Marine snow is central to the marine carbon cycle, and quantifying its small-scale settling dynamics in different physical environments is essential to understanding its role in biogeochemical cycles. Previous field observations of marine aggregate thin layers associated with sharp density gradients have led to the hypothesis that these layers may be caused by a decrease in aggregate settling speed at density interfaces. Here, we present experimental data on aggregate settling behavior, showing that these particles can dramatically decrease their settling velocity when passing through sharp density transitions. This delayed settling can be caused by 2 potential mechanisms: (1) entrainment of lighter fluid from above as the particle passes through the density gradient, and (2) retention at the transition driven by changes in the density of the particle due to its porosity. The aggregates observed in this study exhibited 2 distinct settling behaviors when passing through the density transition. Quantitatively comparing these different behaviors with predictions from 2 models allow us to infer that the delayed settling of the first group of aggregates was primarily driven by diffusion-limited retention, whereas entrainment of lighter fluid was the dominant mechanism for the second group. Coupled with theory, our experimental results demonstrate that both entrainment and diffusion-limited retention can play an important role in determining particle settling dynamics through density transitions. This study thus provides insight into ways that delayed settling can lead to the formation of aggregate thin layers, important biological hotspots that affect trophic dynamics, and biogeochemical cycling in the ocean.

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We present an experimental study of single porous spheres settling in a near two-layer ambient density fluid. Data are compared with a first-principle model based on diffusive processes. The model correctly predicts accelerations of the sphere but does not capture the retention time at the density transition quantitatively. Entrainment of lighter fluid through a shell encapsulating the sphere is included in this model empirically. With this parametrization, which exhibits a power law dependence on Reynolds numbers, retention times are accurately captured. Extrapolating from our experimental data, model predictions are presented.

We study the evaluation of layer potentials close to the domain boundary. Accurate evaluation of layer potentials near boundaries is needed in many applications, including fluid-structure interactions and near-field scattering in nano-optics. When numerically evaluating layer potentials, it is natural to use the same quadrature rule as the one used in the Nystr\"om method to solve the underlying boundary integral equation. However, this method is problematic for evaluation points close to boundaries. For a fixed number of quadrature points, $N$, this method incurs $O(1)$ errors in a boundary layer of thickness $O(1/N)$. Using an asymptotic expansion for the kernel of the layer potential, we remove this $O(1)$ error. We demonstrate the effectiveness of this method for interior and exterior problems for Laplace's equation in two dimensions

Odour capture is an important part of olfaction, where dissolved chemical cues (odours) are brought into contact with chemosensory structures. Antennule flicking by marine crabs is an example of discrete odour capture (sniffing) where an array of chemosensory hairs is waved through the water to create a flow-no flow pattern based on a narrow range of speeds, diameters of and spacings between hairs. Changing the speed of movement and spacing of hairs at this scale to manipulate flow represents a complicated fluid dynamics problem. In this study, we use numerical simulation of the advection and diffusion of a chemical gradient to reveal how morphological differences of the hair arrays affect odour capture. Specifically, we simulate odour capture by a marine crab (Callinectes sapidus) and a terrestrial crab (Coenobita rugosus) in both air and water to compare performance. We find that the antennule morphologies of each species are adaptions to capturing odours in their native habitats. Sniffing is an important part of odour capture for marine crabs in water where the diffusivity of odorant molecules is low and flow through the array is necessary. On the other hand, flow within the hair array diminishes odour-capture performance in air where diffusivities are high. This study highlights some of the adaptations necessary to transition from water to air.

When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular integrals. To address this close evaluation problem, we apply an asymptotic analysis of these nearly singular integrals and obtain an asymptotic approximation. We derive the asymptotic approximation for the case of the double-layer potential in two and three dimensions, representing the solution of the interior Dirichlet problem for Laplace's equation. By doing so, we obtain an asymptotic approximation given by the Dirichlet data at the boundary point nearest to the interior evaluation point plus a nonlocal correction. We present numerical methods to compute this asymptotic approximation, and we demonstrate the efficiency and accuracy of the asymptotic approximation through several examples. These examples show that the asymptotic approximation is useful as it accurately approximates the close evaluation of the double-layer potential while requiring only modest computational resources.

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