AMATH Grad Students
Aiden Huffman | University of Waterloo
Boundary-Bound Reactions: Pattern Formation with and Without Flow
We consider chemical reactions occurring along the boundary of a simple domain and use this to investigate how chemical pattern formation can influence the formation of convective cells. When non-linear chemical reactions occur at or near the boundary, the Turing instability makes chemical pattern formation possible. Moreover, when there are chemical fluxes along the boundary of a domain, they can produce density gradients, which result in the formation of convective cells through a solutal Ryaleigh-Benard instability. To understand how these two behaviours can complement each other, we first look at general reactions involving two general chemical reagents and when pattern formation occurs in a subset of such systems. Afterwards, we present numerical results for two specific examples derived from the Schnakenberg-Selkov reaction system. Our results demonstrate that buoyancy-driven instabilities can occur even in the absence of density variations in the steady state. We also find parameter combinations that result in the formation of convective cells, whether gravity acts upwards or downwards relative to the reactive plate. The wavenumber of the cells and the direction of the flow at regions of high/low concentration depend on the orientation; hence, different patterns can be elicited by simply inverting the device. More generally, our results suggest methods for controlling pattern formation and convection by tuning reaction parameters. Consequently, we can drive and alter fluid flow in a chamber without mechanical pumps by influencing the chemical instabilities.