Rotational Waves in an Oscillatory Electrochemical System

The existence of waves in distributed systems has been observed in chemical systems mainly through reaction-diffusion methods and such waves can be rotational when performed on a ring-shaped surface. In such ring systems, phase model analysis predicts several waves may co-rotate in an even distribution over the ring.

In this contribution, an experimental setup composed of twenty nickel electrodes undergoing electrodissolution is constructed to investigate rotational waves. The electrodes are positioned into the ring topology by coupling. Only complete synchrony is attained when coupled. In order to arrive at a rotational state, the temporary application of topology alterations and global feedback is required.

Four rotational solutions are found, distinguished by the rotational velocity and the number of waves in each rotation. The rotational velocity is defined as ν₀/m where ν₀ is a base velocity of all rotations and m is the integer winding number which is equal to the number of waves in the rotation.  The non-rotational solution, m=0, is characterized by complete synchronization while the rotational solutions are winding numbers m=1,2,3,4 where a specific winding number is achieved by the application of appropriate topological tuning. Any further increase in winding number is shown to not be stable without external assistance. The results indicate rotational waves, predicted by phase model approximations, can be realized by the application of the experimental method.