Gutenberg-Richter's law in sliding friction of gels

We report on experimental studies of spatio-temporally heterogeneous stick-slip motions in the sliding friction between a hard polymethyl methacrylate (PMMA, plexiglass) block and a soft poly-dimethyl siloxane (PDMS, silicone) gel plate. We perform experiments on two PDMS gels with different viscoelastic properties. For the less viscous gel, large and rapid events are preceded by an alternation of active and less active periods. For the more viscous gel, successive slow slip events take place continuously. The probability distributions of the force drop, a quantity analogous to seismic moment, obey a power law similar to Gutenberg-Richter's empirical law for the frequency-size statistics of earthquakes, and the exponents of the power law vary with the plate velocity and the viscosity of the gel. We propose a simple model to explain the dependence of the power law exponent on the plate velocity, which agrees with experimental results.