Stationary spatially complex solutions in cross‐flow reactors with two reactions

Formation of stationary spatially multiperiodic or even chaotic patterns is analyzed for a simple model of a cross-flow reactor with two consecutive reactions and realistically high Le and Pe. Spatial patterns emerge much like dynamic temporal patterns in a mixed system of the same kinetics. The sequence of period doubling bifurcations is determined for the corresponding ODE system and is completely confirmed by direct numerical simulations of the full PDE model. The incorporation of a slow nondiffusing inhibitor led to chaotic spatiotemporal patterns.

[1]  Sergey P. Kuznetsov,et al.  Absolute and convective instabilities in a one-dimensional Brusselator flow model , 1997 .

[2]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[3]  Modelling flow-distributed oscillations in the CDIMA reaction , 2000 .

[4]  M. Sheintuch,et al.  Excitable waves and spatiotemporal patterns in a fixed‐bed reactor , 1994 .

[5]  S. Shvartsman,et al.  Spatiotemporal patterns in catalytic reactors , 1996 .

[6]  Moshe Sheintuch,et al.  Spatiotemporal patterns in thermokinetic models of cross‐flow reactors , 2000 .

[7]  Philip K. Maini,et al.  Parameter space analysis, pattern sensitivity and model comparison for Turning and stationary flow-distributed waves (FDS) , 2001 .

[8]  V. Hlavácek,et al.  A Revision of multiplicity and parametric sensitivity concepts in nonisothermal nonadiabatic packed bed chemical reactors , 1981 .

[9]  Differential flow instability of the exothermic standard reaction in a tubular cross-flow reactor , 1994 .

[10]  Rovinsky,et al.  Chemical instability induced by a differential flow. , 1992, Physical review letters.

[11]  Moshe Sheintuch,et al.  Pattern formation in homogeneous reactor models , 1999 .

[12]  Menzinger,et al.  Non-turing stationary patterns in flow-distributed oscillators with general diffusion and flow rates , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  E Mosekilde,et al.  Stationary space-periodic structures with equal diffusion coefficients. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Spatiotemporal patterns in models of cross-flow reactors. Regular and oscillatory kinetics , 2001 .

[15]  Achim Kienle,et al.  State profile estimation of an autothermal periodic fixed-bed reactor , 1998 .

[16]  A. Merzhanov,et al.  Physics of reaction waves , 1999 .

[17]  M. Sheintuch,et al.  Pattern formation in homogeneous and heterogeneous reactor models , 1999 .

[18]  Arvind Varma,et al.  Dynamics of consecutive reactions in a CSTR—a case study , 1987 .

[19]  Moshe Sheintuch,et al.  Spatially "chaotic" solutions in reaction-convection models and their bifurcations to moving waves. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  M. Abashar,et al.  Existence of complex attractors in fluidized bed catalytic reactors , 1997 .

[21]  D. T. Lynch,et al.  Chaotic behavior of reaction systems: mixed cubic and quadratic autocatalysis , 1992 .

[22]  R. Aris,et al.  More on the dynamics of a stirred tank with consecutive reactions , 1983 .

[23]  G. I. Barenblatt,et al.  Theorv of flame propagation , 1959 .

[24]  David G. Retzloff,et al.  THE DYNAMIC BEHAVIOR AND CHAOS FOR TWO PARALLEL REACTIONS IN A CONTINUOUS STIRRED TANK REACTOR , 1987 .

[25]  E. Doedel,et al.  Numerical computation of periodic solution branches and oscillatory dynamics of the stirred tank reactor with A → B → C reactions , 1983 .

[26]  Marek Berezowski,et al.  Dynamics of heat-integrated pseudohomogeneous tubular reactors with axial dispersion , 2000 .