Settling velocity of quasi-neutrally-buoyant inertial particles

TL;DR

This paper derives general formulas for the sedimentation velocity of quasi-neutrally buoyant inertial particles in incompressible flows, providing a computationally efficient method to analyze their settling behavior.

Contribution

It introduces a novel analytical framework and numerical scheme to compute the terminal velocity of inertial particles in complex fluid flows, reducing problem dimensionality.

Findings

Formulas for particle terminal velocity in periodic and steady flows.

Reduction of computational complexity for velocity calculations.

Applicability to flows with spatial symmetry such as vertical parity.

Abstract

We investigate the sedimentation properties of quasi-neutrally buoyant inertial particles carried by incompressible zero-mean fluid flows. We obtain generic formulae for the terminal velocity in generic space-and-time periodic (or steady) flows, along with further information for flows endowed with some degree of spatial symmetry such as odd parity in the vertical direction. These expressions consist in space-time integrals of auxiliary quantities which satisfy partial differential equations of the advection--diffusion--reaction type, that can be solved at least numerically since our scheme implies a huge reduction of the problem dimensionality from the full phase space to the classical physical space.