydisperse particles and/or they 
are restricted to specific flow regimes (diffusion 
limited or ballistic). Also, in different studies based 
on the MC method, the probability of moving a 
particle is adapted to the flow regime with some rules 
whose expressions are lack of justification (Kim et 
al., 2010). Moreover, in such studies, particles are 
usually displaced along a constant distance in the 
order of monomers’ diameter, regardless of their 
sizes. A few studies have considered size-dependent 
displacement (Hayashi et al., 1999). In this study, we 
propose a new MC method with justified 
probabilities of particles’ movement, considering 
size-dependent displacement and able to bring a 
validated and consistent physical time evolution for 
individual as well as for the ensemble of polydisperse 
particles.  
Results 
 The method is firstly presented and compared 
with previous methods found in the literature to 
finally validate it by a comparison with Langevin 
Dynamics simulations. The evolution of calculated 
mean squared displacements for different-sized 
particles is compared with theoretical values in 
Figure 1, observing a good agreement between the 
numerical simulations and Einstein’s theory 
(Friedlander, 2000). 
Conclusions 
 The method is able to efficiently simulate the 
dynamics of coagulation. For the first time, 
consistent and coherent residence times of particles 
are obtained. The proposed MC method could be 
used to study more complex dynamic processes such 
as surface growth, sintering or breakage of 
aggregates. 
 
Figure 1. The <r2> of a system of 3 off-lattice 
particles (suspended in air at standard conditions). 
Friedlander, S. K. (2000). Smoke, Dust, and Haze: 
Fundamentals of Aerosol Dynamics. New 
York: Oxford University Press. 
Buesser, B., Heine, M. C., & Pratsinis, S. E. (2009). 
J. Aerosol Science, 40(2), 89–100.  
Lazzari, S., Nicoud, L., Jaquet, B., Lattuada, M., & 
Morbidelli, M. (2016). Adv. Colloid Interface 
Sci., 235, 1–13.  
Hasmy, A., & Jullien, R. (1995). J. Non-Cryst. 
Solids, 186, 342–348.  
Lazzari, S., & Lattuada, M. (2017). J. Phys. Chem. B, 
121(11), 2511–2524.  
Kim, S., Lee, K.-S., Zachariah, M. R., & Lee, D. 
(2010). J. Colloid Interface Sci., 344(2), 353–
361.  
Hayashi, S., Hisaeda, Y., Asakuma, Y., Aoki, H., 
Miura, T., Yano, H., & Sawa, Y. (1999). 
Combust. Flame, 117(4), 851–860.  


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Improving Monte Carlo simulations for an accurate modeling of nanoparticles coagulation

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