On the spatio-temporal dynamics of boundary-forced open reactive flows

This thesis investigates the effect of constant or periodic boundary forcing on the spatio-temporal dynamics of open flows of media whose kinetics can be oscillatory, bistable or excitable. The systems investigated are those where the flow profile is uniform (“plug-flow”) and the flow coefficients are equal. Oscillatory and excitable media are investigated experimentally using the ferroin-catalysed Belousov-Zhabotinsky (BZ) reaction medium. Given appropriate flow conditions, stationary space-periodic structures are observed. I refer to them as “flow-distributed oscillations” (FDO) and “flow-stabilised dissipative structures” in oscillatory and excitable media, respectively.; Periodic forcing of oscillatory media leads to travelling waves. They propagate upstream or downstream with either constant or oscillatory velocity. The constant velocity waves are in quantitative agreement with predictions from spatio-temporal phase dynamics. The oscillatory waves are also phase waves. The effect of periodic forcing on bistable and excitable media or on media having a Hopf or Turing unstable steady state is discussed in the context of persistent, downstream advected space-periodic structures. These waves have velocities that are equal to that of the flow and wavelengths that are equal to the product of the flow velocity and the period of the boundary forcing.; The relevance of open reactive flow to biological morphogenesis is discussed. In many organisms, space-periodic structures are formed sequentially, one after the other, during axial growth of the embryo. Axial growth is shown to be equivalent to an open flow. Relative to the growth/flow boundary, the space-periodic structure has a velocity that is equal to the growth/flow velocity. Recent experiments established the operation of a cell-autonomous oscillator in early vertebrate development and showed that the formation of space-periodic structure is preceded by gene expression waves with an intricate spatio-temporal dynamics. They are mimicked in a chemical flow system, which reproduces four of the principal features of the developmental process. The predictions of an FDO-based model are compared to experimental observations and different kinetic schemes are investigated. This reveals a powerful mechanism of wave pattern formation that captures the essence of the regulation of morphogenesis during early development.