Linear stability of two immiscible liquids driven by a constant pressure gradient through a long vertical annulus in the gravitational field is investigated. If viscosity depends on temperature, it is found that thermal conductivity stratification can induce an interfacial instability, which is different from the instability identified by Yih (1986). The effect of temperature-dependent viscosity on various unstable modes and mode competitions are studied.
Issue Section:
Natural and Mixed Convection
1.
Preziosi
, L.
, Chen
, K.
, and Joseph
, D. D.
, 1989
, “Lubricated Pipelining: Stability of Core-Annular Flow
,” J. Fluid Mech.
, 201
, pp. 323
–356
.2.
Charles
, M. E.
, Govier
, G. W.
, and Hodgson
, G. W.
, 1961
, “The Horizontal Pipeline Flow of Equal Density Oil-Water Mixtures
,” Can. J. Chem. Eng.
, 39
, pp. 27
–36
.3.
Chen
, K.
, Bai
, R.
, and Joseph
, D. D.
, 1990
, “Lubricated Pipelining. Part 3 Stability of Core-Annular Flow in Vertical Pipes
,” J. Fluid Mech.
, 214
, pp. 251
–286
.4.
Chen
, K.
, and Zhang
, Y.
, 1993
, “Stability of the Interface in Co-Extrusion Flow of Two Viscoelastic Fluids through a Pipe
,” J. Fluid Mech.
, 247
, pp. 489
–502
.5.
Joseph, D. D., and Renardy, Y., 1992, Fundamentals of Two-Fluid Dynamics I, II, Springer-Verlag, New York.
6.
Chen
, K.
, 1995
, “Interfacial Instabilities in Stratified Shear Flows Involving Multiple Viscous and Viscoelastic Fluids
,” Appl. Mech. Rev.
, 48
, pp. 763
–776
.7.
Yih
, C. S.
, 1986
, “Instability Resulting from Stratification in Thermal Conductivity
,” Phys. Fluids
, 29
, pp. 1769
–1773
.8.
Pinarbasi
, A.
, and Liakopoulos
, A.
, 1995
, “The Effect of Variable Viscosity on the Interfacial Stability of Two-Layer Poiseuille Flow
,” Phys. Fluids
, 7
, pp. 1318
–1324
.9.
Chang, K.-T., 1998, “Linear Stability Theory of Mixed Convection Flow for Two Immiscible Fluids in a Vertical Annulus,” Ph.D. dissertation, Arizona State University, Tempe, AZ.
10.
Arnoldi
, W. E.
, 1951
, “The Principle of Minimized Iterations in the Solution of the Matrix Eigenvalue Problem
,” Quarterly Appl. Math.
, 214
, pp. 17
–29
.11.
Huang, A., 1993, private communication.
12.
Yao
, L. S.
, and Rogers
, B. B.
, 1989
, “The Linear Stability of Mixed Convection in a Vertical Annulus
,” J. Fluid Mech.
, 201
, pp. 279
–298
.13.
Smith
, M. K.
, 1995
, “The Long-Wave Interfacial Instability of Two Liquid Layers Stratified by Thermal Conductivity in an Inclined Channel
,” Phys. Fluids
, 7
, pp. 3000
–3012
.14.
Incropera, F. P., and DeWitt, D. P., 1985, Introduction to Heat Transfer, John Wiley & Sons, New York.
15.
Vargaftik, N. B., 1975, Tables on the Thermophysical Physical Properties of Liquids and Gases, 2nd ed., Hemisphere, Washington, D.C.
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