Settling of inertial nonspherical particles in wavy flow

Microplastics are an increasingly significant problem in the world's oceans. They are transported by various ocean phenomena, one of the most fundamental of which is surface gravity waves. Since microplastics are irregularly shaped and are not typically neutrally buoyant, understanding the settling of negatively buoyant, nonspherical plastic particles under surface gravity waves is important for accurately predicting the fate of microplastics in the ocean. Here we experimentally investigate the settling of plastic rods, disks, and spheres in wavy flows. We find that the average vertical velocities of the particles can both increase and decrease in waves, relative to the particle settling velocity in quiescent flow. This variation is a function of the flow inertia at the length scale of the particle, which we characterize with a particle Reynolds number, ${\mathrm{Re}}_p$, and is also a function of particle shape. We further examine the average vertical particle velocities by looking at two factors contributing to their behavior: The relative velocities between the particles and the flow and the manner in which the particles sample the flow. We find that the average relative velocities between the particles and the flow remain constant with ${\mathrm{Re}}_p$, even though the variation of the relative velocities of the rods with orientation increases with increasing ${\mathrm{Re}}_p$. The observed variation of the average vertical particle velocities with ${\mathrm{Re}}_p$ can be explained instead by how the particles sample the flow, as each of the particle shapes nonuniformly sample the flow as a function of ${\mathrm{Re}}_p$. Accounting for the variation of particle settling velocities with shape and inertia in models is necessary to improve the accuracy of predictions of the transport of microplastics in the ocean.

Figure 1

Experimental setup. Waves were produced by the vertically oscillating wavemaker and dissipated by the horsehair beach. Particles were released into the flow from the swing and illuminated with green LEDs. Flow tracers were illuminated with a laser sheet.

Figure 2

Example raw image of plastic disks in the field of tracers. The disks are clearly identifiable based on their larger size, so the image can be easily separated into particle and tracer components.

Figure 3

Normalized particle vertical velocities $w^{*}$ vs particle Reynolds number ${\mathrm{Re}}_p$. Circles ($\circ$) represent spheres, asterisks (*) represent disks, and triangles ($△$) represent rods. Error bars show the $95\%$ confidence intervals computed with bootstrapping. Spheres have a smaller range of ${\mathrm{Re}}_p$ values because of their smaller length scale.

Figure 4

Normalized relative vertical velocities $\mathrm{\Delta }{w}^{*}$ between the particles and their local flow field. As in Fig. 3, circles ($\circ$) represent spheres, asterisks (*) represent disks, and triangles ($△$) represent rods, and error bars show $95\%$ confidence intervals.

Figure 5

Normalized relative vertical velocities $\mathrm{\Delta }{w}^{*}$ of (a) rods and (b) disks plotted against particle orientations in the plane of the waves. The different colors represent different ranges of ${\mathrm{Re}}_p$: $0\le {\mathrm{Re}}_p\le 300$ (red circles $\circ$), $300\le {\mathrm{Re}}_p\le 600$ (green triangles $▽$), $600\le {\mathrm{Re}}_p\le 900$ (blue squares $\square$), and $900\le {\mathrm{Re}}_p\le 1200$ (black diamonds $\diamond$). As in other figures, error bars represent the $95\%$ confidence intervals computed by bootstrapping.

Figure 6

Definition of orientation $\theta$ of a disk (left) and a rod (right). Axes are in the plane of the waves. Gray vectors show the axes of symmetry of the particles.

Figure 7

(a) Percentage of time the particles spend in wave phases corresponding to downward flow as a function of ${\mathrm{Re}}_p$. (b) Normalized preferentially sampled flow velocities $\mathrm{\Delta }{w}_{\mathrm{samp}}^{*}$, also as a function of ${\mathrm{Re}}_p$, with $95\%$ confidence intervals. In both panels, circles ($\circ$) represent spheres, asterisks (*) represent disks, and triangles ($△$) represent rods.

Figure 8

Normalized settling velocities $w^{*}$ minus the normalized quiescent settling velocity (1), plotted against preferentially sampled flow velocities $\mathrm{\Delta }{w}_{\mathrm{samp}}^{*}$. As in other figures, circles ($\circ$) represent spheres, asterisks (*) represent disks, and triangles ($△$) represent rods.