Abstract
The effects of applying a constant electric field E to an ionic autocatalytic reaction with a general power p (p≥1) are discussed through a consideration of the equations for the corresponding travelling waves. It is shown that, when the ratio of diffusion coefficients D of autocatalyst and substrate is less than some value D0 (which depends on p), the effect of a negative electric field is to increase the wave speed of the reaction front over its field-free value. This is in contrast to previous results for cubic autocatalysis (p=2) [J.H. Merkin and H. Ševčíková. J. Math. Chem. 25 (1999) 111.] for D>D0, where the effect is to decrease the wave speed. This feature, seen in the numerical solutions of the travelling wave equations, is confirmed by an expansion for small E and in an asymptotic analysis for p large
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References
D. Šnita H. Ševčíková M. Marek J.H. Merkin (1997) Proc. R Soc. Lond A453 2325
J.H. Merkin H. Ševčíková D. Šnita M. Marek (1998) IMA Jl. Appl. Math 60 1 Occurrence Handle10.1093/imamat/60.1.1
D. Šnita J. Lindner M. Marek J.H. Merkin (1998) Math Comput. Model 27 1
L. Forštova H. Ševčíková M. Marek J.H. Merkin (2000) Chem. Eng. Sci 55 233 Occurrence Handle10.1016/S0009-2509(99)00319-X
J.H. Merkin H. Ševčíková D. Šnita (2000) IMA Jl Applied Math 64 157 Occurrence Handle10.1093/imamat/64.2.157
S.C. Smith D.J. Needham J.A. Leach (2005) Quart J. Mech Appl. Math 58 17 Occurrence Handle10.1093/qjmamj/hbh012
J.H. Merkin D.J. Needham Z. angew (1993) Math. Phys. (ZAMP) 44 707 Occurrence Handle10.1007/BF00948484
Leach J.A., Needham D.J. Matched Asymptotic Expansions in Reaction–Diffusion Theory (Springer Monographs in Mathematics, 2003)
J.H. Merkin H. Ševčíková (2005) IMA Jl. Appl. Math 70 527 Occurrence Handle10.1093/imamat/hxh045
Needham D.J., Leach J.A., Merkin J.H. To appear in Quart. J. Mech. Appl. Math
J.H. Merkin H. Ševčíková (1999) J. Math. Chem 25 111 Occurrence Handle10.1023/A:1019124231138
D. Šnita M. Marek (1994) Physica D 75 521 Occurrence Handle10.1016/0167-2789(94)00100-6
N.J. Balmforth R.V. Craster S.J.A. Malham (1999) Proc. R. Soc. Lond A455 1401
Miller R.K., Michel A.N., Ordinary Differential Equations (Academic Press, 1982)
M.J. Metcalf J.H. Merkin S.K. Scott (1994) Proc. R. Soc. Lond A447 155
Merkin J.H., Kiss I.Z. Dispersion curves in the diffusional instability of reaction fronts. To appear in Phys. Rev. E
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Merkin, J.H. The Effect of an Electric Field on Reaction Fronts in Autocatalytic Systems. J Math Chem 38, 657–670 (2005). https://doi.org/10.1007/s10910-005-6916-0
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DOI: https://doi.org/10.1007/s10910-005-6916-0