On a three-dimensional implementation of the baker's transformation

Physics of Fluids

Volumn 19, Issue 11, 2007, Pages

  Carrière, Philippe ^a  

^a LABORATOIRE DE MÉCANIQUE DES FLUIDES ET D ACOUSTIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; FLOW VELOCITY; LYAPUNOV METHODS; MATHEMATICAL TRANSFORMATIONS; THREE DIMENSIONAL;

BAKER'S TRANSFORMATION; LYAPUNOV EXPONENT; STEADY FLOW CONFIGURATION; VELOCITY FIELD;

STEADY FLOW;

FINITE ELEMENT METHOD; FLOW VELOCITY; LYAPUNOV METHODS; MATHEMATICAL TRANSFORMATIONS; STEADY FLOW; THREE DIMENSIONAL;

EID: 36849083926     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2804959     Document Type: Article

References (25)

1. M. A. Lichtenberg and A. J. Lieberman, Regular and Chaotic Dynamics (Springer, New York, 1992.
2. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, New York, 1989).
3. S. Wiggins and J. M. Ottino, "Foundations of chaotic mixing," Philos. Trans. R. Soc. London, Ser. APTRMAD0962-842810.1098/ rsta.2003.1356 362, 937 (2004).
4. H. Mensinger, T. Richter, V. Hessel, J. Döpper, and W. Ehrfeld, "Microreactor with integrated static mixer and analysis system," in Micro Total Analysis Systems, edited by A. van den Berg and P. Bergveld (Kluwer, Dordrecht, 1994), pp. 237-243.
5. N. Schwesinger, T. Frank, and H. Wurmus, "A modular microfluid system with an integrated micromixer," J. Micromech. Microeng.JMMIEZ0960-131710.1088/0960-1317/6/1/023 6, 99 (1996).
6. J. Branebjerg, P. Gravesen, J. P. Krog, and C. R. Nielsen, "Fast mixing by lamination," in Proceedings of the 9th IEEE Workshop on Micro Electro Mechanical Systems (IEEE, New York, 1996), pp. 441-446.
7. B. L. Gray, D. Jaeggi, N. J. Mourlas, B. P. van Drieënhuizen, K. R. Williams, N. I. Maluf, and G. T. A. Kovacs, "Novel interconnection technologies for integrated microfluidic systems," Sens. Actuators, A SAAPEB0924-424710.1016/S0924-4247(99)00185-5 77, 57 (1999).
8. H. Chen and J.-S. Meiners, "Topologic mixing on a microfluidic chip," Appl. Phys. Lett. APPLAB0003-695110.1063/1.1686895 84, 2193 (2004).
9. O. Byrde and M. L. Sawley, "Optimization of a Kenics static mixer for non-creeping flow conditions," Chem. Eng. J.CMEJAJ0300-946710.1016/S1385-8947(98)00145-4 72, 163 (1999).
10. M. Regner, K. Östergren, and C. Trägårdh, "Effects of geometry and flow rate on secondary flow and the mixing process in static mixers-a numerical study," Chem. Eng. Sci. CESCAC0009-250910.1016/j.ces.2006.05.044 61, 6133 (2006).
11. J. M. MacInnes, A. Vikhansky, and R. W. K. Allen, "Numerical characterisation of folding flow microchannel mixers," Chem. Eng. Sci.CESCAC0009-250910.1016/j.ces.2007.02.014 62, 2718 (2007).
12. S. W. Jones, O. M. Thomas, and H. Aref, "Chaotic advection by laminar flow in a twisted pipe," J. Fluid Mech. JFLSA70022-112010.1017/S0022112089003137 209, 335 (1989).
13. C. Castelain, D. Berger, P. Legentilhomme, A. Mokrani, and H. Peerhossaini, "Experimental and numerical characterisation of mixing in a steady spatially chaotic flow by means of residence time distribution measurements," Int. J. Heat Mass TransferI JHMAK0017-931010.1016/S0017-9310(99)00363-4 43, 3687 (2000).
14. H. A. Stone, A. D. Stroock, and A. Ajdari, "Engineering flows in small devices, microfluidics toward lab-on-a-chip," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.36.050802.122124 36, 381 (2004).
15. A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezic, H. A. Stone, and G. M. Whitesides, "Chaotic mixer for microchannels," Science SCIEAS0036-807510.1126/science.1066238 295, 647 (2002).
16. A. Dodge, A. Hountondji, M. C. Jullien, and P. Tabeling, "Spatiotemporal resonances in a microfluidic system," Phys. Rev. E \PLEEE81063-651X10.1103/PhysRevE.72.056312 72, 056312, (2005).
17. F. Raynal, F. Plaza, A. Beuf, Ph. Carrière, E. Souteyrand, J.-R. Martin, J.-P. Cloarec, and M. Cabrera, "Study of a chaotic mixing system for DNA chip hybridization chambers," Phys. Fluids PHFLE61070-663110.1063/1.1775807 16, L63 (2004).
18. F. Raynal, A. Beuf, F. Plaza, J. Scott, Ph. Carrière, M. Cabrera, J.-P. Cloarec, and E. Souteyrand, "Towards better DNA chip hybridization using chaotic advection," Phys. FluidsPHFLE61070-663110.1063/1.2431322 19, 017112 (2007).
19. M. K. McQuain, K. Seale, J. Peek, T. S. Fisher, S. Levy, M. A. Stremler, and F. Haselton, "Chaotic mixer improves microarray hybridization," Anal. Biochem. ANBCA20003-269710.1016/ j.ab.2003.10.032, 325, 215 (2004).
20. Ph. Carrière and D. Jeandel, "A 3D finite element method for the simulation of thermoconvective flows and its performances on a vector-parallel computer," Int. J. Numer. Methods FluidsI JNFDW0271-209110.1002/fld.1650121003 12, 929 (1991).
21. Ph. Carrière, "Lyapunov spectrum determination from the FEM simulation of a chaotic advecting flow," Int. J. Numer. Methods FluidsI JNFDW0271-209110.1002/fld.1056 50, 555 (2006).
22. V. Toussaint, Ph. Carrière, and F. Raynal, "A numerical Eulerian approach to mixing by chaotic advection," Phys. Fluids PHFLE61070-663110.1063/1.868707 7, 2587 (1995).
23. V. Toussaint and Ph. Carrière, "Diffusive cut-off of fractal surfaces in chaotic mixing," Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE40218-127410.1142/S0218127499000298 9, 443 (1999).
24. X. Z. Tang and A. H. Boozer, "A Lagrangian analysis of advection-diffusion equation for a three dimensional chaotic flow," Phys. FluidsPHFLE61070-663110.1063/1.870006 11, 1418 (1999).
25. J. P. Eckmann and D. Ruelle, "Ergodic theory of chaos," Rev. Mod. Phys. RMPHAT0034-686110.1103/RevModPhys.57.617 57, 617 (1985).