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Validity of the Reynolds equation for miscible fluids in microchannels
1. | Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France, France |
2. | LMA, Téléport 2- BP 30179, Boulevard Pierre et Marie Curie, 86962 Futuroscope Chasseneuil Cedex, France |
References:
[1] |
G. Bayada and M. Chambat, New models in the theory of the hydrodynamic bifurcation of rough surfaces, J. Tribol., 110 (1988), 402-407.
doi: 10.1115/1.3261642. |
[2] |
F. Boyer, Mathematical study of multi-phase flow under shear through order parameter formulation, Asymptotic Analysis, 20 (1999), 175-212. |
[3] |
F. Boyer and P. Fabrie, "Éléments d'Analyse pour l'Étude de Quelques Modèles d'Écoulements de Fluides Visqueux Incompressibles," Mathématiques & Applications (Berlin), 52, Springer-Verlag, Berlin, 2006. |
[4] |
D. Bresch, C. Choquet, L. Chupin, T. Colin and M. Gisclon, Roughness-induced effect at main order on the Reynolds approximation, Multiscale Modeling and Simulation, 8 (2010), 997-1017.
doi: 10.1137/090754996. |
[5] |
J. Dambrine, "Modélisation et Étude Numérique de Quelques Écoulements de Fluides Complexes en Microfluidiques," Thèse de l'Université Bordeaux 1, 2009. |
[6] |
J. Dambrine, B. Géraud and J. B. Salmon, Interdiffusion of liquids of different viscosities in a microchannel, New Journal of Physics, 2009. |
[7] |
J. Fernandez, P. Kurowski, P. Petitjean and E. Meiburg, Density-driven unstable flows of miscible fluids in a Hele-Shaw cell, J. Fluid. Mech., 451 (2002), 239-260. |
[8] |
C. G. Gal and M. Grasselli, Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system, Physica D, 240 (2011), 629-635.
doi: 10.1016/j.physd.2010.11.014. |
[9] |
D. Gérard-Varet and N. Masmoudi, Relevance of the slip condition for fluid flows near an irregular boundary, Comm. Math. Phys., 295 (2010), 99-137. |
[10] |
A. Günther, K.-F. Jensen, Multiphase microfluidics: From flow characteristics to chemical and material synthesis, Lab on a Chip, 2006. |
[11] |
D. Joseph and Y. Renardy, "Fundamentals of Two Fluid Dynamics. Part I. Mathematical Theory and Applications," Interdisciplinary Applied Mathematics, 3, Springer-Verlag, New York, 1993. |
[12] |
G. Karniadakis and A. Beskok, "Micro Flows: Fundamental and Simulation," Springer-Verlag, 2002. |
[13] |
O. Kuksenok and A. C. Balazs, Simulating the dynamic behavior of immiscible binary fluids in three-dimensional chemically patterned microchannels, Physical Review E, 2003. |
[14] |
O. Kuksenok and A. C. Balazs, Structures formation in binary fluids driven through patterned microchannels: Effect of hydrodynamics and arrangement of surface patterns, Physica D, 2004. |
[15] |
S. Li, J. Lowengrub and P. Leo, A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell, J. Comp. Phys., 225 (2007), 534-567. |
[16] |
X.-D. Liu, S. Osher and T. Chan, Weighted essentially non-oscillatory schemes, Journal of Computational Physics, 115 (1994), 200-212.
doi: 10.1006/jcph.1994.1187. |
[17] |
N.-T. Nguyen and Z. Wu, Micromixers-a review, Journal of Micromechanics and Microengineering, 2010. |
[18] |
P. G. Saffman and G. Taylor, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. of the Roy. Soc. London Ser A, 245 (1958), 312-329.
doi: 10.1098/rspa.1958.0085. |
[19] |
D. Schafroth, N. Goyal and E. Meiburg, Miscible displacements in Hele-Shaw cells: Nonmonotonic viscosity profiles, European Journal of Mechanics B Fluids, 26 (2007), 444-453.
doi: 10.1016/j.euromechflu.2006.09.001. |
[20] |
J. Simon, Compacts sets in the space $L^p(0,T;B)$, Annali. Mat. Pura. Applicata. (4), 146 (1987), 65-96. |
[21] |
A. D. Stroock, S. K. W. Dertinger, A. Adjari, I. Mezić, H. A. Stone and G. M. Whitesides, Chaotic mixers in microchannels, Science, 2002. |
[22] |
A. D. Stroock, S. K. W. Dertinger, G. M. Whitesides and A. Adjari, Patterning flows using grooved surfaces, Analytical Chemistry, 2002. |
show all references
References:
[1] |
G. Bayada and M. Chambat, New models in the theory of the hydrodynamic bifurcation of rough surfaces, J. Tribol., 110 (1988), 402-407.
