Numerical simulation of inertial microfluidics: a review

References

• Alghalibi, D., Rosti, M. E., & Brandt, L. (2019). Inertial migration of a deformable particle in pipe flow. Physical Review Fluids, 4(10), 104201-1–104201-18. https://doi.org/10.1103/PhysRevFluids.4.104201
   Web of Science ®Google Scholar
• Alnaimat, F., & Mathew, B. (2020). Magnetophoretic microdevice for size-based separation: Model-based study. Engineering Applications of Computational Fluid Mechanics, 14(1), 738–750. https://doi.org/10.1080/19942060.2020.1760941
   Web of Science ®Google Scholar
• Altay, R., Yapici, M. K., & Koşar, A. (2022). A hybrid spiral microfluidic platform coupled with surface acoustic waves for circulating tumor cell sorting and separation: A numerical study. Biosensors, 12(3), 171. https://doi.org/10.3390/bios12030171
   PubMedGoogle Scholar
• Amini, H., Sollier, E., Weaver, W. M., & Di Carlo, D. (2012). Intrinsic particle-induced lateral transport in microchannels. Proceedings of the National Academy of Sciences, 109(29), 11593–11598. https://doi.org/10.1073/pnas.1207550109
   PubMed Web of Science ®Google Scholar
• Asmolov, E. S. (1999). The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. Journal of Fluid Mechanics, 381(1), 63–87. https://doi.org/10.1017/S0022112098003474
   Google Scholar
• Asmolov, E. S., Dubov, A. L., Nizkaya, T. V., Harting, J., & Vinogradova, O. I. (2018). Inertial focusing of finite-size particles in microchannels. Journal of Fluid Mechanics, 840, 613–630. https://doi.org/10.1017/jfm.2018.95
   Web of Science ®Google Scholar
• Auton, T. R. (1987). The lift force on a spherical body in a rotational flow. Journal of Fluid Mechanics, 183, 199–218. https://doi.org/10.1017/S002211208700260X
   Web of Science ®Google Scholar
• Avino, G. D., & Maffettone, P. L. (2015). Particle dynamics in viscoelastic liquids. Journal of Non-Newtonian Fluid Mechanics, 215, 80–104. https://doi.org/10.1016/j.jnnfm.2014.09.014
   Web of Science ®Google Scholar
• Bahrami, D., & Bayareh, M. (2022). Experimental and numerical investigation on a novel spiral micromixer with sinusoidal channel walls. Chemical Engineering & Technology, 45(1), 100–109. https://doi.org/10.1002/ceat.202100368
   Web of Science ®Google Scholar
• Banerjee, I., Rosti, M. E., Kumar, T., Brandt, L., & Russom, A. (2021). Analogue tuning of particle focusing in elasto-inertial flow. Meccanica, 56(7), 1739–1749. https://doi.org/10.1007/s11012-021-01329-z
   Web of Science ®Google Scholar
• Bazaz, S. R., Mashhadian, A., Ehsani, A., Saha, S. C., Krüger, T., & Warkiani, M. E. (2020). Computational inertial microfluidics: A review. Lab on A Chip, 20(6), 1023–1048. https://doi.org/10.1039/C9LC01022J
   PubMed Web of Science ®Google Scholar
• Bazaz, S. R., Mihandust, A., Salomon, R., Joushani, H. A. N., Li, W., Amiri, H. A., Mirakhorli, F, Zhand, S., Shrestha, J., Miansari, M., Thierry, B., Jin, D., & Warkiani, M. E.  (2022). Zigzag microchannel for rigid inertial separation and enrichment (Z-RISE) of cells and particles. Lab on A Chip, 22(21), 4093–4109. https://doi.org/10.1039/D2LC00290F
   PubMed Web of Science ®Google Scholar
• Beris, A. N., Avgousti, M., & Souvaliotis, A. (1992). Spectral calculations of viscoelastic flows: Evaluation of the giesekus constitutive equation in model flow problems. Journal of Non-Newtonian Fluid Mechanics, 44, 197–228. https://doi.org/10.1016/0377-0257(92)80051-X
   Web of Science ®Google Scholar
• Cannon, I., Izbassarov, D., Tammisola, O., Brandt, L., & Rosti, M. E. (2021). The effect of droplet coalescence on drag in turbulent channel flows. Physics of Fluids, 33(8), 085112-1–085112-9. https://doi.org/10.1063/5.0058632
   Web of Science ®Google Scholar
• Carlo, D. D., Edd, J. F., Humphry, K. J., Stone, H. A., & Toner, M. (2009). Particle segregation and dynamics in confined flows. Physical Review Letters, 102(9), 094503. https://doi.org/10.1103/PhysRevLett.102.094503
   PubMed Web of Science ®Google Scholar
• Chen, X., Xue, C., Zhang, L., Hu, G., Jiang, X., & Sun, J. (2014). Inertial migration of deformable droplets in a microchannel. Physics of Fluids, 26(11), 112003-1–112003-25. https://doi.org/10.1063/1.4901884
   Web of Science ®Google Scholar
• Cheng, I. F., Huang, W. L., Chen, T. Y., Liu, C. W., Lin, Y. D., & Su, W. C. (2015). Antibody-free isolation of rare cancer cells from blood based on 3D lateral dielectrophoresis. Lab on A Chip, 15(14), 2950–2959. https://doi.org/10.1039/C5LC00120J
   PubMed Web of Science ®Google Scholar
