Linear stability analysis predicts that the onset of convection for an ascending autocatalytic reaction front in a vertical cylinder corresponds to a nonaxisymmetric mode. This mode consists of a single convective roll confined to the region near the reaction front, with fluid rising in half of the cylinder and falling in the other half. Experiments show a flat front below the onset of convection and an axisymmetric front well above the onset of convection. New experiments are called for to closely examine the onset of convection in order to test this prediction.
REFERENCES
1.
T. McManus, “Chemical waves in the iodate-arsenous acid reaction,” Ph.D. thesis, West Virginia University, Chap. 3, 1989.
2.
J. A.
Pojman
, I. R.
Epstein
, T. J.
McManus
, and K.
Showalter
, “Con-vective effects on chemical waves. 2. Simple convection in the iodate-arsenous acid system
,” J. Phys. Chem.
95
, 1299
(1991
).3.
N.
Ganapathisubramanian
and K.
Showalter
, “Relaxation behavior in a bistable chemical system near the critical point and hysterisis limit
,” J. Chem. Phys.
84
, 5427
(1986
).4.
J. A.
Pojman
and I. R.
Epstein
, “Convective effects on chemical waves. 1. Mechanisms and stability criteria
,” J. Phys. Chem.
94
, 4966
(1990
);J. A.
Pojman
, I. P.
Nagy
, and I. R.
Epstein
, “Convective effects on chemical waves. 3. Multicomponent convection in the iron(II)—nitric acid system
,” J. Phys. Chem.
95
, 1306
(1991
).5.
G.
Bazsa
and I. R.
Epstein
, “Traveling waves in the nitric acid-iron(II) reaction
,” J. Phys. Chem.
89
, 3050
(1985
);I.
Nagypal
, G.
Bazsa
, and I. R.
Epstein
, “Gravity-induced anisotropies in chemical waves
,” J. Am. Chem. Soc.
108
, 3635
(1986
).6.
R. J. Field and M. Burger, Oscillations and Traveling Waves in Chemical Systems (Wiley, New York, 1985);
A. T. Winfree, When Time Breaks Down (Princeton U.P., Princeton, NJ, 1987).
7.
A.
Karma
, “Scaling regime of spiral wave propagation in single-diffusive media
,” Phys. Rev. Lett.
66
, 2274
(1991
);8.
W. T.
Tam
, J. A.
Vastano
, H. L.
Swinney
, and W.
Horsthemke
, “Regular and chaotic chemical spatiotemporal patterns
,” Phys. Rev. Lett.
61
, 2163
(1988
).9.
I.
Lengyel
and I. R.
Epstein
, “Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system
,” Science
251
, 650
(1991
).10.
P.
Kolodner
, “Drifting pulses of traveling-wave convection
,” Phys. Rev. Lett.
66
, 1165
(1991
).11.
P. Manneville, Dissipative Structures and Weak Turbulence (Academic, New York, 1990), and references therein.
12.
G. I.
Taylor
, “Diffusion and mass transport in tubes
,” Proc. R. Soc. London Ser. B
67
, 857
(1954
).13.
R. A.
Wooding
, “The stability of a viscous liquid in a vertical tube containing porus material
,” Proc. R. Soc. London Ser. A
252
, 120
(1959
).14.
B. F.
Edwards
, J. W.
Wilder
, and K.
Showalter
, “Onset of convection for autocatalytic reaction fronts: Laterally unbounded systems
,” Phys. Rev. A
43
, 749
(1991
).15.
D. A.
Vasquez
, B. F.
Edwards
, and J. W.
Wilder
, “Onset of convection for autocatalytic reaction fronts: Laterally bounded systems
,” Phys. Rev. A
43
, 6694
(1991
).16.
J. W.
Wilder
, B. F.
Edwards
, and D. A.
Vasquez
, “Finite thermal diffusivity at onset of convection in autocatalytic systems: Continuous fluid density
,” Phys. Rev. A
45
, 2320
(1992
).17.
J. Boussinesq, Théorie Analytique de la Chaleur (Gauthier-Villars, Paris, 1903) Vol., 2;
A.
Oberbeck
, “Uber die Wärmeleitung der Flussigkeiten bei der Berüchsichtingung der Strömungen infolge von Temperaturdifferenzen
,” Ann. Phys. Chem. (Leipzig)
7
, 271
(1879
);A.
Oberbeck
, “Uber die Bewegungsercheinungen der Atmosphere
,” Sitz. Ber. K. Preuss. Akad. Miss.
, 383
and
(1888
).18.
S.
Rosenblat
, “Thermal convection in a vertical circular cylinder
,” J. Fluid Mech.
122
, 395
(1982
).19.
J. C. Maxwell, Scientific Papers (Cambridge U.P., Cambridge, England, 1890);
P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge U.P., Cambridge, England, 1981).
20.
G. Z. Gershuni and E. M. Zhukhovitskii, Convective Stability of Incompressible Fluids (Keterpress, Jerusalem, 1976).
This content is only available via PDF.
© 1992 American Institute of Physics.
1992
American Institute of Physics
You do not currently have access to this content.