Controlled pattern formation in the CDIMA reaction with a moving boundary of illumination

Abstract

A reaction–diffusion (RD) system that grows axially as one of its boundaries moves is equivalent to a boundary-forced open flow in which all species have identical flow coefficients. Depending on the flow or growth rate, ϕ, and on the intrinsic spreading velocity, c₀, of the RD structure, such systems are either absolutely (ϕ < c₀) or convectively (ϕ > c₀) unstable. We previously showed how periodic boundary forcing of an axially growing domain could be used to control the formation of space-periodic structures in biological morphogenesis. This paper proposes, as a chemical equivalent of an axially growing embryo, the design of a continuously fed unstirred flow reactor (CFUR), characterized by a photo-chemically controlled moving boundary. Using the Turing-unstable CDIMA system as an example, we illustrate by simulations the kinds of wave structures that are expected to arise in the absolutely and convectively unstable regimes when boundary forcing is either constant or time-periodic.