• Cheng, W., Xu, J., Guo, Z., Yang, D., Chen, X., Yan, W., &  Miao, P.(2018). Hydrothermal synthesis of N,S co-doped carbon nanodots for highly selective detection of living cancer cells. Journal of Materials Chemistry B, 6(36), 5775–5780. https://doi.org/10.1039/C8TB01271G
   PubMed Web of Science ®Google Scholar
• Chung, A. J. (2019). A minireview on inertial microfluidics fundamentals: Inertial particle focusing and secondary flow. BioChip Journal, 13(1), 1–11. https://doi.org/10.1007/s13206-019-3110-1
   Web of Science ®Google Scholar
• Collins, D. J., Ma, Z., & Ai, Y. (2016). Highly localized acoustic streaming and size-selective submicrometer particle concentration using high frequency microscale focused acoustic fields. Analytical Chemistry 88(10), 5513–5522. https://doi.org/10.1063/1.4901884
   PubMed Web of Science ®Google Scholar
• Condina, M. R., Dilmetz, B. A., Bazaz, S. R., Meneses, J., Warkiani, M. E., & Hoffmann, P. (2019). Rapid separation and identification of beer spoilage bacteria by inertial microfluidics and MALDI-TOF mass spectrometry. Lab on A Chip, 19(11), 1961–1970. https://doi.org/10.1039/C9LC00152B
   PubMed Web of Science ®Google Scholar
• Cruz, J., Graells, T., Walldén, M., & Hjort, K. (2019). Inertial focusing with sub-micron resolution for separation of bacteria. Lab on A Chip, 19(7), 1257–1266. https://doi.org/10.1039/C9LC00080A
   PubMed Web of Science ®Google Scholar
• Dhar, M., Wong, J., Karimi, A., Che, J., Renier, C., Matsumoto, M., Triboulet, M., Garon, E. B., Goldman, J. W., VRettig, M. B., Jeffrey, S. S., Kulkarni, R. P., Sollier, E., & Carlo, D. D. (2015). High efficiency vortex trapping of circulating tumor cells. Biomicrofluidics, 9(6), 064116-1–064116-12. https://doi.org/10.1063/1.4937895
   Web of Science ®Google Scholar
• Do, Q.-V., Van, D.-A., Nguyen, V.-B., & Pham, V.-S. (2020). A numerical modeling study on inertial focusing of microparticle in spiral microchannel. AIP Advances, 10(7), 075017-1–075017-12. https://doi.org/10.1063/5.0006975
   Web of Science ®Google Scholar
• Doddi, S. K., & Bagchi, P. (2008). Lateral migration of a capsule in a plane Poiseuille flow in a channel. International Journal of Multiphase Flow, 34(10), 966–986. https://doi.org/10.1016/j.ijmultiphaseflow.2008.03.002
   Web of Science ®Google Scholar
• Dotto, D., & Marchioli, C. (2019). Orientation, distribution, and deformation of inertial flexible fibers in turbulent channel flow. Acta Mechanica, 230(2), 597–621. https://doi.org/10.1007/s00707-018-2355-4
   Web of Science ®Google Scholar
• Dotto, D., Soldati, A., & Marchioli, C. (2020). Deformation of flexible fibers in turbulent channel flow. Meccanica, 55(2), 343–356. https://doi.org/10.1007/s11012-019-01074-4
   Web of Science ®Google Scholar
• Ebrahimi, S., & Bagchi, P. (2021). Inertial and non-inertial focusing of a deformable capsule in a curved microchannel. Journal of Fluid Mechanics, 929, A30-1–A30-38. https://doi.org/10.1017/jfm.2021.868
   Web of Science ®Google Scholar
• Ebrahimi, S., Balogh, P., & Bagchi, P. (2021). Motion of a capsule in a curved tube. Journal of Fluid Mechanics, 907, A28-1–A28-35. https://doi.org/10.1017/jfm.2020.831
   Web of Science ®Google Scholar
• Feng, H., Huang, H., & Lu, X.-Y. (2021). Rheology of capsule suspensions in plane Poiseuille flows. Physics of Fluids, 33(1), 013302. https://doi.org/10.1063/5.0032113
   Web of Science ®Google Scholar
• Feng, J., Hu, H. H., & Joseph, D. D. (1994). Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid part 1. Sedimentation. Journal of Fluid Mechanics, 261, 95–134. https://doi.org/10.1017/S0022112094000285
   Web of Science ®Google Scholar
• Gai, G., Hadjadj, A., Kudriakov, S., & Thomine, O. (2020). Particles-induced turbulence: A critical review of physical concepts, numerical modelings and experimental investigations. Theoretical and Applied Mechanics Letters, 10(4), 241–248. https://doi.org/10.1016/j.taml.2020.01.026
   Web of Science ®Google Scholar
• Gao, T., Hu, H. H., & Castaneda, P. P. (2012). Shape dynamics and rheology of soft elastic particles in a shear flow. Physical Review Letters, 108(5), 058302-1–058302-4. https://doi.org/10.1103/PhysRevLett.108.058302
   Web of Science ®Google Scholar
• Garcia, M., & Pennathur, S. (2019). A model for inertial particles in curvilinear flows. Microfluidics and Nanofluidics, 23(5), 1–9. https://doi.org/10.1007/s10404-019-2234-x
   Web of Science ®Google Scholar
