publication . Preprint . 2009

Chemical reactions in the presence of surface modulation and stirring

Kamhawi, Khalid; Náraigh, Lennon Ó;
Open Access English
  • Published: 24 Feb 2009
We study the dynamics of simple reactions where the chemical species are confined on a general, time-modulated surface, and subjected to externally-imposed stirring. The study of these inhomogeneous effects requires a model based on a reaction-advection-diffusion equation, which we derive. We use homogenization methods to show that up to second order in a small scaling parameter, the modulation effects on the concentration field are asymptotically equivalent for systems with or without stirring. This justifies our consideration of the simpler reaction-diffusion model, where we find that by modulating the substrate, we can modify the reaction rate, the total yiel...
free text keywords: Physics - Fluid Dynamics, Physics - Biological Physics
Related Organizations
Download from
29 references, page 1 of 2

2"cd0 (t) 2 [d (t) c0 + d0 (t) c0] :

[2] J. G. Skellam. Random dispersal in theoretical populations. Biometrika, 38:196, 1951. [OpenAIRE]

[3] J. D. Murray. Mathematical Biology. Springer, Berlin, second edition, 1993.

[4] S. A. Newman and H. L. Frisch. Dynamics of skeletal pattern formation in developing chick limb. Science, 205:4407, 1979. [OpenAIRE]

[5] S. Kondon and R. Asal. A reaction-di usion wave on the skin of the marine angel sh Pomacanthus. Nature, 376:765, 1995.

[6] E. J. Crampin, E. A. Ga ney, and P. K. Maini. Reaction and di usion on growing domains: Scenarios for robust pattern formation. Bull. of Math. Biol, 61:1093, 1999.

[7] J. Gomatam and F. Amdjadi. Reaction-di usion equations on a sphere: Meandering of spiral waves. Phys. Rev. E, 56:3913, 1997.

[8] C. Varea, J. L. Aragon, and R. A. Barrio. Turing patterns on a sphere. Phys. Rev. E, 60:4588, 1999.

[9] M. A. J. Chaplain, M. Ganesh, and I. G. Graham. Spatio-temporal pattern formation on spherical surfaces: Numerical simulation and application to tumour growth. J. Math. Biol., 42:387, 2001.

[10] R. G. Plaza, F. Sanchez-Garduno, P. Padilla, R. A. Barrio, and P. K. Maini. The e ect of growth and curvature on pattern formation. Journal of dynamics and di erential equations, 16:1093, 2004.

[11] J. Gjorgjieva and J. Jacobsen. Turing patterns on growing spheres: The exponential case. Journal of Discrete and Continuous Dynamical Systems, Supplement:436, 2007.

[12] R. Aris. Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Prentice-Hall, New Jersey, 1962.

[13] Z. Neufeld. Excitable media in a chaotic ow. Phys. Rev. Lett., 87:108301, 2001. [OpenAIRE]

[14] Z. Neufeld, C. Lopez, and P. H. Haynes. Smooth- lamental transition of active tracer elds stirred by chaotic advection. Phys. Rev. Lett., 82:2606, 1999.

[15] S. N. Menon and G. A. Gottwald. On bifurcations in reaction-di usion systems in chaotic ows. Phys. Rev. E, 71:066201, 2005.

29 references, page 1 of 2
Any information missing or wrong?Report an Issue