Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally und er strongly nonequilibrium conditions. By injecting an electrical current i nto a suspension of conducting nanoparticles we are able to initiate a proc ess of self-organization which leads, in certain cases, to formation of a s table pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such a system is a complex proces s. It starts as an avalanche process characterized by nucleation, growth, a nd thermal destruction of such dissipative elements as continuous conductin g chains of particles as well as electroconvective vortices. A power-law di stribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of c onducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum p ower condition and also shows a power-law distribution of the avalanche siz es.