• Ghadami, S., Kowsari-Esfahan, R., & Saidi, M. (2017a). Spiral microchannel with stair-like cross section for size-based particle separation. Microfluidics & Nanofluidics, 21(7), 1–10. https://doi.org/10.1007/s10404-017-1950-3
   Web of Science ®Google Scholar
• Ghadami, S., Kowsari-Esfahan, R., Saidi, M. S., & Firoozbakhsh, K. (2017b). Spiral microchannel with stair-like cross section for size-based particle separation. Microfluidics and Nanofluidics, 21(7), 1–10. https://doi.org/10.1007/s10404-017-1950-3
   Web of Science ®Google Scholar
• Glowinski, R., Pan, T. W., Hesla, T. I., & Joseph, D. D. (1998). A distributed Lagrange multiplier/fictitious domain method for particulate flows. International Journal of Multiphase Flow, 25(5), 755–794. https://doi.org/10.1016/S0301-9322(98)00048-2
   Web of Science ®Google Scholar
• Gou, Y., Jia, Y., Wang, P., & Sun, C. (2018). Progress of inertial microfluidics in principle and application. Sensors, 18(6), 1762. https://doi.org/10.3390/s18061762
   PubMed Web of Science ®Google Scholar
• Hadikhani, P., Hashemi, S. M. H., Balestra, G., Zhu, L., Modestino, M. A., Gallaire, F., & Psaltis, D. (2018). Inertial manipulation of bubbles in rectangular microfluidic channels. Lab on A Chip, 18(7), 1035–1046. https://doi.org/10.1039/C7LC01283G
   PubMed Web of Science ®Google Scholar
• Hafemann, T., Tschisgale, S., & Fröhlich, J. (2020). A simulation method for particle migration in microfluidic spirals with application to small and medium particle concentrations. Physics of Fluids, 32(12), 123303-1–123303-30. https://doi.org/10.1063/5.0024472
   Web of Science ®Google Scholar
• Ho, B., & Leal, L. (1974). Inertial migration of rigid spheres in two-dimensional unidirectional flows. Journal of Fluid Mechanics, 65(2), 365–400. https://doi.org/10.1017/S0022112074001431
   Web of Science ®Google Scholar
• Ho, B. P., & Leal, L. G. (1976). Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. Journal of Fluid Mechanics, 76(4), 783–799. https://doi.org/10.1017/S002211207600089X
   Web of Science ®Google Scholar
• Hood, K., Kahkeshani, S., Di Carlo, D., & Roper, M. (2016). Direct measurement of particle inertial migration in rectangular microchannels. Lab on A Chip, 16(15), 2840–2850. https://doi.org/10.1039/C6LC00314A
   PubMed Web of Science ®Google Scholar
• Hood, K., Lee, S., & Roper, M. (2015). Inertial migration of a rigid sphere in three-dimensional Poiseuille flow. Journal of Fluid Mechanics, 765, 452–479. https://doi.org/10.1017/jfm.2014.739
   Web of Science ®Google Scholar
• Hu, X., Zhu, D., Chen, M., Chen, K., Liu, H., Liu, W., & Yang, Y. (2019). Precise and non-invasive circulating tumor cell isolation based on optical force using homologous erythrocyte binding. Lab on A Chip, 19(15), 2549–2556. https://doi.org/10.1039/C9LC00361D
   PubMed Web of Science ®Google Scholar
• Hughes, T., Liu, W. K., & Zimmermann, T. K. (1981). Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Computer Methods in Applied Mechanics & Engineering, 29(3), 329–349. https://doi.org/10.1016/0045-7825(81)90049-9
   Web of Science ®Google Scholar
• Hymel, S. J., Lan, H., Fujioka, H., & Khismatullin, D. B. (2019). Cell trapping in Y-junction microchannels: A numerical study of the bifurcation angle effect in inertial microfluidics. Physics of Fluids, 31(8), 082003-1–082003-11. https://doi.org/10.1063/1.5113516
   Web of Science ®Google Scholar
• Issakhov, A., Bulgakov, R., & Zhandaulet, Y. (2019). Numerical simulation of the dynamics of particle motion with different sizes. Engineering Applications of Computational Fluid Mechanics, 13(1), 1–25. https://doi.org/10.1080/19942060.2018.1545253
   Web of Science ®Google Scholar
• Jeon, H., Kwon, T., Yoon, J., & Han, J. (2022). Engineering a deformation-free plastic spiral inertial microfluidic system for CHO cell clarification in biomanufacturing. Lab on A Chip, 22(2), 272–285. https://doi.org/10.1039/D1LC00995H
   PubMed Web of Science ®Google Scholar
• Jiang, D., Huang, D., Zhao, G., Tang, W., & Xiang, N. (2019). Numerical simulation of particle migration in different contraction–expansion ratio microchannels. Microfluidics and Nanofluidics, 23(1), 1–11. https://doi.org/10.1007/s10404-018-2168-8
   Web of Science ®Google Scholar
• Joseph, D. D., & Ocando, D. (2002). Slip velocity and lift. Journal of Fluid Mechanics, 454, 263–286. https://doi.org/10.1017/S0022112001007145
   Web of Science ®Google Scholar
• Keunings, R. (2003). Finite element methods for integral viscoelastic fluids. Rheology Reviews, 167–196.
