Abstract
Using the method of multi-particle collision dynamics (MPCD), we investigate inertial focussing in microfluidic channels that gives rise to the Segré-Silberberg effect. At intermediate Reynolds numbers, we model the motion of a spherical colloid in a circular microchannel under pressure-driven flow. We determine the radial distribution function and show how its width and the location of its maximum are strongly influenced by the colloid size and the Reynolds number of the Poiseuille flow. We demonstrate that MPCD is well suited for calculating mean values for the lift force acting on the colloid in the cross-sectional plane and for its mean axial velocity. We introduce a Langevin equation for the cross-sectional motion whose steady state is the Boltzmann distribution that contains the integrated lift force as potential energy. It perfectly coincides with the simulated radial distribution function.
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References
G. Segré, A. Silberberg, Nature 189, 209 (1961)
G. Segré, A. Silberberg, J. Fluid Mech. 14, 136 (1962)
F.P. Bretherton, J. Fluid Mech. 14, 284 (1962)
J. Matas, J. Morris, E. Guazzelli, J. Fluid Mech. 515, 171 (2004)
J. Matas, V. Glezer, É. Guazzelli, J. Morris, Phys. Fluids 16, 4192 (2004)
B.P. Ho, L.G. Leal, J. Fluid Mech. 65, 365 (1974)
J.A. Schonberg, E.J. Hinch, J. Fluid Mech. 203, 517 (1989)
E.S. Asmolov, J. Fluid Mech. 381, 63 (1999)
D. Di Carlo, D. Irimia, R.G. Tompkins, M. Toner, Proc. Natl. Acad. Sci. U.S.A. 104, 18892 (2007)
B. Chun, A.J.C. Ladd, Phys. Fluids 18, 031704 (2006)
B. Yang, J. Wang, D. Joseph, H. Hu, T. Pan, R. Glowinski, J. Fluid Mech. 540, 109 (2005)
D. Di Carlo, Lab on a Chip 9, 3038 (2009)
A.A.S. Bhagat, S.S. Kuntaegowdanahalli, I. Papautsky, Microfluidics Nanofluidics 7, 217 (2009)
A.A.S. Bhagat, S.S. Kuntaegowdanahalli, I. Papautsky, Phys. Fluids 20, 101702 (2008)
S.C. Hur, H.T.K. Tse, D. Di Carlo, Lab on a Chip 10, 274 (2010)
S.S. Kuntaegowdanahalli, A.A.S. Bhagat, I. Papautsky, Lab on a Chip 9, 2973 (2009)
J. Seo, M.H. Lean, A. Kole, Appl. Phys. Lett. 91, 033901 (2007)
D. Di Carlo, J.F. Edd, D. Irimia, R.G. Tompkins, M. Toner, Anal. Chem. 80, 2204 (2008)
Z. Wu, B. Willing, J. Bjerketorp, J. Jansson, K. Hjort, Lab on a Chip 9, 1193 (2009)
J.P. Matas, J.F. Morris, E. Guazzelli, Oil Gas Sci. Technol. Rev. 59, 59 (2004)
P.G. Saffman, J. Fluid Mech. 22, 384 (1965)
D. Di Carlo, J.F. Edd, K.J. Humphry, H.A. Stone, M. Toner, Phys. Rev. Lett. 102, 094503 (2009)
J. Feng, H.H. Hu, D.D. Joseph, J. Fluid Mech. 277, 271 (1994)
A. Malevanets, R. Kapral, J. Chem. Phys. 110, 8605 (1999)
A. Malevanets, R. Kapral, J. Chem. Phys. 112, 7260 (2000)
D.A. Reid, H. Hildebrandt, J.T. Padding, C.K. Hemelrijk, Phys. Rev. E 79, 046313 (2009)
A. Lamura, G. Gompper, T. Ihle, D.M. Kroll, Europhys. Lett. 56, 319 (2001)
G. Batchelor, An introduction to fluid dynamics, Cambridge mathematical library (Cambridge University Press, 2000), ISBN 9780521663960
G. Gompper, T. Ihle, D. Kroll, R. Winkler, in Advanced Computer Simulation Approaches for Soft Matter Sciences III, edited by C. Holm, K. Kremer (Springer Berlin/Heidelberg, 2009) Vol. 221 of Advances in Polymer Science, pp. 1--87, ISBN 978-3-540-87705-9
H. Noguchi, N. Kikuchi, G. Gompper, EPL 78, 10005 (2007)
T. Ihle, D.M. Kroll, Phys. Rev. E 63, 020201 (2001)
H. Noguchi, G. Gompper, Phys. Rev. E 78, 016706 (2008)
J.T. Padding, A. Wysocki, H. Löwen, A.A. Louis, J. Phys.: Condens. Matter 17, S3393 (2005)
I.O. Götze, H. Noguchi, G. Gompper, Phys. Rev. E 76, 046705 (2007)
I.O. Götze, G. Gompper, Phys. Rev. E 82, 041921 (2010)
J.T. Padding, A.A. Louis, Phys. Rev. E 74, 031402 (2006)
B.W. Silverman, Density Estimation (Chapman and Hall, 1986)
M.C. Jones, Biometrika 78, 511 (1991)
S.J. Sheather, M.C. Jones, J. Roy. Stat. Soc., Ser. B (Methodological) 53, 683 (1991)
B. Van der Waerden, Mathematische Statistik (Springer, 1957)
C.A. Silebi, J.G. Dosramos, AIChE J. 35, 1351 (1989)
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Prohm, C., Gierlak, M. & Stark, H. Inertial microfluidics with multi-particle collision dynamics. Eur. Phys. J. E 35, 80 (2012). https://doi.org/10.1140/epje/i2012-12080-3
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DOI: https://doi.org/10.1140/epje/i2012-12080-3