We derive a new criterion for transversal instability of planar fronts in packed bed reactors (PBR's) in which nth order or Langmuir-Hinshelwood kinetics reaction occurs using a pseudo-homogeneous two-variables (C,T)-model. The derivation follows the analysis of combustion of reaction-diffusion systems by Sivashinsky, Comb. Sci. Tech. 15 (1977). The new criterion is expressed as a complicated relation of the ratio of the heat to mass dispersivities on the kinetic parameters. A necessary (but not sufficient) condition for emerging patterns in the reactor cross-section for the kinetic models studied is that (δTad/δTm)/(PeC/PeT)>1, where δTad and δTm are the adiabatic and the maximal temperature rise, respectively, PeC and PeT are the mass and the heat Peclet numbers, respectively. This condition agrees with our previous results that were limited to first order kinetics and is unlikely to be satisfied in PBR's. Also, unlike the previous condition, the new criterion allows to determine the critical wave number (minimal reactor radius) that can exhibit transversal patterns. The new criterion is verified by comparison with the linear stability results and with 3-D simulations.
- Bifurcation criterion
- Mathematical modeling and simulations
- Nonlinear dynamics
- Packed bed
- Transversal patterns