   Google Scholar
• Kim, J. A., Lee, J. R., Je, T. J., Jeon, E. C., & Lee, W. (2018). Size-dependent inertial focusing position shift and particle separations in triangular microchannels. Analytical Chemistry, 90(3), 1827–1835. https://doi.org/10.1021/acs.analchem.7b03851
   PubMed Web of Science ®Google Scholar
• Kim, L., Wu, N., & Carlo, D. (2016). Inertial focusing in non-rectangular cross-section microchannels and manipulation of accessible focusing positions. Lab on A Chip, 16(6), 992–1001. https://doi.org/10.1039/C5LC01100K
   PubMed Web of Science ®Google Scholar
• Kommajosula, A., Kim, J. A., Lee, W., & Ganapathysubramanian, B. (2019). High throughput, automated prediction of focusing patterns for inertial microfluidics. arXiv, 190105561. https://doi.org/10.48550/arXiv.1901.05561
   Google Scholar
• Kulrattanarak, T., Van Der Sman, R. G. M., Schroën, C. G. P. H., & Boom, R. M. (2008). Classification and evaluation of microfluidic devices for continuous suspension fractionation. Advances in Colloid & Interface Science, 142(1-2), 53–66. https://doi.org/10.1016/j.cis.2008.05.001
   PubMed Web of Science ®Google Scholar
• Kwak, B., Lee, S., Lee, J., Lee, J., Cho, J., Woo, H., Heo, & Y. S.  (2018). Hydrodynamic blood cell separation using fishbone shaped microchannel for circulating tumor cells enrichment. Sensors and Actuators B: Chemical, 261, 38–43. https://doi.org/10.1016/j.snb.2018.01.135
   Web of Science ®Google Scholar
• Kwon, T., Prentice, H., Oliveira, J. D., Madziva, N., Warkiani, M. E., Hamel, J.-F. P., & Han, J. (2017). Microfluidic cell retention device for perfusion of mammalian suspension culture. Scientific Reports, 7(1), 1–11. https://doi.org/10.1038/s41598-016-0028-x
   PubMedGoogle Scholar
• Lac, E., Barthes-Biesel, D., Pelekasis, N., & Tsamopoulos, J. (2004). Spherical capsules in three-dimensional unbounded stokes flows: Effect of the membrane constitutive law and onset of buckling. Journal of Fluid Mechanics, 516, 303–334. https://doi.org/10.1017/S002211200400062X
   Web of Science ®Google Scholar
• Larson, R. G. (2013). Constitutive equations for polymer melts and solutions: Butterworths series in chemical engineering. Butterworth-Heinemann.
