Effect of inertia on the Marangoni instability of two-layer channel flow, Part I: Numerical simulations

Journal of Engineering Mathematics

Volumn 50, Issue 2-3, 2004, Pages 311-327

  Pozrikidis, C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Channel flow; Immersed interface method; Liquid films; Marangoni instability; Surfactants

Indexed keywords

APPROXIMATION ALGORITHMS; BOUNDARY ELEMENT METHOD; CHANNEL FLOW; FINITE DIFFERENCE METHOD; FINITE VOLUME METHOD; INTERFACES (MATERIALS); LINEAR STABILITY ANALYSIS; LIQUID FILMS; NAVIER STOKES EQUATIONS; NUMERICAL MODELS; SAILING VESSELS; STABILITY; SURFACE ACTIVE AGENTS;

DIFFUSE INTERFACE APPROXIMATION; IMMERSED INTERFACE METHOD; INSOLUBLE SURFACTANTS; INTERFACIAL TRACTION; MARANGONI INSTABILITIES; STEP DISCONTINUITY; SURFACTANT TRANSPORT EQUATIONS; TWO DIMENSIONAL CHANNELS;

NUMERICAL METHODS;

EID: 32044474076     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-004-3690-0     Document Type: Article

References (24)

1. C. Pozrikidis, Instability of multi-layer channel and film flows. Adv. Appl. Mech. 40 (2004) In press.
2. C.S. Yih, Instability due to viscosity stratification. J. Fluid Mech. 27 (1967) 337-352.
3. A.L. Frenkel and D. Halpern, Stokes-flow instability due to interfacial surfactant. Phys. Fluids 14 (2002) 45-48.
4. D. Halpern and A.L. Frenkel, Destabilization of a creeping flow by interfacial surfactant: linear theory extended to all wavenumbers. J. Fluid Mech. 485 (2003) 191-220.
5. M. Blyth and C. Pozrikidis, Effect of surfactants on the stability of two-layer channel flow. J. Fluid Mech. 505 (2004) 59-86.
6. M.G. Blyth and C. Pozrikidis, Effect of inertia on the Marangoni instability of two-layer channel flow, Part II: normal-mode analysis. J. Engng. Math. 50 (2004) 329-341.
7. C. Pozrikidis, Instability of two-layer creeping flow in a channel with parallel-sided walls. J. Fluid Mech. 351 (1997) 139-165.
8. C. Pozrikidis, Gravity-driven creeping flow of two adjacent layers or superimposed films through a channel and down a plane wall. J. Fluid Mech. 371 (1998) 345-376.
9. A.V. Coward, Y.Y. Renardy, M. Renardy and J.R. Richards, Temporal evolution of periodic disturbances in two-layer Couette flow. J. Comp. Phys. 132 (1997) 346-361.
10. J. Li, Y.Y. Renardy and M. Renardy, A numerical study of periodic disturbances in two-layer Couette flow. Phys. Fluids 10 (1998) 3056-3071.
11. R.R. Yiu and K.P. Chen, Numerical experiments on disturbed two-layer flows in a channel. In: Y. Renardy, A.V. Coward, D. Papageorgiou and S.M. Sun (eds.), Advances in Multi-Fluid Flows. Philadelphia: SIAM (1996) pp. 368-382.
12. S. Zaleski, J. Li, R. Scardovelli and G. Zanetti, Direct simulation of multiphase flows with density variations. In: L. Fulachier, J.L. Lumley, and F. Anselmet (eds.), IUTAM Symposium on Variable Density Low Speed Turbulent Flows. Proc. IUTAM Symposium, Marseille, France, 1996. Dordrecht: Kluwer (1997).
13. P. Yecko and S. Zaleski, Two-phase shear instability: waves, fingers, and drops. Ann. NY Acad. Sci. 898 (2000) 127-143.
14. G. Tryggvason and S.O. Unverdi, The shear breakup of an immiscible fluid interface. In: W. Shyy and R. Narayanan (eds.), Fluid Dynamics at Interfaces. New York: Cambridge University Press (1999) pp. 142-155.
15. J. Zhang, M.J. Miksis, S.G. Bankoff and G. Tryggvason, Non-linear dynamics of an interface in an inclined channel. Phys. Fluids 14 (2002) 1877-1885.
16. C.S. Peskin, The immersed boundary method. Acta Numer. 11 (2002) 479-517.
17. K. Sheth, and C. Pozrikidis, Effects of inertia on the deformation of liquid drops in simple shear flow. Comput. Fluids 24 (1995) 101-119.
18. C. Pozrikidis, Introduction to Theoretical and Computational Fluid Dynamics. New York: Oxford University Press (1997) 675 pp.
19. X. Li and C. Pozrikidis, The effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow. J. Fluid Mech. 341 (1997) 165-194.
20. S. Yon and C. Pozrikidis, A finite-volume/boundary-element method for flow past interfaces in the presence of surfactants, with application to shear flow past a viscous drop. Comput. Fluids 27 (1998) 879-902.
21. A.W. Adamson, Physical Chemistry of Surfaces. 5th edn., New York: Wiley (1990) 777 pp.
22. C. Pozrikidis, Numerical Computation in Science and Engineering. New York: Oxford Univ. Press (1998) 627 pp.
23. C. Pozrikidis, On the relationship between the pressure and the projection function for the numerical computation of incompressible flow. Euro. J. Mech. B/Fluids 22 (2003) 105-121.
24. C.S. Peskin, Numerical analysis of blood flow in the heart. J. Comp. Phys. 25 (1977) 220-252.