Chemical and hydrodynamic instabilities produced by enzymatic surface reactions

Chemical oscillations are ubiquitous in nature and have a variety of promising applications. Here, we examine a linear stability of a multicomponent reactive fluid that contains two species, X and Y, which undergo transformations catalyzed by enzymes immobilized at two infinite horizontal plates confining the fluid. The surface reactions with the enzymes provide a negative feedback in the system. The first enzyme, localized on the first plate, promotes production of chemical X, while the second enzyme, immobilized on the second plate, promotes production of chemical Y, which inhibits the production of chemical X. Depending on the reaction rates and densities of the reactants, the monotonic and oscillatory instabilities could occur in the system. The first instability (similar to Rayleigh-Benard case) leads to roll-like convective structures that are periodically distributed along the layer. The second instability produces horizontally uniform temporal oscillations of concentrations of the chemicals X and Y. The findings provide guidance for designing micro-scale chemical reactors with improved functionalities.