Bifurcations in inertial focusing of a particle suspended in flow through curved rectangular ducts

TL;DR

This paper analyzes how particles focus within curved rectangular ducts under flow, revealing bifurcations like saddle-node, pitchfork, and Hopf, which can inform the design of microfluidic particle separation devices.

Contribution

It provides a combined analytical and numerical study of particle equilibria and bifurcations in curved ducts, extending understanding of inertial focusing mechanisms.

Findings

Identification of multiple bifurcation types in particle equilibria

Analytical solutions for particle stability in certain regimes

Numerical analysis of bifurcations in complex parameter spaces

Abstract

Particles suspended in a fluid flow through a curved duct can focus to specific locations within the duct cross-section. This particle focusing is a result of a balance between two dominant forces acting on the particle: (i) the inertial lift force arising from small but non-negligible inertia of the fluid, and (ii) the secondary drag force due to the cross-sectional vortices induced by the curvature of the duct. By adopting a simplified particle dynamics model developed by Ha et al.~[1], we investigate both analytically and numerically, the particle equilibria and their bifurcations when a small particle is suspended in low-flow-rate fluid flow through a curved duct having a $2\times1$ and a $1\times2$ rectangular cross-section. In certain parameter regimes of the model, we analytically obtain the particle equilibria and deduce their stability, while for other parameter regimes, we numerically calculate the particle equilibria and stability. Moreover, we observe a number of different bifurcations in particle equilibria such as saddle-node, pitchfork and Hopf, as the model parameters are varied. These results may aid in the design of inertial microfluidic devices aimed at particle separation by size.