   Google Scholar
• Lashgari, I., Ardekani, M. N., Banerjee, I., Russom, A., & Brandt, L. (2017). Inertial migration of spherical and oblate particles in straight ducts. Journal of Fluid Mechanics, 819, 540–561. https://doi.org/10.1017/jfm.2017.189
   Web of Science ®Google Scholar
• Lee, J. H., Lee, S. K., Kim, J. H., & Park, J. H. (2019). Separation of particles with bacterial size range using the control of sheath flow ratio in spiral microfluidic channel. Sensors and Actuators A: Physical, 286, 211–219. https://doi.org/10.1016/j.sna.2018.12.047
   Web of Science ®Google Scholar
• Lee, W., Amini, H., Stone, H. A., & Di Carlo, D. (2010). Dynamic self-assembly and control of microfluidic particle crystals. Proceedings of the National Academy of Sciences, 107(52), 22413–22418. https://doi.org/10.1073/pnas.1010297107
   PubMed Web of Science ®Google Scholar
• Li, G., McKinley, G. H., & Ardekani, A. M. (2015). Dynamics of particle migration in channel flow of viscoelastic fluids. Journal of Fluid Mechanics, 785, 486–505. https://doi.org/10.1017/jfm.2015.619
   Web of Science ®Google Scholar
• Lin, S., Xia, H., Liu, J., & Wang, H. (2022). The effect of particles on the dynamics of fluid flows around an obstacle. AIP Conference Proceedings, 2425(1), 020006-1–020006-4. https://doi.org/10.1063/5.0081348
   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. https://doi.org/10.1039/C4LC01216J
   PubMed Web of Science ®Google Scholar
• Liu, C., Xue, C., Sun, J., & Hu, G. (2016). A generalized formula for inertial lift on a sphere in microchannels. Lab on A Chip, 16(5), 884–892. https://doi.org/10.1039/C5LC01522G
   PubMed Web of Science ®Google Scholar
• Liu, C. X. (2016). Jiashu Sunb and Guoqing Hu A generalized formula for inertial lift on a sphere in microchannels. Lab on A Chip, 16(5), 884–892. https://doi.org/10.1039/C5LC01522G
   PubMed Web of Science ®Google Scholar
• Liu, J., & Pan, Z. (2022). Self-ordering and organization of in-line particle chain in a square microchannel. Physics of Fluids, 34(2), 023309-1–023309-19. https://doi.org/10.1063/5.0082577
   Web of Science ®Google Scholar
• Liu, Y., Li, T., Xu, M., Zhang, W., Xiong, Y., Nie, L., Wang, Q., Li, H., & Wang, W. (2018). A high-throughput liquid biopsy for rapid rare cell separation from large-volume samples. Lab on A Chip, 19(1), 68–78. https://doi.org/10.1039/C8LC01048J
   PubMed Web of Science ®Google Scholar
• Loutherback, K., D'Silva, J., Liu, L., Wu, A., & Sturm, J. (2012). Deterministic separation of cancer cells from blood at 10 mL/min. Nature Precedings, 2(4), 042107-1–042107-7.https://doi.org/10.1063/1.4758131
   Google Scholar
• Manz, A., Graber, N., & Widmer, H. M. (1990). Miniaturized total chemical analysis systems: A novel concept for chemical sensing. Sensors and Actuators B: Chemical, 1(1-6), 244–248. https://doi.org/10.1016/0925-4005(90)80209-I
   Web of Science ®Google Scholar
• Masaeli, M., Sollier, E., Amini, H., Mao, W., Camacho, K., Doshi, N., Mitragotri, S., Alexeev, A., & Carlo, D. D. (2012). Continuous inertial focusing and separation of particles by shape. Physical Review X, 2(3), 031017-1–031017-13. https://doi.org/10.1103/PhysRevX.2.031017
   Web of Science ®Google Scholar
• Mashhadian, A., & Shamloo, A. (2019). Inertial microfluidics: A method for fast prediction of focusing pattern of particles in the cross section of the channel. Analytica Chimica Acta, 1083, 137–149. https://doi.org/10.1016/j.aca.2019.06.057
   PubMed Web of Science ®Google Scholar
• Miao, P., & Tang, Y. (2019). Gold nanoparticles-based multipedal DNA walker for ratiometric detection of circulating tumor cell. Analytical Chemistry, 91(23), 15187–15192. https://doi.org/10.1021/acs.analchem.9b04000
   PubMed Web of Science ®Google Scholar
• Miao, T., & Xiao, Z. (2021). Numerical investigation on motion of an ellipsoidal particle inside confined microcavity flow. Theoretical and Applied Mechanics Letters, 11(1), 100234. https://doi.org/10.1016/j.taml.2021.100234
   Google Scholar
• Müller, S. J., Weigl, F., Bezold, C., Bächer, C., Albrecht, K., & Gekle, S. (2021). A hyperelastic model for simulating cells in flow. Biomechanics and Modeling in Mechanobiology, 20(2), 509–520. https://doi.org/10.1007/s10237-020-01397-2
   PubMed Web of Science ®Google Scholar
