The coagulation of aerosol particles plays an important role in the structural morphological changes suspended at any time and space. In this study, based on Smoluchowski equation population balance, a kinetic model coalescence considering Brownian motion collision is established. By applying developed Lie group method, we derive allowed infinitesimal symmetries group-invariant solutions integr...

A previously published model of homogeneous nucleation [Villarica et al., J. Chem. Phys. 98, 4610 (1993)] based on the Smoluchowski [Phys. Z. 17, 557 (1916)] equations is used to simulate the experimentally measured size distributions of 4He clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive coll...

The phase-field-crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field-crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density-functional theory. The different underlying approximations are discussed. In particu...

Smoke reduction processes in an indoor room-scale chamber are generated by injecting nanoparticle aggregates. A numerical model, with a flow solver implemented with a particle collision model, is used to simulate the smoke-reduction effect. The collision model, developed particularly for simulating collisions among particles with significantly different sizes, enables real-time simulations of t...

We construct Markov processes for modeling the rupture of edges in a two-dimensional foam. first describe network model tracking topological information foam networks with state space combinatorial embeddings. Through mean-field rule randomly selecting neighboring cells rupturing edge, we consider simplified version sequence $$\ell _1({\mathbb {N}})$$ which counts total numbers $$n\ge 3$$ sides...

We revisit the scaling theory of the Smoluchowski equation with special emphasis on the dimensional analysis to derive the scaling ansatz and to give an insightful foundation to it. It has long been argued that the homogeneity exponent λ of the aggregation kernel divides the aggregation process into two regimes (i) λ ≤ 1 nongelling and (ii) λ > 1 gelling. However, our findings contradict with t...