Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles

Abstract: The aggregation kinetics of settling particles is studied theoretically and numerically using the advection–diffusion equation. Agglomeration caused by these mechanisms (diffusion and advection) is important for both small particles (e.g., primary ash or soot particles in the atmosphere) and large particles of identical or close size, where the spatial inhomogeneity is less pronounced. Analytical results can be obtained for small and large Péclet numbers, which determine the relative importance of diffusion and advection. For small numbers (spatial inhomogeneity is mainly due to diffusion), an expression for the aggregation rate is obtained using an expansion in terms of Péclet numbers. For large Péclet numbers, when advection is the main source of spatial inhomogeneity, the aggregation rate is derived from ballistic coefficients. Combining these results yields a rational approximation for the whole range of Péclet numbers. The aggregation rates are also estimated by numerically solving the advection–diffusion equation. The numerical results agree well with the analytical theory for a wide range of Péclet numbers (extending over four orders of magnitude)

Swirlonic state of active matter

We report a novel state of active matter—a swirlonic state. It is comprised of swirlons, formed by groups of active particles orbiting their common center of mass. These quasi-particles demonstrate a surprising behavior: In response to an external load they move with a constant velocity proportional to the applied force, just as objects in viscous media. The swirlons attract each other and coalesce forming a larger, joint swirlon. The coalescence is extremely slow, decelerating process, resulting in a rarified state of immobile quasi-particles. In addition to the swirlonic state, we observe gaseous, liquid and solid states, depending on the inter-particle and self-driving forces. Interestingly, in contrast to molecular systems, liquid and gaseous states of active matter do not coexist. We explain this unusual phenomenon by the lack of fast particles in active matter. We perform extensive numerical simulations and theoretical analysis. The predictions of the theory agree qualitatively and quantitatively with the simulation results

Steady oscillations in aggregation-fragmentation processes

We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels Ki,j = iν jμ + j ν iμ homogeneous in masses i and j of merging clusters and fragmentation kernels, Fij = λKij , with parameter λ quantifying the intensity of the disruptive impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a power law with an exponential cutoff. This prediction agrees with simulation results when θ ≡ ν − μ < 1. For θ = ν − μ > 1, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very small λ, they become steady if θ is close to 2 and λ is very small. Simulation results lead to a conjecture that for θ < 1 the system has a stable fixed point, corresponding to the steady-state density distribution, while for any θ > 1 there exists a critical value λc, such that for λ<λc, the system has an attracting limit cycle. This is rather striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass