On the terminal velocity of sedimenting particles in a flowing fluid

TL;DR

This paper investigates how different flow conditions affect the terminal velocity of sedimenting particles using analytical methods and numerical simulations, providing a general framework applicable to various laminar and turbulent flows.

Contribution

It introduces a perturbation-based theoretical framework and numerical approach to analyze sedimentation in complex flow fields, extending understanding beyond static conditions.

Findings

Flow type influences sedimentation velocity

Analytical PDE solutions capture key sedimentation dynamics

Numerical simulations validate theoretical predictions

Abstract

The influence of an underlying carrier flow on the terminal velocity of sedimenting particles is investigated both analytically and numerically. Our theoretical framework works for a general class of (laminar or turbulent) velocity fields and, by means of an ordinary perturbation expansion at small Stokes number, leads to closed partial differential equations (PDE) whose solutions contain all relevant information on the sedimentation process. The set of PDE's are solved by means of direct numerical simulations for a class of 2D cellular flows (static and time dependent) and the resulting phenomenology is analysed and discussed.