Transport and orientation of anisotropic particles settling in surface gravity waves

TL;DR

The study develops a coupled translation–rotation framework for anisotropic (spheroidal) particles settling in a two-dimensional deep-water wave field, incorporating buoyancy, inertial torque, and finite-size Faxén corrections. Through asymptotic analysis and numerical validation, it identifies how the settling parameter $Sv$, wave Reynolds number $Re_w$, and particle shape (via the Bretherton constant and mobility factors) govern long-time orientation and horizontal transport, revealing regimes where inertia drives broadside alignment and confines drift, and finite-size effects nontrivially modify drift and orientation. The findings show that buoyancy can yield unbounded drift for neutrally buoyant or weakly settling particles, while inertia enforces a broadside state with finite spreading, and finite-size corrections couple translation to rotation, significantly altering transport of non-spherical microplastics in oceanic and atmospheric contexts. Collectively, the work provides a unified theoretical framework linking microphysical particle properties to macroscopic dispersion in wave-driven environments, with implications for predictive models of non-spherical particulate transport.

Abstract

We study the translation and orientation dynamics of an anisotropic particle settling in monochromatic linear surface gravity waves. Recent work has shown that a neutrally buoyant spheroid attains a preferred mean orientation in such wave fields, independent of its initial state and determined solely by its aspect ratio. Comparing the settling parameter $\mathrm{Sv}$, the ratio of settling speed to wave speed, with the asymptotically small wave steepness $ε$, we investigate the long time dynamics of a negatively buoyant particle. We examine the transition from aspect ratio-dependent equilibrium orientation in the weak settling regime ($\mathrm{Sv} \ll ε^2$) to initial-condition-dependent alignment in the strong settling limit ($\mathrm{Sv} \gg 1$). Since translation and orientation are coupled for anisotropic particles, we use orientation dynamics to predict net horizontal transport. Fluid inertia induces an inertial torque that breaks the Stokesian degeneracy and drives broadside alignment. We analyze the influence of this torque on drift and alignment rate as functions of settling and wave parameters. Finally, we evaluate finite-size effects through the parameter $σ$, showing that a neutrally buoyant finite-size spheroid exhibits $σ$-dependent drift, validating the finite-size approximation when the spheroid size approaches the wavelength.

Figures (25)

• Figure 1: Contour plot of $\mathrm{Sv}$ as a function of semi-minor length $b$ of a particle and wavelength $\lambda$. Here, $c_p$ represents the phase speed of the wave, and $W$ denotes the settling velocity of a particle.
• Figure 2: Schematic diagram of an anisotropic particle subjected to the wavy flow field. The orientation vector along the symmetry axis of the particle is denoted by $\boldsymbol{p}$, making an angle $\theta$ with a vertical axis. $\lambda$ and $A$ are the wavelength and amplitude of the wave. Here, $H$ represents the total depth of the flow field. The direction of gravity is taken parallel to the $z$ axis.
• Figure 3: Schematic diagram illustrating various inertial regimes based on particle and shear Reynolds numbers. The green region denotes the viscosity-dominated Stokes regime, while fluid inertia becomes increasingly important outside this region.
• Figure 4: Comparison of asymptotic predictions of $x_{\infty}$ and $\theta_{\infty}$ with numerical results. Scatter points denote numerical simulations, and solid lines show the corresponding asymptotic approximations. (a) Horizontal spreading $x_{\infty}$ versus $\mathrm{Sv}$, and (b) Preferred orientation $\theta_{\infty}$ versus $\mathrm{Sv}$. Here, $\mathcal{B}=0.9$, $\epsilon=0.05$.
• Figure 5: (a) Contour plot of long-time orientation $\theta_{\infty}$ in a $\mathrm{Sv}-\mathcal{B}$ plane obtained from (\ref{['eq:isoem']}), and (b) temporal evolution of $\theta$ for prolate and oblate spheroids, computed from (\ref{['eq:velff']}). For this figure, parameters are: $\gamma=0.99$, $\epsilon=0.05$ and $\mathrm{Sv}=5\times10^{-3}$.