• Nasiri, R., Shamloo, A., & Akbari, J. (2022). Design of two inertial-based microfluidic devices for cancer cell separation from blood: A serpentine inertial device and an integrated inertial and magnetophoretic device. Chemical Engineering Science, 252, 117283. https://doi.org/10.1016/j.ces.2021.117283
   Web of Science ®Google Scholar
• Nizkaya, T. V., Gekova, A. S., Harting, J., Asmolov, E. S., & Vinogradova, O. I. (2020). Inertial migration of oblate spheroids in a plane channel. Physics of Fluids, 32(11), 112017. https://doi.org/10.1063/5.0028353
   Web of Science ®Google Scholar
• Ozkumur, E., Shah, A. M., Ciciliano, J. C., Emmink, B. L., Miyamoto, D. T., Brachtel, E., Yu, M., Chen, P., Morgan, B., Trautwein, J, Kimura, A., Sengupta, S., Stott, S. L., Karabacak, N. M., Barber, T. A., Walsh, J. R., Smith, K., Spuhler, P. S., Sullivan, J. P., et al. (2013). Inertial focusing for tumor antigen–dependent and–independent sorting of rare circulating tumor cells. Science Translational Medicine, 5(179), 179ra47. https://doi.org/10.1126/scitranslmed.3005616
   PubMed Web of Science ®Google Scholar
• Palumbo, J., Navi, M., Tsai, S. S., Spelt, J. K., & Papini, M. (2020). Inertial particle separation in helical channels: A calibrated numerical analysis. AIP Advances, 10(12), 125101-1–125101-12. https://doi.org/10.1063/5.0030930
   Web of Science ®Google Scholar
• Patankar, N. A., Huang, P. Y., Ko, T., & Joseph, D. D. (2001). Lift-off of a single particle in Newtonian and viscoelastic fluids by direct numerical simulation. Journal of Fluid Mechanics, 438, 67–100. https://doi.org/10.1017/S0022112001004104
   Web of Science ®Google Scholar
• Patel, K., & Stark, H. (2021). A pair of particles in inertial microfluidics: Effect of shape, softness, and position. Soft Matter, 17(18), 4804–4817. https://doi.org/10.1039/D1SM00276G
   PubMed Web of Science ®Google Scholar
• Prosperetti, A., & Tryggvason, G. (2009). Computational methods for multiphase flow. Cambridge university press.
   Google Scholar
• Raffiee, A. H., Ardekani, A. M., & Dabiri, S. (2019). Numerical investigation of elasto-inertial particle focusing patterns in viscoelastic microfluidic devices. Journal of Non-Newtonian Fluid Mechanics, 272, 104166. https://doi.org/10.1016/j.jnnfm.2019.104166
   Web of Science ®Google Scholar
• Raffiee, A. H., Dabiri, S., & Ardekani, A. M. (2017). Elasto-inertial migration of deformable capsules in a microchannel. Biomicrofluidics, 11(6), 064113-1–064113-16. https://doi.org/10.1063/1.5004572
   Web of Science ®Google Scholar
• Raffiee, A. H., Dabiri, S., & Ardekani, A. M. (2019b). Suspension of deformable particles in Newtonian and viscoelastic fluids in a microchannel. Microfluidics and Nanofluidics, 23(2), 1–12. https://doi.org/10.1007/s10404-018-2182-x
   Web of Science ®Google Scholar
• Raoufi, M. A., Mashhadian, A., Niazmand, H., Asadnia, M., & Warkiani, M. E. (2019). Experimental and numerical study of elasto-inertial focusing in straight channels. Biomicrofluidics, 13(3), 034103-1–034103-13. https://doi.org/10.1063/1.5093345
   Web of Science ®Google Scholar
• Rasooli, R., & Çetin, B. (2018). Assessment of lagrangian modeling of particle motion in a spiral microchannel for inertial microfluidics. Micromachines, 9(9), 433. https://doi.org/10.3390/mi9090433
   PubMed Web of Science ®Google Scholar
• Rosén, T., Do-Quang, M., Aidun, C., & Lundell, F. (2015). Effect of fluid and particle inertia on the rotation of an oblate spheroidal particle suspended in linear shear flow. Physical Review E, 91(5), 053017-1–053017-15. https://doi.org/10.1103/PhysRevE.91.053017
   Web of Science ®Google Scholar
• Ruan, J., Zhang, W., Zhang, C., Li, N., Jiang, J., & Su, H. (2022). A magnetophoretic microdevice for multi-magnetic particles separation based on size: A numerical simulation study. Engineering Applications of Computational Fluid Mechanics, 16(1), 1781–1795. https://doi.org/10.1080/19942060.2022.2109064
   Web of Science ®Google Scholar
• Rubinow, S. I., & Keller, J. B. (1961). The transverse force on a spinning sphere moving in a viscous fluid. Journal of Fluid Mechanics, 11((03|3)), 447–459. https://doi.org/10.1017/S0022112061000640
   Web of Science ®Google Scholar
