Simulation of Large Aggregate Particles System With a New Morphological Model




Colloidal structure, Fractal dimension, Morphological model


For the development of a new porous material such as catalytic carrier, the control of the textural properties is of fundamental importance. In order to move towards rational synthesis, it is necessary to better understand the physical phenomena that generate a defined solid structure. A contribute to this purpose can be achieved by studying the aggregation process inside colloidal suspensions, leading to porosity generation: this phenomenon can be described with a Brownian dynamics model that, for any set of chemical parameters, gives access to the mass distribution and the fractal dimension of colloidal aggregates. However, this model cannot be used for the simulation of large colloidal systems, due to its high computational time, limiting comparison with analytical methods, which probe the whole multi-scale system. This problem is solved by developing a new aggregation morphological model, wherein the fractal dimension is tuned with two compactness parameters. An efficient simulation algorithm is proposed in case of spheres, for which the fractal dimension of the generated aggregates varies between 1.2 and 3. Brownian dynamics results are used to parametrize this purely geometric model, in order to constrain the size and the morphology of the aggregates created. The large numerical solid will be representative of the textural properties of a real solid and will give more information on the porous network. It could be used, for example, to simulate diffusive transport coupled with chemical reaction and to study the impact of the geometry of the porous system on the catalytic performance.

Author Biography

Maxime Moreaud, IFP Energies Nouvelles, Rond-Point de l’échangeur de Solaize, 69360, Solaize, France




Adamczyk Z, Siwek B, Zembala M, Weronski P(1997). Influence of Polydispersity on Random Sequential Adsorption of Spherical Particles. J Colloid Interf Sci 185:236–44.

Altendorf H, Jeulin D (2011). Random-walk-based stochastic modeling of three dimensional fiber systems. Phys Rev E 83:041804.

Anovitz LM, Zhang X, Soltis J, Nakouzi E, Krzysko AJ, Chun J, Schenter GK, Graham TR, Rosso KM, De Yoreo JJ, Stack AG, Bleuel M, Gagnon C, Mildner DFR, Ilavsky J, Kuzmenko I (2018). Effects of Ionic Strength, Salt, and pH on Aggregation of Boehmite Nanocrystals: Tumbler Small-Angle Neutron and X-ray Scattering and Imaging Analysis. Langmuir 34:15839158-53.

Baranau V, Tallarek U (2014).Random-close packing limits for monodisperse and plydisperse hard spheres. Soft Matter 10:3826.

Cerbelaud M, Ferrando R, Videcoq A (2010). Simulations of heteroaggregation in a suspension of alumina and silica particles: Effect of dilution. J Chem Phys 132.

Chiche D, Digne M, Revel R, Chanéac C, Jolivet J-P (2008).Accurate Determination of Oxide Nanoparticle Size and Shape Based on X-Ray Powder Pattern Simulation: Application to Boehmite AlOOH. J Phys Chem-US C 112:8524–33.

Cordelair J, Greil P (2004). Flocculation and coagulation kinetics of Al2O3 suspensions. J Eur Ceram Soc 24:2717–22.

Delarue, A. and Jeulin, D. (2001). Multi-scale simulation os spherical aggregates. Image Anal Stereol 20:181–6.

Donev A, Torquato S, Stillinger FH (2005). Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles. I. Algorithmic details. J Comput Phys 202:737–64.

Długosz M, Zielinski P, Trylska J (2011). Brownian dynamics simulations on CPU and GPU with BD BOX. J Comput Chem 32:2734-44.

Euzen P, Raybaud P, Krokidis X, Toulhoat H, Le Loarer J-L, Jolivet J-P, Froidefond C (2002). Alumina. In Handbook of Porous Solids. Wiley.

Fabbri R, Da F, Costa L, Torelli JC, Bruno OM (2008). 2D Euclidean distance transform algorithms: A comparative survey. ACM Comput Surv 40.

Filippov AV, Zurita M, Rosner DE (2000). Fractal-like Aggregates: Relation between Morphology and Physical. J Colloid Interf Sci 229:261–73.

Greco A, Jeulin D, Serra J (1979). The use of the texture analyser to study sinter structure: application to the morphology of calcium ferrites encountered in basic sinters of rich iron ores. J Microsc 116:199–211.

Hamaker (1937). Theory of the stability of lyophobic colloids: the interaction of sol particles having an electric double layer. Physica IV 10:1058–72.

Hutter (2000). Local Structure Evolution in Particle Network Formation Studied by Brownian Dynamics Simulation. J Colloid Interf Sci 231:337–50.

Iler RK (2004).The chemistry of silica: Solubility, polymerization, colloid and surface properties, and biochemistry. Wiley.

Jeulin D (2000). Random texture models for material structures. Stat Comput 10:121–32.

Jeulin D (2012). Morphology and effective properties of multi-scale random sets:a review. Cr Mecanique 340:219–29.

Jeulin D (2019). Some dense random packings generated by the dead leaves model. Image Anal Stereol 38:3–13.

Krinninger P, Fortini A, Schmidt M (2016). Minimal Model for Dynamic Bonding in Colloidal Transient Networks. Phys Rev E 93.

Kolitcheff S, Jolimaitre E, Hugon A, Verstraete J, Carrette P-L, Tayakout-Fayolle M (2017). Tortuosity of mesoporous alumina catalyst supports: Influence of the pore network organization. Micropor Mesopor Mat 248:91–98.

Köylü UO, Faeth GM, Farias TL, Carvalho MG (1995). Fractal and projected Structure Properties of Soot Aggregates. Combust Flame 100:621–33.

