Electrical conductivity of microemulsions : a case of stirred percolation

Overview & Synopsis

The electrical conductivity G of water in oil microemulsions may be described by percolation models [1] : below a critical water concentration Øc, G seems to diverge as (Øc - Ø)- S', while for Ø > Øc G increases as (Ø - Ø c)-T'. This physical situation may be called stirred percolation, referring to the Brownian motion of the medium. The exponents S' and T' are a priori different from the corresponding S and T in the classical situation of frozen percolation. A simple model of stirred percolation accounts fairly well for the measured value of S' = 1.2 ± 0.1 while the accepted value for S is 0.7. The exponent T' (1.4 to 1.6 in our experimental case) is less significant of the difference between stirred and frozen percolation : the values for S' should be about 1.8 and the value accepted for S should be about 1.6.