Abstract
We introduce a reaction-diffusion-convection (RDC) model to study the combined effect of buoyancy- and Marangoni-driven flows around a traveling front. The model allows for a parametric control of the two contributions via the solutal Rayleigh number, Ra c , which rules the buoyancy component and the solutal Marangoni number, Ma c , governing the intensity of the velocity field at the interface between the reacting solution and air. Complex dynamics may arise when the bulk and the surface flows describe an antagonistic interplay. Typically, spatiotemporal oscillations are observed in the parameter region (Ra c <0, Ma c >0).
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- 1.
The equations are scaled by using the time scale of the chemical process \(t_{0} = 1/(ka_{0}^{2})\) and the reaction-diffusion characteristic length \(L_{0} = \sqrt{Dt_{0}}\); D is the diffusivity of the autocatalytic species; k the kinetic rate constant of the reaction; μ is the water dynamic viscosity, which is related to the kinematic viscosity, ν, via ν=μ/ρ 0, where ρ 0 is the water density; the vorticity, ω, and the stream function, ψ, are tied to the velocity field \({\bf v}= (u, v)^{T}\) through the relations \(\omega= \nabla \times{\bf v}\), ψ, u=∂ z ψ and v=−∂ x ψ. In Eqs. (12.1)–(12.4), the Schmidt number, S c =ν/D, gives the balance between momentum and mass diffusion.
- 2.
See footnote 1.
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Budroni, M.A., Rongy, L., De Wit, A. (2013). Comparative Analysis of Buoyancy- and Marangoni-Driven Convective Flows Around Autocatalytic Fronts. In: Gilbert, T., Kirkilionis, M., Nicolis, G. (eds) Proceedings of the European Conference on Complex Systems 2012. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-00395-5_12
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DOI: https://doi.org/10.1007/978-3-319-00395-5_12
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