Laganapan AM, Mouas M, Videcoq A, Cerbelaud M, Bienia M, Bowen P, Ferrando R (2015). How colloid-colloid interactions and hydrodynamic effects influence the percolation threshold: A simulation study in alumina suspensions. J Colloid Interf Sci 458:241–46.

Langevin P (1908). Sur la théorie du mouvement brownien. Cr Acad Sci 17:499–503.

Lebdioua K, Cerbelaud M, Aimable A, Videcoq A (2020). Aggregation behavior of onepatch inverse patchy particles: an experimental and numerical study. hal-02613670.

Lu PJ, Zaccarelli E, Ciulla F, Schofield AB, Sciortino F, Weitz DA (2008). Gelation of particles with short-range attraction. Nature 453:499–503.

Lubachevsky BD, Stillinger FH, (1990). Geometric properties of random disk packings. J Stat Phys 60:561–83.

Matern, B (2013). Spatial Variation. Lect Notes Stat.

Matheron, G (1975). Random Sets and Integral Geometry. New York. Wiley.

Meakin P (1983). Formation of Fractal Clusters and Networks by Irreversible Diffusion-Limited Aggregation. Phys Rev Lett 51:1119–22.

Moscinski J, Bargieł M, Rycerz Z A, Jacobs P W M (1989). The Force-Biased Algorithm for the Irregular Close Packing of Equal Hard Spheres. Mol Simulat 3:201-12.

Moreaud M, Jeulin D, Morard V, Revel R (2012). TEM image analysis and modelling: Application to boehmite nanoparticles. J Microsc 245:186–99.

Moreaud M, Chaniot J, Fournel T, Becker JM, Sorbier L (2012). Multi-scale stochastic morphological models for 3D complex microstructures. IEEE Worksh Inf Opt Proceedings.

Munhoz AH, de Paiva H, Figueiredo de Miranda L, de Oliveira EC, Andrades RC, Ribeiro RR (2014). Study of Gamma Alumina Synthesis – Analysis of the Specific Surface Area. Adv Sci Tech 87:54–60

Nikunen P, Vattulainen I, Karttunen M (2007). Reptational dynamics in dissipative particle dynamics simulations of polymer melts. Phys Rev E 75.

Park JD, Myung JS, Ahn KH, (2016). A review on particle dynamics simulation techniques for colloidal dispersions: Methods and applications. Korean J Chem Eng 33:3069–78.

”plug im!” an open access and customizable software for signal and image processing (2018).

Sasanuma Y, Kitano Y, Ishitani K (1989). Characterization of industrial materials by small angle X-ray scattering. J Mater Sci 24:1133–39 .

Schaefer DW, Hurd AJ (1990). Growth and Structure of Combustion Aerosols: Fumed Silica. Aerosol Sci Tech 12:876–890.

Schmidt PW, Dacai X (1986). Calculation of the small-angle x-ray and neutron scattering from nonrandom (regular) fractals. Phys Rev A 33:560.

Schmidt PW (1991). Small–angle scattering studies of disordered, porous and fractal systems. J Appl Crystallogr 24: 414–35.

Serra J (1988). Image analysis and mathematical morphology. Cambridge. Academic Press

Seyed-Ahmadi A, Wachs A (2019). Dynamics and wakes of freely settling and rising cubes. Phys Rev Fluids 4:074304.

Sorbier L, Moreaud M,Humbert S (2019). Small-angle X-ray scattering intensity of multiscale models of spheres. J Appl Crystallogr 52:1348–57.

Sorensen CM (2001). Light Scattering by Fractal Aggregates: A Review. Aerosol Sci Tech 35:648–87.

Sorensen CM, Roberts GC (1997). The prefactor of Fractal Aggregates. J Colloid Interf Sci 186:447-52.

Tence M, Chevalier JP, Jullien R (1986). On the measurement of the fractal dimension of aggregated particles by electron microscopy: Experimental method, corrections and comparison with numerical models. J Physique 47:1989–98.

Tomchuk OV, Avdeev MV, Bulavin LA (2020). Modeling fractal aggregates of polydisperse particles with tunable dimension. Colloid Surface A 605:125331.

Torquato S, Jiao Y (2010). Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming. Phys Rev E 82:061302.

Thouy R, Jullien R (1996). A cluster-cluster aggregation model with tunable fractal dimension. J Phys A-Math Gen 27: 2953.

Verwey EJ, Overbeek JTG. (1948). Theory of the stability of lyophobic colloids: the interaction of sol particles having an electric double layer. Elsevier.

Wang H, Pietrasanta A, Jeulin D, Willot F, Faessel M, Sorbier L, Moreaud M (2015). Modelling mesoporous alumina microstructure with 3D random models of platelets. J Microsc 260:287–301.

Widom B (1996). Random sequential addition of hard spheres to a volume. J Chem Phys 44:3888.

Witten TA, Sander LM (1983). Diffusion-limited aggregation. Phys Rev B 27:5686.

Zaccarelli E (2007). Colloidal gels: Equilibrium and non-equilibrium routes. J Phys Condens Matter 19.

Zhang G, Torquato S. (2013). Precise algorithm to generate random sequential addition of hard hyperspheres at saturation. Phys Rev E 88:053312.

multi-scale aggregate generated with our proposed morphological model




How to Cite

Moreaud, M., Ferri, G., Humbert, S., Digne, M., & Schweitzer, J.-M. (2021). Simulation of Large Aggregate Particles System With a New Morphological Model. Image Analysis and Stereology, 40(2), 71–84.



Original Research Paper