• Rzhevskiy, A. S., Bazaz, S. R., Lin, D., Kapitannikova, A., & Zvyagin, A. V. (2020). Rapid and label-free isolation of tumour cells from the urine of patients with localised prostate cancer using inertial microfluidics. Cancers, 12(1), 81. https://doi.org/10.3390/cancers12010081
   Web of Science ®Google Scholar
• Saffman, P. G. (1965). The lift on a small sphere in a slow shear. Journal of Fluid Mechanics, 22(2), 385–400. https://doi.org/10.1017/S0022112065000824
   Web of Science ®Google Scholar
• Segr, G., & Silberberg, A. (1961). Radial particle displacements in poiseuille flow of suspensions. Nature, 189(4760), 209–210. https://doi.org/10.1038/189209a0
   Google Scholar
• Shamloo, A., & Mashhadian, A. (2018). Inertial particle focusing in serpentine channels on a centrifugal platform. Physics of Fluids, 30(1), 012002-1–012002-13. https://doi.org/10.1063/1.5002621
   Web of Science ®Google Scholar
• Shao, X., Yu, Z., & Sun, B. (2008). Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers. Physics of Fluids, 20(10), 103307-1–103307-11. https://doi.org/10.1063/1.3005427
   Web of Science ®Google Scholar
• Shen, S., Chang, T., Li, T., Xu, J., Chen, S. W., Qin, T., Yuan, A. S., Liu, W., & Wang, J. (2017). Spiral microchannel with ordered micro-obstacles for continuous and highly-efficient particle separation. Lab on A Chip, 17(21), 3578–3591. https://doi.org/10.1039/C7LC00691H
   PubMed Web of Science ®Google Scholar
• Shiriny, A., & Bayareh, M. (2021). Inertial focusing of CTCs in a novel spiral microchannel. Chemical Engineering Science, 229, 116102. https://doi.org/10.1016/j.ces.2020.116102
   Web of Science ®Google Scholar
• Shiriny, A., Bayareh, M., & Usefian, A. (2022). Inertial separation of microparticles suspended in shear-thinning fluids. Chemical Papers, 76(7), 4341–4350. https://doi.org/10.1007/s11696-022-02184-2
   Web of Science ®Google Scholar
• Singh, R. K., & Sarkar, K. (2011). Inertial effects on the dynamics, streamline topology and interfacial stresses due to a drop in shear. Journal of Fluid Mechanics, 683, 149–171. https://doi.org/10.1017/jfm.2011.257
   Web of Science ®Google Scholar
• Stoecklein, D., & Di Carlo, D. (2018). Nonlinear microfluidics. Analytical Chemistry, 91(1), 296–314. https://doi.org/10.1021/acs.analchem.8b05042
   PubMed Web of Science ®Google Scholar
• Su, J., Chen, X., Zhu, Y., & Hu, G. (2021). Machine learning assisted fast prediction of inertial lift in microchannels. Lab on A Chip, 21(13), 2544–2556. https://doi.org/10.1039/D1LC00225B
   PubMed Web of Science ®Google Scholar
• Subramaniam, D. R., & Gee, D. J. (2016). Shape oscillations of elastic particles in shear flow. Journal of the Mechanical Behavior of Biomedical Materials, 62, 534–544. https://doi.org/10.1016/j.jmbbm.2016.05.031
   PubMed Web of Science ®Google Scholar
• Sugiyama, K., Ii, S., Takeuchi, S., Takagi, S., & Matsumoto, Y. (2011). A full eulerian finite difference approach for solving fluid–structure coupling problems. Journal of Computational Physics, 230(3), 596–627. https://doi.org/10.1016/j.jcp.2010.09.032
   Web of Science ®Google Scholar
• Tabatabaei, S. A., Javaherchian, J., & Yaghoubi, M. (2022). Basic concepts of biological microparticles isolation by inertia spiral microchannels in simple terms: A review. Journal of Micromechanics and Microengineering, 32(1), 013001. https://doi.org/10.1088/1361-6439/ac388c
   Web of Science ®Google Scholar
• Tam, C. K. W., & Hyman, W. A. (1973). Transverse motion of an elastic sphere in a shear field. Journal of Fluid Mechanics, 59(1), 177–185. https://doi.org/10.1017/S0022112073001497
   Web of Science ®Google Scholar
• Thorp, I. R., & Lister, J. R. (2019). Motion of a non-axisymmetric particle in viscous shear flow. Journal of Fluid Mechanics, 872, 532–559. https://doi.org/10.1017/jfm.2019.367
   Web of Science ®Google Scholar
• Tohme, T., Magaud, P., & Baldas, L. (2021). Transport of non-spherical particles in square microchannel flows: A review. Micromachines, 12(3), 277. https://doi.org/10.3390/mi12030277
   PubMed Web of Science ®Google Scholar
• Trofa, M., Vocciante, M., D’Avino, G., Hulsen, M. A., & Maffettone, P. L. (2015). Numerical simulations of the competition between the effects of inertia and viscoelasticity on particle migration in Poiseuille flow. Computers & Fluids, 107, 214–223. https://doi.org/10.1016/j.compfluid.2014.11.015
