Ruelle–Takens–Newhouse scenario in reaction-diffusion-convection system

Abstract

Direct numerical simulations of the transition process from periodic to chaotic dynamics are presented for two variable Oregonator-diffusion model coupled with convection. Numerical solutions to the corresponding reaction-diffusion-convection system of equations show that natural convection can change in a qualitative way, the evolution of concentration distribution, as compared with convectionless conditions. The numerical experiments reveal distinct bifurcations as the Grashof number is increased. A transition to chaos similar to Ruelle- Takens The process by which a laminar viscous flow undergoes transition to turbulence is a topic of notable fluid-dynamical interest. Experiments 1 and numerical simulations 2 of closed system flows like Rayleigh-Bernard convection 3-5 have pointed out how the evolution to turbulence follows a specific route and well-definite sequence of transition on the basis of flow features. 6 In particular it was observed 7 that transitions to chaos in self-sustained oscillatory flows are consistent with the well-known Ruelle-Takens-Newhouse ͑RTN͒ scenario. 8 The onset of convection in self-sustained oscillating chemical reactions such as the BelousovZhabotinsky ͑BZ͒ reaction 9 had been extensively studied 10,11 proving an effective coupling between kinetic and hydrodynamic of the system. On the other hand, it was shown 12,13 how autocatalytic systems exhibit aperiodic and chaotic dynamics by the coupling of reaction kinetics to transport phenomena. This coupling is expected in particular for the BZ reaction in closed unstirred reactors 14,15 by the strict experimental dependence in the onset of chaos on ͑i͒ the percent in volume of initial reactants concentrations, 16 ͑ii͒ the system viscosity, 17 ͑iii͒ the temperature, 18 and ͑iv͒ the reactor geometry. 19 A suitable choice of starting values for these parameters results in a RTN transition to chaos when the system is far from equilibrium and the inverse RTN scenario as the reaction drifts to the ultimate state. 20 Taking into account the combination of the parameters controlling the fluid dynamics and the chemistry of the system would be useful to understand the instabilities occurring in the BZ reaction in a close unstirred reactor. The model used to simulate the system is a two-dimensional vertical slab which had been demonstrated to be a good approximation to the three-dimensional problem. 10 A set of reactiondiffusion-convection partial derivative equations is solved by means of numerical integration over a suitable grid. This model allows one to focus on the contribution of convection and to neglect the consumption of reactants. Chemical kinetics is formulated using the well-known two-variables Oregonator model [21][22][23] proposed for the first time by Fields-Köros-Noyes. They defined two nonlinear coupled differential equations,where c 1 and c 2 are, respectively, the nondimensional concentrations of the intermediate species HBrO 2 and Ce 4+ derived by the dimensional ones C 1 and C 2 as follows:A , B being the starting reactant...

Water: A medium where dissipative structures are produced by a coherent dynamics

“…In order to mimic the biological complexity of a cell environment, the Siena Ecodynamics group studied the BZ-oscillator in the aqueous compartment of different phospholipid/water lamellar phases (Magnani et al, 2004;Marchettini et al, 2006;Biosa et al, 2005;Ristori et al, 2007;Budroni et al, 2008).…”

Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers

“…In closed horizontal solution layers (no surface open to air), convection triggered by the density jump across a propagating front has been shown both experimentally [30][31][32][33][34] and numerically [35][36][37][38][39][40][41] to deform and to speed up this front in isothermal conditions. When the reaction is exothermic, the combination of solutal and thermal density changes comes into play and has been noted to affect for instance the propagation of polymerization fronts in horizontal layers 42,43 and to result in new dynamical behaviors for the case of chemical fronts of the chlorite-tetrathionate (CT) reaction [44][45][46] and of the IAA reaction.…”

Dynamics due to combined buoyancy- and Marangoni-driven convective flows around autocatalytic fronts

“…In past years many efforts have been devoted towards understanding how the mutual interaction between kinetics and convective transport phenomena enhances complex behaviours. The influence of bulk and surface flows on the front dynamics has been pointed out in both experimental [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and theoretical works, [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] showing that chemical fronts can be distorted, accelerated or even broken by the hydrodynamic feedback. The reaction-diffusion-convection coupling has proved to be also responsible for order-disorder transitions in chemical oscillators, where it controls the route from periodic regimes to spatiotemporal chaos.…”