Instabilities in Upward Propagating Flames

Rakib, Zubayed; Sivashinsky, G. I.

doi:10.1080/00102208708947045

Cited by 42 publications

(16 citation statements)

References 10 publications

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“…The Rayleigh-Taylor instability, caused by a heavier fluid placed on top of a lighter one, appears in a wide variety of physical systems, such as laser ablation [1,2], astrophysics [3], liquid-gas interfaces [4], combustion [5,6], and chemical reaction fronts [7,8]. The fluids involved are usually separated by an interface that contains a stabilizing mechanism, such as surface tension [9] or molecular diffusivity (as in the case of a chemical front) [10].…”

Section: Introductionmentioning

confidence: 99%

Convection in stable and unstable fronts

Elliott

Vasquez

2012

Phys. Rev. E

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Density gradients across a reaction front can lead to convective fluid motion. Stable fronts require a heavier fluid on top of a lighter one to generate convective fluid motion. On the other hand, unstable fronts can be stabilized with an opposing density gradient, where the lighter fluid is on top. In this case, we can have a stable flat front without convection or a steady convective front of a given wavelength near the onset of convection. The fronts are described with the Kuramoto-Sivashinsky equation coupled to hydrodynamics governed by Darcy's law. We obtain a dispersion relation between growth rates and perturbation wave numbers in the presence of a density discontinuity accross the front. We also analyze the effects of this density change in the transition to chaos.

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Section: Introductionmentioning

confidence: 99%

Convection in stable and unstable fronts

Elliott

Vasquez

2012

Phys. Rev. E

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“…As a mathematical model we shall employ the weakly nonlinear flame interface evolution equation similar to that proposed by Rakib and Sivashinsky [18]. In Appendix B, we specify the framework of approximation and carry out the formal derivation of the equation-which appears here for the first time.…”

Section: Introductionmentioning

confidence: 99%

Metastability in a flame front evolution equation

Berestycki

Kamin

Sivashinsky

2001

Interfaces Free Bound.

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A weakly nonlinear parabolic equation pertinent to the flame front dynamics subject to the buoyancy effect, and to a statistical description of biological evolution is considered. In the context of combustion it is shown that the parabolic interface occurring in upward propagating flames in vertical channels may actually be merely quasi-equilibrium transient states which eventually collapse to a stable configuration in which the flame tip slides along the channel wall.

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“…has gotten a lot of attention and interest from both the engineering and the mathematical communities to model several problems including but not limited to the control of turbulent flow [2,9], the excitation of long water waves by a moving pressure distribution [1], the dispersal of a population [32], and the behavior of the flame front interface under physical assumption [29]. Rakib and Sivashinsky [29] derived a nonlinear evolution equation as a model for the flame front interface:…”

Section: Introductionmentioning

confidence: 99%