   Web of Science ®Google Scholar
• Udono, H., & Sakai, M. (2017). A numerical study on dynamic inertial focusing of microparticles in a confined flow. Granular Matter, 19(4), 1–9. https://doi.org/10.1007/s10035-017-0758-x
   Web of Science ®Google Scholar
• Villone, M., d'Avino, G., Hulsen, M., & Maffettone, P. (2015). Dynamics of prolate spheroidal elastic particles in confined shear flow. Physical Review E, 92(6), 062303-1–062303-12. https://doi.org/10.1103/PhysRevE.92.062303
   Web of Science ®Google Scholar
• Villone, M. M., & Maffettone, P. L. (2019). Dynamics, rheology, and applications of elastic deformable particle suspensions: A review. Rheologica Acta, 58(3-4), 109–130. https://doi.org/10.1007/s00397-019-01134-2
   Web of Science ®Google Scholar
• Wang, Q., Yuan, D., & Li, W. (2017). Analysis of hydrodynamic mechanism on particles focusing in micro-channel flows. Micromachines, 8(7), 197. https://doi.org/10.3390/mi8070197
   PubMed Web of Science ®Google Scholar
• Warkiani, M. E., Guan, G., Luan, K. B., Lee, W. C., Bhagat, A., Chaudhuri, P. K., Tan, D. S. W., Lim, W. T., Lee, S. C., Chen, P. C. Y., Lim, C. K., & Han, J. (2013). Slanted spiral microfluidics for the ultra-fast, label-free isolation of circulating tumor cells. Lab on A Chip, 14(1), 128–137. https://doi.org/10.1039/C3LC50617G
   Web of Science ®Google Scholar
• Warkiani, M. E., Khoo, B. L., Wu, L., Tay, A., & Lim, C. T. (2016). Ultra-fast, label-free isolation of circulating tumor cells from blood using spiral microfluidics. Nature Protocols, 11(1), 134–148. https://doi.org/10.1038/nprot.2016.003
   PubMed Web of Science ®Google Scholar
• WenlaiTang, S., DiJiang, L., & JiquanYang, N. (2020). Channel innovations for inertial microfluidics. Lab on A Chip, 20(19), 3485–3502. https://doi.org/10.1039/D0LC00714E
   PubMed Web of Science ®Google Scholar
• Wu, J., & Aidun, C. K. (2010). Simulating 3D deformable particle suspensions using lattice boltzmann method with discrete external boundary force. International Journal for Numerical Methods in Fluids, 62(7), 765–783.
   Web of Science ®Google Scholar
• Xia, Z., Shi, Y., Zhang, Q., & Chen, S. (2016). Modulation to compressible homogenous turbulence by heavy point particles. I. Effect of particles’ density. Physics of Fluids, 28(1), 016103-1–016103-14. https://doi.org/10.1063/1.4939794
   Web of Science ®Google Scholar
• Xu, S., Xu, F., Kommajosula, A., Hsu, M. C., & Ganapathysubramanian, B. (2019). Immersogeometric analysis of moving objects in incompressible flows. Computers & Fluids, 189, 24–33. https://doi.org/10.1016/j.compfluid.2019.05.018
   Web of Science ®Google Scholar
• Yan, Y., Li, X., Fang, X., Yan, P., & Tu, J. (2021). Transmission of COVID-19 virus by cough-induced particles in an airliner cabin section. Engineering Applications of Computational Fluid Mechanics, 15(1), 934–950. https://doi.org/10.1080/19942060.2021.1922124
   Web of Science ®Google Scholar
• Yang, B. H., Wang, J., Joseph, D. D., Hu, H. H., Pan, T.-W., & Glowinski, R. (2005). Migration of a sphere in tube flow. Journal of Fluid Mechanics, 540(-1), 109–131. https://doi.org/10.1017/S0022112005005677
   Google Scholar
• Yang, L.-J., Joseph, V.-J., Unnam, N.-K., & Esakki, B. (2022). Design and numerical simulation of biomimetic structures to capture particles in a microchannel. Fluids, 7(1), 32. https://doi.org/10.3390/fluids7010032
   Web of Science ®Google Scholar
• Yu, Z., Wang, P., Lin, J., & Hu, H. H. (2019). Equilibrium positions of the elasto-inertial particle migration in rectangular channel flow of Oldroyd-B viscoelastic fluids. Journal of Fluid Mechanics, 868, 316–340. https://doi.org/10.1017/jfm.2019.188
   Web of Science ®Google Scholar
• Zhang, T., Hong, Z.-Y., Tang, S.-Y., Li, W., Inglis, D. W., Hosokawa, Y., Yalikun, Y., & Li, M. (2020). Focusing of sub-micrometer particles in microfluidic devices. Lab on A Chip, 20(1), 35–53. https://doi.org/10.1039/C9LC00785G
   PubMed Web of Science ®Google Scholar
• Zhou, Y., Song, L., Yu, L., & Xuan, X. (2017). Inertially focused diamagnetic particle separation in ferrofluids. Microfluidics and Nanofluidics, 21(1), 1–11. doi:10.1007/s10404-016-1833-z
   Web of Science ®Google Scholar