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A linearised model for calculating inertial forces on a particle in the presence of a permeate flow

Published online by Cambridge University Press:  20 December 2018

Mike Garcia ,
B. Ganapathysubramanian  and
S. Pennathur Open the ORCID record for S. Pennathur [Opens in a new window]
Mike Garcia
Affiliation:
Department of Mechanical Engineering, University of California Santa Barbara, Engineering II, Room 2355 University of California, Santa Barbara, CA 93106, USA
B. Ganapathysubramanian
Affiliation:
Department of Mechanical Engineering, Iowa State University, 306 Lab of Mechanics, Ames, IA 50011, USA
S. Pennathur*
Affiliation:
Department of Mechanical Engineering, University of California Santa Barbara, Engineering II, Room 2355 University of California, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: [email protected]
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Abstract

Understanding particle transport and localisation in porous channels, especially at moderate Reynolds numbers, is relevant for many applications ranging from water reclamation to biological studies. Recently, researchers experimentally demonstrated that the interplay between axial and permeate flow in a porous microchannel results in a wide range of focusing positions of finite-sized particles (Garcia & Pennathur, Phys. Rev. Fluids, vol. 2 (4), 2017, 042201). We numerically explore this interplay by computing the lateral forces on a neutrally buoyant spherical particle that is subject to both inertial and permeate forces over a range of experimentally relevant particle sizes and channel Reynolds numbers. Interestingly, we show that the lateral forces on the particle are well represented using a linearised model across a range of permeate-to-axial flow rate ratios. Specifically, our model linearises the effects of the permeate flow, which suggests that the interplay between axial and permeate flow on the lateral force on a particle can be represented as a superposition between the lateral (inertial) forces in pure axial flow and the viscous forces in pure permeate flow. We experimentally validate this observation for a range of flow conditions. The linearised behaviour observed significantly reduces the complexity and time required to predict the migration of inertial particles in permeate channels.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 253 - 274
Copyright
© 2018 Cambridge University Press 

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References

Altena, F. W. & Belfort, G. 1984 Lateral migration of spherical particles in porous flow channels: application to membrane filtration. Chem. Engng Sci. 39 (2), 343–355.Google Scholar
Amini, H., Lee, W. & Di Carlo, D. 2014 Inertial microfluidic physics. Lab on a Chip 14 (15), 2739–2761.Google Scholar
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.Google Scholar
Belfort, G., Davis, R. H. & Zydney, A. L. 1994 The behavior of suspensions and macromolecular solutions in crossflow microfiltration. J. Membr. Sci. 96 (1–2), 1–58.Google Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3–4), 242–251.Google Scholar
Chang, I.-S. & Kim, S.-N. 2005 Wastewater treatment using membrane filtration – effect of biosolids concentration on cake resistance. Process Biochem. 40 (3–4), 1307–1314.Google Scholar
Charcosset, C. 2006 Membrane processes in biotechnology: an overview. Biotechnol. Adv. 24 (5), 482–492.Google Scholar
Chun, B. & Ladd, A. J. C. 2006 Inertial migration of neutrally buoyant particles in a square duct: an investigation of multiple equilibrium positions. Phys. Fluids 18 (3), 031704.Google Scholar
Cox, R. G. & Brenner, H. 1968 The lateral migration of solid particles in Poiseuille flow – I theory. Chem. Engng Sci. 23 (2), 147–173.Google Scholar
Di Carlo, D., Edd, J. F., Humphry, K. J., Stone, H. A. & Toner, M. 2009 Particle segregation and dynamics in confined flows. Phys. Rev. Lett. 102 (9), 094503.Google Scholar
Drew, D. A., Schonberg, J. A. & Belfort, G. 1991 Lateral inertial migration of a small sphere in fast laminar flow through a membrane duct. Chem. Engng Sci. 46 (12), 3219–3224.Google Scholar
Fernández García, L., Álvarez Blanco, S. & Riera Rodríguez, F. A. 2013 Microfiltration applied to dairy streams: removal of bacteria. J. Sci. Food Agric. 93 (2), 187–196.Google Scholar
Garcia, M. & Pennathur, S. 2017 Inertial particle dynamics in the presence of a secondary flow. Phys. Rev. Fluids 2 (4), 042201.Google Scholar
Gossett, D. R., Tse, H. T. K., Dudani, J. S., Goda, K., Woods, T. A., Graves, S. W. & Di Carlo, D. 2012 Inertial manipulation and transfer of microparticles across laminar fluid streams. Small 8 (17), 2757–2764.Google 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.Google 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.Google Scholar
Kim, J., Lee, J., Wu, C., Nam, S., Di Carlo, D. & Lee, W. 2016 Inertial focusing in non-rectangular cross-section microchannels and manipulation of accessible focusing positions. Lab on a Chip 16 (6), 992–1001.Google Scholar
Lebedeva, N. A. & Asmolov, E. S. 2011 Migration of settling particles in a horizontal viscous flow through a vertical slot with porous walls. Intl J. Multiphase Flow 37 (5), 453–461.Google Scholar
Liu, C., Hu, G., Jiang, X. & Sun, J. 2015 Inertial focusing of spherical particles in rectangular microchannels over a wide range of Reynolds numbers. Lab on a Chip 15 (4), 1168–1177.Google Scholar
Martel, J. M. & Toner, M. 2014 Inertial focusing in microfluidics. Annu. Rev. Biomed. Engng 16 (1), 371–396.Google Scholar
Miura, K., Itano, T. & Sugihara-Seki, M. 2014 Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels. J. Fluid Mech. 749, 320–330.Google Scholar
Otis, J. R., Altena, F. W., Mahar, J. T. & Belfort, G. 1986 Measurements of single spherical particle trajectories with lateral migration in a slit with one porous wall under laminar flow conditions. Exp. Fluids 4 (1), 1–10.Google Scholar
Pall Corporation2015 Breweries using Pall’s Keraflux™ tangential flow filtration (TFF) technology increase yield and reduce waste streams, pp. 1–2.Google Scholar
Palmer, A. F., Sun, G. & Harris, D. R. 2009 Tangential flow filtration of hemoglobin. Biotechnol. Prog. 25 (1), 189–199.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22 (2), 385–400.Google Scholar
Shichi, H., Yamashita, H., Seki, J., Itano, T. & Sugihara-Seki, M. 2017 Inertial migration regimes of spherical particles suspended in square tube flows. Phys. Rev. Fluids 2 (4), 044201.Google Scholar
White, F. M. 2006 Viscous fluid flow, 2nd edn. McGraw Hill.Google Scholar
Zhang, J., Yan, S., Yuan, D., Alici, G., Nguyen, N.-T., Warkiani, M. E. & Li, W. 2016 Fundamentals and applications of inertial microfluidics: a review. Lab on a Chip 16 (1), 10–34.Google Scholar