A specific feature of pattern formation in electrochemical systems is the occurrence of accelerated fronts; they can be attributed to long-range spatial coupling. In this paper we demonstrate that different coupling functions can be realized by tuning easily accessible parameters: The range of the coupling crucially depends on the length scales of the system, and the strength of the coupling is proportional to the conductivity of the electrolyte. Simulations in the bistable regime are presented which illustrate how the front behavior changes qualitatively when length scales or conductivity are varied. ͓S1063-651X͑97͒12702-7͔PACS number͑s͒: 64.10.ϩh, 82.20.Mj, 82.45.ϩz, 47.54.ϩr SYSTEM AND MODELElectrochemical reactions take place at the electrodeelectrolyte interface, the reaction rate being decisively deter-*Present address:

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The potential distribution in front of a Ag ring electrode during the reduction of peroxodisulfate was measured with potential microprobes. Inhomogeneous stationary potential distributions were observed when using a Haber-Luggin capillary, i.e., placing the reference electrode close to the working electrode on the axis of the ring. It is shown that such an arrangement introduces a negative global coupling into the system which destabilizes homogeneous stationary states if the current-potential characteristics exhibits a negative differential resistance. Further consequences of the negative global coupling are discussed, and the effect of an additional, external series resistor is demonstrated.

Experiments on pattern formation in electrochemical systems show qualitative differences in comparison with phenomena observed with other chemical systems. In this paper we derive a general model from the basic transport equations which takes into account the special aspects of electrochemical systems. Stepwise introduction of three approximations considerably simplifies the equations and demonstrates the dominant role the electric potential plays for pattern formation. The simplest form of the model contains migration as the only transport mechanism, and the importance of intrinsic global coupling for the dynamic behavior of electrochemical systems becomes apparent. This simple model already reproduces the experimentally observed front behavior we recently reported ͓G. Flätgen and K. Krischer, Phys. Rev. E 51, 3997 ͑1995͔͒.