Transport limited pattern formation in catalytic monoliths

Linear stability analysis of high- and low-dimensional models for describing mixing-limited pattern formation in homogeneous autocatalytic reactors

“…Our results show that for all the three models, the two asymptotes of the neutral stability curve correspond to the two limit points (ignition and extinction points) of the bifurcation diagram. Thus, we may conclude that for the case of homogeneous autocatalysis patterned states may emanate from the unstable middle branch connecting the ignition and extinction points in the S-shaped bifurcation curve as in the case of catalytic reactors [18]. Our neutral stability results indicate that the patterned states may be observed more readily for low values of (inlet feeding ratio of B to A).…”

“…Large Da values imply longer reactors that make axial averaging less accurate. It has been shown for the case of catalytic reactors [18] that non-uniform pattern states emerge from the unstable middle branch of the bifurcation diagram. We shall illustrate with the help of linear stability computations that the same also holds true for the present case.…”

“…Benneker et al [16] indicated that hydrodynamic instabilities observed in packed-bed reactors may disturb the plug-flow character and may lead to hot spots and deactivated catalysts. Balakotaiah and coworkers predicted transverse pattern formation in adiabatic packed bed reactors in which a bimolecular reaction (with Langmuir-Hinshelwood kinetics) occurs [17], and in catalytic monolith reactors in which an exothermic surface reaction occurs [18]. Sheintuch and Nekhamkina [19] analyzed the pattern formation in homogeneous model of a fixed catalytic bed for reactions with oscillatory kinetics.…”

Transport limited pattern formation in catalytic fluid–particle systems

“…(Note also that the reasoning used for Turing patterns applies only when the homogeneous state is stable to homogeneous perturbations.) At the other extreme, the earlier literature on asymmetric steady states (Pismen and Kharkats, 1968;Luss et al, 1972) and our recent work (Dommeti et al, 1999;Balakotaiah et al, 2002) use the intuitive reasoning that stable patterned states must exist (even with constant activity, porosity and physical properties) whenever multiplicity exists at the particle level and the interparticle communication (either direct or through the fluid) is sufficiently weak. What is not clear in the prior literature is how these transport limited patterns bifurcate and gain stability.…”

“…Sheintuch and Nekhamkina (1999a reviewed and compared the spatiotemporal patterns in homogeneous, heterogeneous and detailed models of adiabatic fixed catalytic beds for reactions with oscillatory kinetics. Balakotaiah et al (2002) demonstrated that transport limited patterns form in a catalytic monolith due to slow relative rate of heat and mass communication between the gas and the catalyst surface. Marwaha et al (2004) and Sundarram et al (2005) have shown that global coupling can lead to formation of hot zones on the top of a packed-bed reactor.…”