Aggregation and fragmentation dynamics of inertial particles in chaotic flows

Lagrangian flow networks for passive dispersal: Tracers versus finite-size particles

The transport and distribution of organisms such as larvae, seeds, or litter in the ocean as well as particles in industrial flows is often approximated by a transport of tracer particles. We present a theoretical investigation to check the accuracy of this approximation by studying the transport of inertial particles between different islands embedded in an open hydrodynamic flow aiming at the construction of a Lagrangian flow network reflecting the connectivity between the islands. To this end, we formulate a two-dimensional kinematic flow field which allows the placement of an arbitrary number of islands at arbitrary locations in a flow of prescribed direction. To account for the mixing in the flow, we include a von Kármán vortex street in the wake of each island. We demonstrate that the transport probabilities of inertial particles making up the links of the Lagrangian flow network essentially depend on the properties of the particles, i.e., their Stokes number, the properties of the flow, and the geometry of the setup of the islands. We find a strong segregation between aerosols and bubbles. Upon comparing the mobility of inertial particles to that of tracers or neutrally buoyant particles, it becomes apparent that the tracer approximation may not always accurately predict the probability of movement. This can lead to inconsistent forecasts regarding the fate of marine organisms, seeds, litter, or particles in industrial flows.

Aggregation and fragmentation dynamics in random flows: From tracers to inertial aggregates

We investigate the aggregation and fragmentation dynamics of tracers and inertial aggregates in random flows leading to steady-state size distributions. Our objective is to elucidate the impact of changes in aggregation rates due to differences in advection dynamics, especially with respect to the influence of inertial effects. This aggregation process is, at the same time, balanced by fragmentation triggered by local hydrodynamic stress. Our study employs an individual-particle-based model, tracking the position, velocity, and size of each aggregate. We compare the steady-state size distribution formed by tracers and inertial aggregates, characterized by different sizes and densities. On the one hand, we show that the size distributions change their shape with changes in the dilution rate of the suspension. On the other hand, we obtain that the size distributions formed with different binding strengths between monomers can be rescaled to a single form with the use of a characteristic size for both dense inertial particles and tracer monomers. Nevertheless, this last scaling relation also fails if the size distribution contains aggregates that behave as tracer-like and inertial-like, which results in a crossover between different scalings.

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

We analyze the effect of the Basset history force on the sedimentation or rising of inertial particles in a two-dimensional convection flow. When memory effects are neglected, the system exhibits rich dynamics, including periodic, quasiperiodic, and chaotic attractors. Here we show that when the full advection dynamics is considered, including the history force, both the nature and the number of attractors change, and a fractalization of their basins of attraction appears. In particular, we show that the history force significantly weakens the horizontal diffusion and changes the speed of sedimentation or rising. The influence of the history force is dependent on the size of the advected particles, being stronger for larger particles.

Chaotic saddles in a gravitational field: the case of inertial particles in finite domains

The motion of inertial particles is investigated numerically in a time-periodic flow in the presence of gravity. The flow is restricted to a finite (or semi-infinite) vertical column, and the dynamics is therefore transiently chaotic. The long-term motion of the center of mass is a uniform settling. The settling velocity is found to differ from the one that would characterize a still fluid, and the distribution of an ensemble of settling particles spreads with a well-defined diffusion coefficient. The underlying chaotic saddle appears to have a height-dependent fractal dimension. The coarse-grained density of both the natural measure and the conditionally invariant measure (defined along the unstable manifold) of the saddle is smooth, and exhibits a local maximum as a function of the height. The latter density corresponds to the eigenfunction of the first eigenvalue of an effective Fokker-Planck equation subject to an absorbing boundary condition at the bottom. The transport coefficients can be determined as averages taken with respect to the conditionally invariant measure.

Coagulation and fragmentation dynamics of inertial particles

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process in time-periodic incompressible flows. We find that this process approaches an asymptotic dynamical steady state where the average number of particles of each size is roughly constant. We compare the steady-state size distributions corresponding to two fragmentation mechanisms and for different flows and find that the steady state is mostly independent of the coagulation process. While collision rates determine the transient behavior, fragmentation determines the steady state. For example, for fragmentation due to shear, flows that have very different local particle concentrations can result in similar particle size distributions if the temporal or spatial variation in shear forces is similar.