Aggregation and fragmentation dynamics of inertial particles in chaotic flows

Abstract

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new particles formed in this process are larger and follow the equation of motion with a new parameter. These particles can in turn fragment when they reach a certain size or shear forces become sufficiently large. The resulting system consists of a large set of coexisting dynamical systems with a varying number of particles. We find that the combination of aggregation and fragmentation leads to an asymptotic steady state. The asymptotic particle size distribution depends on the mechanism of fragmentation. The size distributions resulting from this model are consistent with those found in raindrop statistics and in stirring tank experiments.

Influence of the history force on inertial particle advection: Gravitational effects and horizontal diffusion

“…(1) as a dynamical system and are interested in the properties of the system for different particle sizes α. The diversity of possible behaviors was already described in [3,5,37] by neglecting the history force.…”

“…1,5). This corresponds to changing the particle size from 0.46r 1 = 0.23 mm to 1.7r 1 = 0.85 mm, which implies, in view of Eqs.…”

“…Hence, m α = αm 1 and r p ≡ r α = α 1/3 r 1 . This representation of the size turns out to be useful in studies of aggregation processes (see, e.g., [5]). The inertial parameter scales, therefore, with the size parameter, α, as…”

“…[1] and references therein). Theoretical studies consider the particle dynamics either in simplified kinematic flows [2][3][4][5], which yields chaotic advection of particles, as well as random [6,7] or turbulent flows [8]. Recent studies have emphasized the importance of the phenomenon of preferential concentration, observed in the advection of finite size particles [8,9].…”

A map for heavy inertial particles in fluid flows

“…The dynamics of collisional growth of inertial particles was studied in the context of chaotic advection by Zahnow et al [22,23]. The use of the Stokes map could allow the consideration of a much larger number of particles because it reduces the computational cost involved in the time evolution of their trajectories.…”