• DOI:10.1103/PhysRevE.100.031104
• Corpus ID: 174799243

A spatial analog of the Ruelle-Takens-Newhouse scenario developing in reactive miscible fluids

@inproceedings{Bratsun2019ASA,
  title={A spatial analog of the Ruelle-Takens-Newhouse scenario developing in reactive miscible fluids},
  author={Dmitry A. Bratsun},
  year={2019}
}

• D. Bratsun
• Published 5 June 2019
• Physics

We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction A + B → S in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent diffusion of species coupled with a frontal neutralization reaction can produce a multi-layer system where low density depleted zones could be embedded between the denser layers. This leads to the excitation of chemoconvective modes spatially separated from each other by a motionless fluid. In this paper, we show that the layers can interact via a diffusion mechanism. Since diffusively-coupled instabilities initially have different wavelengths, this causes a long-wave modulation of one pattern by another. We have developed a mathematical model which includes a system of reaction-diffusion-convection equations. The linear stability of a transient base state is studied by calculating the growth rate of the Lyapunov exponent for each unstable layer. Numerical simulations supported by the phase portrait reconstruction and Fourier spectra calculation have revealed that nonlinear dynamics consistently passes through (i) a perfect spatially periodic system of chemoconvecar X iv :1 90 6. 02 05 0v 1 [ ph ys ic s. fl udy n] 5 J un 2 01 9 tive cells; (ii) a quasi-periodic system of the same cells; (iii) a disordered fingering structure. We show that in this system, the coordinate co-directed to the reaction front paradoxically plays the role of time, time itself acts as a bifurcation parameter, and a complete spatial analog of the Ruelle-Takens-Newhouse scenario of the chaos onset is observed. In recent decades, the study of the interaction between reaction-diffusion phenomena and convective instabilities brought many surprises. Let us focus on a neutralization reaction: a second-order A + B → C reaction is distinguished by a comparatively simple, albeit nonlinear, kinetics. If two species are initially separated in space, the reaction proceeds in a frontal manner due to the high value of the reaction rate constant. In this case, it may result in various buoyancy-driven instabilities if the reaction occurs either in immiscible two-layer systems [1, 2, 3, 4, 5] or in miscible acid-base systems [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. Among the important effects that have been observed here, we highlight the pattern convection in the form of a perfectly periodic system of cellular-like fingers keeping contact with the interface when an organic solvent containing an acid A is in contact with an aqueous solution of an inorganic base B [3]. At that time, a liquid-liquid interface has been recognized as the main reason for this unusual regularity of salt fingering [2, 5]. However, then a perfectly organized structure of fingers has been observed already in the miscible system, where two aqueous solutions of base and acid have been brought into contact [13, 15]. It was shown that this pattern arises due to the strong dependence of the diffusion coefficients of the initial reactants and the reaction product on their concentrations. The effect of concentration-dependent diffusion (hereinafter CDD) coupled with a fast neutralization reaction has been demonstrated to produce a spatially localized zone with unstable density stratification (figuratively, a density pocket) in a system with inherently stable configuration, when a less dense solution is placed above a more dense one. It should be noted that such an effect creates a new situation in fluid mechanics when the convective modes arise in different parts of the medium and compete on the distance. In this case, the patterns can be coupled by the diffusion of heat or matter which transmit a signal through an interlayer of the motionless fluid. Generally, the CDD effect means a significant expansion of the degrees of freedom for the system to produce various types of instabilities and nonlinear dynamics that do not fit into the traditional classification [14]. For example,