Numerical study of collisions between settling non-spherical particles in turbulence

The dynamics of microplastics in the ocean can be modeled similarly to natural particles such as sediment grains, marine snow, phyto- and zooplankton. The settling of the particle is important not only for the individual particle motion, but it also affects the encounter rate, which is important for several physical processes such as nutrient uptake, biofouling, the degradation of microplastics and transport of pollutants into the food chain in the marine environment.

Some of the factors that determine the collision and accumulation of the particles are the level of turbulence, buoyancy, particle shape and diffusivity. Microplastics are often elongated in shape, whereas phytoplankton often form long chains colonies and filaments, even if these are unicellular, which makes the investigation as nonspherical particles in turbulent flows relevant. The objective of this study is to quantify how turbulence affects collision kernels of the nonspherical settling particles. This work is motivated by recent studies in laminar flows showing how collisions between fiber-like particles are much more frequent than those between spherical particles, even in the presence of turbulence (Slomka, J., Stocker, R., 2020. On the collision of rods in a quiescent fluid, Proceedings of the National Academy of Sciences 117, 3372-3374). To this end, we shall consider particles as elongated spheroids. Given the low-density ratios, close to 1, and the size, order of microns, inertia can be neglected, and the particle velocity is assumed to be equal to the sum of the fluid velocity at the particle position and the settling speed. The settling speed is taken to be the Stokes settling velocity for oblate spheroids, function of the object orientation and aspect ratio; note that this is not parallel to gravity for any general orientation. We report results from simulations of sinking inertia-less elongated spheroids in homogeneous isotropic turbulence (HIT). The velocity field is assumed to be incompressible and to obey the Navier-Stokes and continuity equation. To maintain the turbulent velocity in a statistically steady state, a random forcing field is needed. The elongated spheroids studied here are small compared to the Kolmogorov length scale of the turbulence and have different aspect ratios: 1 (spheres), 2, 5, 10 and 20.  We will present results for two different settling velocities – equal to 1 Kolmogorov and 3 times the Kolmogorov velocity, velocity scale of the smallest vortices in the flow. In order to quantify clustering in fully three-dimensional isotropic turbulent flows, the radial pair distribution function (r.d.f.) is used, which provides information about the collision rates when combined with the relative particle velocity at distances of the order of the particle size.

We show that the effect of the different collisional relative velocity has a greater impact than the patchiness on the increase of the collision rate. For larger settling velocities, i.e. larger particle sizes, the collision rates of elongated particles increase with the aspect ratio, an increase however smaller than that observed in quiescent flows. Results obtained for the collision of particles of different buoyancy will also be presented.