Propagation of chemical waves across inexcitable gaps

Abstract

The propagation of chemical reaction-diffusion waves across a sequence of gaps is studied experimentally using catalyst-printed membranes. We find that a wave fails to propagate across the entire reaction domain if the width W of a gap is greater than a critical value W cr or if the spacing S between two successive gaps is less than a critical value S cr . For values of W ( W cr and S ) S cr then successful propagation across the entire domain is highly probable, irrespective of the number of gaps. For values of W and S close to the critical values, the probability of failure increases with increasing number of gaps.

Modelling wave propagation across a series of gaps

“…1) agrees well with that observed in experiments: 0.13 mm. 8 The frequency transformation (f n ) of a train of waves crossing a gap can be explained by considering the medium as a periodically forced excitable system 14,20,21 where the diffusing activator perturbs the excitable medium after the gap. There is a shift in the phase of oscillation when the medium is perturbed by an incoming wave.…”

“…In aqueous media D is typically 2 Â 10 À5 cm 2 s À1 but since we are modelling a fixed-catalyst system we assume a reduced diffusion coefficient that was chosen so as to match experimental wave speeds. 8 Therefore the value of D was chosen to be 5 Â 10 À6 cm 2 s À1 . Note, however, that with the scaling applied the dimensionless value of diffusion coefficient is set exactly to unity.…”

“…a region of low or no excitability. [8][9][10] Passage of the wave is thought to involve passive diffusion of an activator species across the gap and a supercritical threshold of activator is required to initiate activity on the other side of the gap. There exists a critical gap width (W cr ) for which waves passing across a larger gap will fail, a phenomenon known as wave block.…”

“…Recent experiments investigated the passage of a wave across a series of gaps in the excitable domain. 8 The excitable domain was constructed by using a DeskJet printer to print the reaction catalyst onto a membrane thereby fixing the catalyst in a defined pattern. This pattern had a fixed-frequency wave source and several lanes of catalyst interrupted by gaps.…”