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Inertial focusing of non-neutrally buoyant spherical particles in curved microfluidic ducts

Published online by Cambridge University Press:  04 September 2020

Brendan Harding Open the ORCID record for Brendan Harding [Opens in a new window]  and
Yvonne M. Stokes Open the ORCID record for Yvonne M. Stokes [Opens in a new window]
Brendan Harding*
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia5005, Australia
Yvonne M. Stokes
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia5005, Australia
*
†Email address for correspondence: [email protected]
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Abstract

We examine the effect of gravity and (rotational) inertia on the inertial focusing of spherical non-neutrally buoyant particles suspended in flow through curved microfluidic ducts. In the neutrally buoyant case, examined in Harding et al. (J. Fluid Mech., vol. 875, 2019, pp. 1–43), the gravitational contribution to the force on the particle is exactly zero and the net effect of centrifugal and centripetal forces (due to the motion around the curved duct) is negligible. Inertial lift force and drag from the secondary fluid flow vortices interact and lead to focusing behaviour which is sensitive to the bend radius of the device and the particle size (each measured relative to the height of the cross-section). In the case of non-neutrally buoyant particles the behaviour becomes more complex with the two additional perturbing forces. The gravitational force, relative to the inertial lift force, scales with the inverse square of the flow velocity, making it a potentially important factor for devices operating at low flow rates with a suspension of non-neutrally buoyant particles. In contrast, the net centripetal/centrifugal force scales with the inverse of the bend radius, similar to the drag force from the secondary flow. We examine how these forces perturb the stable equilibria within the cross-sectional plane to which neutrally buoyant particles ultimately migrate.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A4
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Asmolov, E. S. 1999 The inertial lift on a spherical particle in a plane poiseuille flow at large channel Reynolds number. J. Fluid Mech. 381, 63–87.CrossRefGoogle Scholar
Asmolov, E. S., Dubov, A. L., Nizkaya, T. V., Harting, J. & Vinogradova, O. I. 2018 Inertial focusing of finite-size particles in microchannels. J. Fluid Mech. 840, 613–630.CrossRefGoogle Scholar
Asmolov, E. S., Lebedeva, N. A. & Osiptsov, A. A. 2009 Inertial migration of sedimenting particles in a suspension flow through a Hele-Shaw cell. Fluid Dyn. 44 (3), 405–418.CrossRefGoogle Scholar
Asmolov, E. S. & Osiptsov, A. A. 2009 The inertial lift on a spherical particle settling in a horizontal viscous flow through a vertical slot. Phys. Fluids 21 (6), 063301.CrossRefGoogle Scholar
Ault, J. T., Rallabandi, B., Shardt, O., Chen, K. K. & Stone, H. A. 2017 Entry and exit flows in curved pipes. J. Fluid Mech. 815, 570–591.CrossRefGoogle Scholar
Bhagat, A. A. S., Kuntaegowdanahalli, S. S. & Papautsky, I. 2008 Continuous particle separation in spiral microchannels using dean flows and differential migration. Lab Chip 8, 1906–1914.CrossRefGoogle ScholarPubMed
Harding, B. 2019 Convergence analysis of inertial lift force estimates using the finite element method. In Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2018 (ed. Lamichhane, B., Tran, T. & Bunder, J.), ANZIAM Journal, vol. 60, pp. C65–C78.Google Scholar
Harding, B., Stokes, Y. M. & Bertozzi, A. L. 2019 Effect of inertial lift on a spherical particle suspended in flow through a curved duct. J. Fluid Mech. 875, 1–43.CrossRefGoogle Scholar
Ho, B. P. & Leal, L. G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65 (2), 365–400.CrossRefGoogle Scholar
Hogg, A. J. 1994 The inertial migration of non-neutrally buoyant spherical particles in two-dimensional shear flows. J. Fluid Mech. 272, 285–318.CrossRefGoogle Scholar
Hood, K., Lee, S. & Roper, M. 2015 Inertial migration of a rigid sphere in three-dimensional poiseuille flow. J. Fluid Mech. 765, 452–479.CrossRefGoogle Scholar
Ookawara, S., Oozeki, N., Ogawa, K., Löb, P. & Hessel, V. 2010 Process intensification of particle separation by lift force in arc microchannel with bifurcation. Chem. Engng Process. 49 (7), 697–703, process Intensification on Intensified Transport by Complex Geometries.CrossRefGoogle Scholar
Oozeki, N., Ookawara, S., Ogawa, K., Löb, P. & Hessel, V. 2009 Characterization of microseparator/classifier with a simple arc microchannel. AIChE J. 55 (1), 24–34.CrossRefGoogle Scholar
Priest, C., Zhou, J., Sedev, R., Ralston, J., Aota, A., Mawatari, K. & Kitamori, T. 2011 Microfluidic extraction of copper from particle-laden solutions. Intl J. Miner. Process. 98 (3), 168–173.CrossRefGoogle Scholar
Rafeie, M., Hosseinzadeh, S., Taylor, R. A. & Warkiani, M. E. 2019 New insights into the physics of inertial microfluidics in curved microchannels. I. Relaxing the fixed inflection point assumption. Biomicrofluidics 13 (3), 034117.CrossRefGoogle ScholarPubMed
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22 (2), 385–400.CrossRefGoogle Scholar
Schonberg, J. A. & Hinch, E. J. 1989 Inertial migration of a sphere in poiseuille flow. J. Fluid Mech. 203, 517–524.CrossRefGoogle Scholar
Warkiani, M. E., Guan, G., Luan, K. B., Lee, W. C., Bhagat, A. A. S., Kant Chaudhuri, P., Tan, D. S.-W., Lim, W. T., Lee, S. C., Chen, P. C. Y. et al. . 2014 Slanted spiral microfluidics for the ultra-fast, label-free isolation of circulating tumor cells. Lab Chip 14, 128–137.CrossRefGoogle ScholarPubMed
Yin, C.-Y., Nikoloski, A. N. & Wang, M. 2013 Microfluidic solvent extraction of platinum and palladium from a chloride leach solution using Alamine 336. Miner. Engng 45, 18–21.CrossRefGoogle Scholar