Onset of convection for autocatalytic reaction fronts: Laterally bounded systems

Abstract

Linear hydrodynamics yields the onset of convection for ascending autocatalytic reaction fronts in laterally bounded geometries. The system is studied in the limit of infinite and zero thermal diffusivity. For convection in a vertical slab of thickness a or a long vertical cylinder of radius a, the appropriate dimensionless driving parameter scrS=\ensuremath{\delta}${\mathit{ga}}^{3}$/\ensuremath{\nu}${\mathit{D}}_{\mathit{c}}$ involves the fractional density difference \ensuremath{\delta} between the unreacted and reacted fluids, the acceleration of gravity g, the kinematic viscosity \ensuremath{\nu}, and the catalyst molecular diffusivity ${\mathit{D}}_{\mathit{c}}$. Calculated critical values ${\mathit{scrS}}_{\mathit{c}}$ for onset of convection agree with recent experiments on iodate--arsenous acid systems. We also show that, compared with the unbounded system, the sidewalls tend to suppress convection.