doi: 10.1115/1.3261642. |
[2] |
F. Boyer, Mathematical study of multi-phase flow under shear through order parameter formulation, Asymptotic Analysis, 20 (1999), 175-212. |
[3] |
F. Boyer and P. Fabrie, "Éléments d'Analyse pour l'Étude de Quelques Modèles d'Écoulements de Fluides Visqueux Incompressibles," Mathématiques & Applications (Berlin), 52, Springer-Verlag, Berlin, 2006. |
[4] |
D. Bresch, C. Choquet, L. Chupin, T. Colin and M. Gisclon, Roughness-induced effect at main order on the Reynolds approximation, Multiscale Modeling and Simulation, 8 (2010), 997-1017.
doi: 10.1137/090754996. |
[5] |
J. Dambrine, "Modélisation et Étude Numérique de Quelques Écoulements de Fluides Complexes en Microfluidiques," Thèse de l'Université Bordeaux 1, 2009. |
[6] |
J. Dambrine, B. Géraud and J. B. Salmon, Interdiffusion of liquids of different viscosities in a microchannel, New Journal of Physics, 2009. |
[7] |
J. Fernandez, P. Kurowski, P. Petitjean and E. Meiburg, Density-driven unstable flows of miscible fluids in a Hele-Shaw cell, J. Fluid. Mech., 451 (2002), 239-260. |
[8] |
C. G. Gal and M. Grasselli, Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system, Physica D, 240 (2011), 629-635.
doi: 10.1016/j.physd.2010.11.014. |
[9] |
D. Gérard-Varet and N. Masmoudi, Relevance of the slip condition for fluid flows near an irregular boundary, Comm. Math. Phys., 295 (2010), 99-137. |
[10] |
A. Günther, K.-F. Jensen, Multiphase microfluidics: From flow characteristics to chemical and material synthesis, Lab on a Chip, 2006. |
[11] |
D. Joseph and Y. Renardy, "Fundamentals of Two Fluid Dynamics. Part I. Mathematical Theory and Applications," Interdisciplinary Applied Mathematics, 3, Springer-Verlag, New York, 1993. |
[12] |
G. Karniadakis and A. Beskok, "Micro Flows: Fundamental and Simulation," Springer-Verlag, 2002. |
[13] |
O. Kuksenok and A. C. Balazs, Simulating the dynamic behavior of immiscible binary fluids in three-dimensional chemically patterned microchannels, Physical Review E, 2003. |
[14] |
O. Kuksenok and A. C. Balazs, Structures formation in binary fluids driven through patterned microchannels: Effect of hydrodynamics and arrangement of surface patterns, Physica D, 2004. |
[15] |
S. Li, J. Lowengrub and P. Leo, A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell, J. Comp. Phys., 225 (2007), 534-567. |
[16] |
X.-D. Liu, S. Osher and T. Chan, Weighted essentially non-oscillatory schemes, Journal of Computational Physics, 115 (1994), 200-212.
doi: 10.1006/jcph.1994.1187. |
[17] |
N.-T. Nguyen and Z. Wu, Micromixers-a review, Journal of Micromechanics and Microengineering, 2010. |
[18] |
P. G. Saffman and G. Taylor, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. of the Roy. Soc. London Ser A, 245 (1958), 312-329.
doi: 10.1098/rspa.1958.0085. |
[19] |
D. Schafroth, N. Goyal and E. Meiburg, Miscible displacements in Hele-Shaw cells: Nonmonotonic viscosity profiles, European Journal of Mechanics B Fluids, 26 (2007), 444-453.
doi: 10.1016/j.euromechflu.2006.09.001. |
[20] |
J. Simon, Compacts sets in the space $L^p(0,T;B)$, Annali. Mat. Pura. Applicata. (4), 146 (1987), 65-96. |
[21] |
A. D. Stroock, S. K. W. Dertinger, A. Adjari, I. Mezić, H. A. Stone and G. M. Whitesides, Chaotic mixers in microchannels, Science, 2002. |
[22] |
A. D. Stroock, S. K. W. Dertinger, G. M. Whitesides and A. Adjari, Patterning flows using grooved surfaces, Analytical Chemistry, 2002. |
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