×

A linearised model for calculating inertial forces on a particle in the presence of a permeate flow. (English) Zbl 1421.76240

Summary: 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 [the first author and the third author, “Inertial particle dynamics in the presence of a secondary flow”, Phys. Rev. Fluids 2, No. 4, Article ID 042201, 7 p. (2017; doi:10.1103/PhysRevFluids.2.042201)]. 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.

MSC:

76T20 Suspensions
76D05 Navier-Stokes equations for incompressible viscous fluids
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Altena, F. W.; Belfort, G., Lateral migration of spherical particles in porous flow channels: application to membrane filtration, Chem. Engng Sci., 39, 2, 343-355, (1984) · doi:10.1016/0009-2509(84)80033-0
[2] Amini, H.; Lee, W.; Di Carlo, D., Inertial microfluidic physics, Lab on a Chip, 14, 15, 2739-2761, (2014) · doi:10.1039/c4lc00128a
[3] Asmolov, E. S., The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number, J. Fluid Mech., 381, 63-87, (1999) · Zbl 0935.76025 · doi:10.1017/S0022112098003474
[4] Belfort, G.; Davis, R. H.; Zydney, A. L., The behavior of suspensions and macromolecular solutions in crossflow microfiltration, J. Membr. Sci., 96, 1-2, 1-58, (1994) · doi:10.1016/0376-7388(94)00119-7
[5] Brenner, H., The slow motion of a sphere through a viscous fluid towards a plane surface, Chem. Engng Sci., 16, 3-4, 242-251, (1961) · doi:10.1016/0009-2509(61)80035-3
[6] Chang, I.-S.; Kim, S.-N., Wastewater treatment using membrane filtration – effect of biosolids concentration on cake resistance, Process Biochem., 40, 3-4, 1307-1314, (2005) · doi:10.1016/j.procbio.2004.06.019
[7] Charcosset, C., Membrane processes in biotechnology: an overview, Biotechnol. Adv., 24, 5, 482-492, (2006) · doi:10.1016/j.biotechadv.2006.03.002
[8] Chun, B.; Ladd, A. J. C., Inertial migration of neutrally buoyant particles in a square duct: an investigation of multiple equilibrium positions, Phys. Fluids, 18, 3, (2006) · doi:10.1063/1.2176587
[9] Cox, R. G.; Brenner, H., The lateral migration of solid particles in Poiseuille flow - I theory, Chem. Engng Sci., 23, 2, 147-173, (1968) · doi:10.1016/0009-2509(68)87059-9
[10] Di Carlo, D.; Edd, J. F.; Humphry, K. J.; Stone, H. A.; Toner, M., Particle segregation and dynamics in confined flows, Phys. Rev. Lett., 102, 9, (2009)
[11] Drew, D. A.; Schonberg, J. A.; Belfort, G., Lateral inertial migration of a small sphere in fast laminar flow through a membrane duct, Chem. Engng Sci., 46, 12, 3219-3224, (1991) · doi:10.1016/0009-2509(91)85023-Q
[12] Fernández García, L.; Álvarez Blanco, S.; Riera Rodríguez, F. A., Microfiltration applied to dairy streams: removal of bacteria, J. Sci. Food Agric., 93, 2, 187-196, (2013) · doi:10.1002/jsfa.5935
[13] Garcia, M.; Pennathur, S., Inertial particle dynamics in the presence of a secondary flow, Phys. Rev. Fluids, 2, 4, (2017) · doi:10.1103/PhysRevFluids.2.042201
[14] Gossett, D. R.; Tse, H. T. K.; Dudani, J. S.; Goda, K.; Woods, T. A.; Graves, S. W.; Di Carlo, D., Inertial manipulation and transfer of microparticles across laminar fluid streams, Small, 8, 17, 2757-2764, (2012) · doi:10.1002/smll.201200588
[15] Ho, B. P.; Leal, L. G., Inertial migration of rigid spheres in two-dimensional unidirectional flows, J. Fluid Mech., 65, 2, 365-400, (1974) · Zbl 0284.76076 · doi:10.1017/S0022112074001431
[16] Hood, K.; Lee, S.; Roper, M., Inertial migration of a rigid sphere in three-dimensional Poiseuille flow, J. Fluid Mech., 765, 452-479, (2015) · Zbl 1331.76039 · doi:10.1017/jfm.2014.739
[17] Kim, J.; Lee, J.; Wu, C.; Nam, S.; Di Carlo, D.; Lee, W., Inertial focusing in non-rectangular cross-section microchannels and manipulation of accessible focusing positions, Lab on a Chip, 16, 6, 992-1001, (2016) · doi:10.1039/C5LC01100K
[18] Lebedeva, N. A.; Asmolov, E. S., Migration of settling particles in a horizontal viscous flow through a vertical slot with porous walls, Intl J. Multiphase Flow, 37, 5, 453-461, (2011) · doi:10.1016/j.ijmultiphaseflow.2010.12.005
[19] Liu, C.; Hu, G.; Jiang, X.; Sun, J., Inertial focusing of spherical particles in rectangular microchannels over a wide range of Reynolds numbers, Lab on a Chip, 15, 4, 1168-1177, (2015) · doi:10.1039/C4LC01216J
[20] Martel, J. M.; Toner, M., Inertial focusing in microfluidics, Annu. Rev. Biomed. Engng, 16, 1, 371-396, (2014) · doi:10.1146/annurev-bioeng-121813-120704
[21] Miura, K.; Itano, T.; Sugihara-Seki, M., Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels, J. Fluid Mech., 749, 320-330, (2014) · doi:10.1017/jfm.2014.232
[22] Otis, J. R.; Altena, F. W.; Mahar, J. T.; Belfort, G., 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, (1986) · doi:10.1007/BF00316779
[23] 2015 Breweries using Pall’s Keraflux™ tangential flow filtration (TFF) technology increase yield and reduce waste streams, pp. 1-2.
[24] Palmer, A. F.; Sun, G.; Harris, D. R., Tangential flow filtration of hemoglobin, Biotechnol. Prog., 25, 1, 189-199, (2009) · doi:10.1002/btpr.119
[25] Saffman, P. G., The lift on a small sphere in a slow shear flow, J. Fluid Mech., 22, 2, 385-400, (1965) · Zbl 0218.76043 · doi:10.1017/S0022112065000824
[26] Shichi, H.; Yamashita, H.; Seki, J.; Itano, T.; Sugihara-Seki, M., Inertial migration regimes of spherical particles suspended in square tube flows, Phys. Rev. Fluids, 2, 4, (2017) · doi:10.1103/PhysRevFluids.2.044201
[27] White, F. M., Viscous fluid flow, (2006), McGraw Hill
[28] Zhang, J.; Yan, S.; Yuan, D.; Alici, G.; Nguyen, N.-T.; Warkiani, M. E.; Li, W., Fundamentals and applications of inertial microfluidics: a review, Lab on a Chip, 16, 1, 10-34, (2016) · doi:10.1039/C5LC01159K
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.