Memory effects in wave-induced microplastic transport

Microplastics are transported by ocean surface waves in ways that cannot always be described by the Stokes drift of fluid parcels, and accurate modeling of this transport requires accounting for forces beyond linear drag. Existing models of microplastic transport often neglect the Basset–Boussinesq history force, effectively limiting their use to the smallest particle sizes. Here, we extend the applicability of models under the classical Maxey–Riley framework by implementing the history term with a multi-step integration scheme, allowing us to capture the transport of larger microplastics in linear surface waves of arbitrary depth. We quantify when the Basset–Boussinesq history force significantly affects microplastic transport by surface gravity waves, with both relative and absolute metrics, under the classical Maxey–Riley framework. We show that, under this framework, memory effects become the leading-order horizontal drag once S=St̂/γ exceeds S≈0.25, where St̂ is the density-independent Stokes number, and γ is the density ratio of the particle and the fluid. The corresponding critical St number is found to be a factor of about three smaller than that given by classical inertial estimates that neglect history effects. These results help provide regime maps that can be used as guidance for when history effects can be safely neglected. Our simulations also reveal that history effects significantly increase horizontal transport distances and alter orbit deformation of particle ensembles.