Viscous parallel flows in finite aspect ratio Hele-Shaw cell: Analytical and numerical results

Physics of Fluids

Volumn 9, Issue 6, 1997, Pages 1841-1843

  Gondret, P ^a   Rakotomalala, N ^a   Rabaud, M ^a   Salin, D ^a   Watzky, P ^a  

^a Laboratoire FAST   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; MODELLING-MATHEMATICAL; VISCOUS FLOW;

EID: 0030822016     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869301     Document Type: Article

References (13)

1. H. J. S. Hele-Shaw, "On the motion of a viscous fluid between two parallel plates," Nature 58, 34 (1898).
2. H. Darcy, Les Fontaines Publiques de la Ville de Dijon: Distribution d'eau et Filtrage des Eaux (Victor Dalmont, Paris, 1856).
3. P. Saffman and G. I. Taylor, "The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid," Proc. R. Soc. London 39, 65 (1958); D. Bensimon, L. P. Kadanoff, S. Laing, B. I. Shraiman, and C. Tang, "Viscous flows in two dimentions," Rev. Mod. Phys. 58, 977 (1986).
4. P. Saffman and G. I. Taylor, "The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid," Proc. R. Soc. London 39, 65 (1958); D. Bensimon, L. P. Kadanoff, S. Laing, B. I. Shraiman, and C. Tang, "Viscous flows in two dimentions," Rev. Mod. Phys. 58, 977 (1986).
5. M. Zeybek and Y. C. Yortsos, "Parallel flow in Hele-Shaw cells," J. Fluid Mech. 241, 421 (1992).
6. P. Gondret and M. Rabaud, "Gas-liquid shear instability in a Hele-Shaw cell," Communication at the Euromech Colloquium on "Interfacial Instabilities, 11-13 September 1996, Palaiseau/Paris, France.
7. Y. P. Tang, and D. M. Himmelblau, "Velocity distribution for isothermal two-phase co-current laminar flow in a horizontal rectangular duct," Chem. Eng. Sci. 18, 143 (1963); A. Nadim, A. Borhan, and H. Haj-Hariri, "Tangential stress and Maragoni effects at a fluid-fluid interface in a Heel-Shaw cell," J. Colloid Interface Sci. 181, 159 (1996).
8. Y. P. Tang, and D. M. Himmelblau, "Velocity distribution for isothermal two-phase co-current laminar flow in a horizontal rectangular duct," Chem. Eng. Sci. 18, 143 (1963); A. Nadim, A. Borhan, and H. Haj-Hariri, "Tangential stress and Maragoni effects at a fluid-fluid interface in a Heel-Shaw cell," J. Colloid Interface Sci. 181, 159 (1996).
9. n[4/(2n-1)π]cos((2n-1)π(y/e)) is equal to 1 in the interval - e/2≤y≤e/2.
10. 2 in the interval -e/2≤y≤e/2.
11. P. L. Bhatnagar, E. P. Gross, and M. Krook, "A model for collision processes in gases: I. Small amplitude processes in charged and neutral one-component systems," Phys. Rev. 94, 511 (1954).
12. Y. H. Qian, D. d'Humières, and P. Lallemand, "Lattice BGK models for Navier - Stokes equation," Europhys. Lett. 17, 479 (1992).
13. N. Rakotomalala, D. Salin, and P. Watzky, "Simulations of viscous flows of complex fluids with a Bhamagar - Gross - Krook lattice gas," Phys. Fluids 8, 3200 (1996).