Chemical convection in the methylene-blue-glucose system: Optimal perturbations and three-dimensional simulations

A case of convection driven by chemical reactions is studied by linear stability theory and direct numerical simulations. In a plane aqueous layer of glucose, the methylene-blue-enabled catalytic oxidation of glucose produces heavier gluconic acid. As the oxygen is supplied through the top surface, the production of gluconic acid leads to an overturning instability. Our results complement earlier experimental and numerical work by Pons et al. First, we extend the model by including the top air layer with diffusive transport and Henry's law for the oxygen concentration at the interface to provide a more realistic oxygen boundary condition. Second, a linear stability analysis of the diffusive basic state in the layers is performed using an optimal perturbation approach. This method is appropriate for the unsteady basic state and determines the onset time of convection and the associated wavelength. Third, the nonlinear evolution is studied by the use of three-dimensional numerical simulations. Three typical parameters sets are explored in detail showing significant differences in pattern formation. One parameter set for which the flow is dominated by viscous forces, displays persistently growing convection cells. The other set with increased reaction rate displays a different flow regime marked by local chaotic plume emission. The simulated patterns are then compared to experimental observations.