Diffusion-limited settling of highly porous particles in density-stratified fluids

TL;DR

This study investigates the diffusion-limited settling behavior of highly porous particles in density-stratified fluids, deriving a simple velocity expression, validating it experimentally, and providing a framework for arbitrary shapes and profiles.

Contribution

It introduces a novel simple model for particle settling velocity in diffusion-limited regimes and validates it with experiments, extending to arbitrary shapes and density profiles.

Findings

Smaller particles settle faster in the diffusion-limited regime.

Derived a simple expression for steady settling velocity based on particle and fluid properties.

Validated predictions with hydrogel experiments across various parameters.

Abstract

The vertical transport of solid material in a stratified medium is fundamental to a number of environmental applications, with implications for the carbon cycle and nutrient transport in marine ecosystems. In this work, we study the diffusion-limited settling of highly porous particles in a density-stratified fluid through a combination of experiment, analysis, and numerical simulation. By delineating and appealing to the diffusion-limited regime wherein buoyancy effects due to mass adaptation dominate hydrodynamic drag, we derive a simple expression for the steady settling velocity of a sphere as a function of the density, size, and diffusivity of the solid, as well as the density gradient of the background fluid. In this regime, smaller particles settle faster, in contrast with most conventional hydrodynamic drag mechanisms. Furthermore, we outline a general mathematical framework for computing the steady settling speed of a body of arbitrary shape in this regime and compute exact results for the case of general ellipsoids. Using hydrogels as a highly porous model system, we validate the predictions with laboratory experiments in linear stratification for a wide range of parameters. Lastly, we show how the predictions can be applied to arbitrary slowly varying background density profiles and demonstrate how a measured particle position over time can be used to reconstruct the background density profile.