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We study chemical pattern formation in a fluid between two flat plates andthe effect of such patterns on the formation of convective cells. Thispatterning is made possible by assuming the plates are chemically reactive orrelease reagents into the fluid, both of which we model as chemical fluxes. Weview this as a specific example of boundary-bound reactions. In the absence ofcoupling with flow, we show that the two-reagent system with nonlinearreactions admits instabilities equivalent to diffusion-driven Turinginstabilities. In the other extreme, when chemical fluxes at the two boundingplates are constant, diffusion-driven instabilities do not occur buthydrodynamic phenomena analogous to Rayleigh-Benard convection are possible.Assuming we can influence the chemical fluxes along the domain and selectsuitable reaction systems, this presents a means for the control of chemicaland hydrodynamic instabilities and pattern formation. We study a generic classof models and find conditions for a bifurcation to pattern formation.Afterwards, we present two examples derived from the Schnakenberg reaction.Unlike the classical Rayleigh-Benard instability, which requires a sufficientlylarge unstable density gradient, a chemo-hydrodynamic instability based onTuring-style pattern formation emerges from a state that is uniform in density.We also find parameters that result in the formation of convective cellswhether gravity acts upwards or downwards relative to the reactive plate. Thewavenumber of the cells and the direction of the flow at regions of high/lowconcentration depend on the orientation, hence, different patterns can beelicited by simply inverting the device. More generally, our results suggestmethods for controlling pattern formation and convection by tuning reactionparameters. As a consequence, we can drive and alter fluid flow in a chamberwithout mechanical pumps.

Boundary-Bound Reactions: Pattern Formation with and without Hydrodynamics