Unpinning of spiral waves by electrical forcing in excitable chemical media

Abstract

We present experimental observations on the electrically forced release of spiral waves pinned to unexcitable circular obstacles in the Belosov-Zhabotinsky reaction. When the applied electric current density reaches the necessary current density J(unpin), the spiral tip is detached and subsequently drifts away from the obstacle. J(unpin) is found to increase with the obstacle diameter d. The growth rate ΔJ(unpin)/Δd is much higher for obstacles larger than the free spiral core compared to that for smaller obstacles. The experimental findings are confirmed by numerical simulations using the Oregonator model. The results imply that it is more difficult to release spiral waves pinned to larger obstacles, especially when the obstacle size exceeds that of the free spiral core.

Influence of excitability on unpinning and termination of spiral waves

“…In the second series of experiments, the release of a pinned spiral wave by electrical forcing is investigated using the same strategy as in [28], which results in a precise critical value of electrical forcing while the aging of the BZ reaction can be minimized. For a given [H 2 SO 4 ], a constant current density J is applied to the medium for an interval of three to five spiral rotations, before it is increased by a step of J = 10 mA cm −2 .…”

“…As in Ref. [28], we set the uniform grid space x = y = 0.025 s.u. and the time step t = 1.9 × 10 −4 t.u., while the size of the system is reduced to 20 × 20 s.u.…”

“…Single spiral waves are initiated in the thin layers of the BZ reaction by a two-layer method as illustrated in [39] for free spiral waves and in [28] for pinned ones. In all experiments, the reactor is placed in a transparent thermostating bath to remove Ohmic heat and to set the temperature at 24 ± 1°C.…”

“…[38]: q = 0.002, f = 1.4, diffusion coefficients D u = 1.0 and D v = 0.6, with the excitability modulated by parameter ε −1 = 20 − 200. As in [15,28], when the electric field is applied, the ionic mobilities M u and M v are set to −1.0 and 2.0, respectively. The simulations are performed using an explicit Euler method with a nine-point approximation of the two-dimensional Laplacian operator and a centered-space approximation of the gradient term.…”

“…It has been demonstrated that such electric-field application causes reorientation and deformation of ring-shaped filaments that are pinned to a pair of unexcitable spheres, before the filaments are detached from these spheres [27]. Our recent investigation [28] on unpinning of spiral waves by electrical forcing revealed that it is more difficult to release spiral waves pinned to larger obstacles, especially when the obstacle size exceeds that of the core of free spiral waves.…”