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Effect of inertial lift on a spherical particle suspended in flow through a curved duct

Published online by Cambridge University Press:  18 July 2019

Brendan Harding*
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia 5005, Australia
Yvonne M. Stokes
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia 5005, Australia
Andrea L. Bertozzi
Affiliation:
Departments of Mathematics and Mechanical and Aerospace Engineering, University of California, Los Angeles, California 90095, USA
*
Email address for correspondence: brendan.harding@adelaide.edu.au

Abstract

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane towards which particles migrate. The Navier–Stokes equations determine the hydrodynamic forces acting on a particle. A leading-order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. We predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales: specifically, the particle radius, duct height and duct bend radius. Additionally, a trapezoidal-shaped cross-section is considered in order to demonstrate how changes in the cross-section design influence the dynamics of particles.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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