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

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journal contribution
posted on 31.10.2021, 19:59 by Thomas HardingThomas Harding, YM Stokes, AL Bertozzi
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.

History

Preferred citation

Harding, B., Stokes, Y. M. & Bertozzi, A. L. (2019). Effect of inertial lift on a spherical particle suspended in flow through a curved duct. Journal of Fluid Mechanics, 875, 1-43. https://doi.org/10.1017/jfm.2019.323

Journal title

Journal of Fluid Mechanics

Volume

875

Publication date

25/09/2019

Pagination

1-43

Publisher

Cambridge University Press (CUP)

Publication status

Published

Online publication date

18/07/2019

ISSN

0022-1120

eISSN

1469-7645

Article number

PII S0022112019003239

Language

en