  We introduce a novel apparatus designed for stress-controlled rheometers to
perform simultaneous rheological and electrical measurements on strongly
conductive complex fluids under shear. By means of a non-toxic liquid metal at
room temperature, the electrical connection to the rotating shaft is completed
with minimal additional mechanical friction, allowing for simultaneous stress
measurements as low as 1 Pa. We use the capabilities of this design to perform
an extensive set of rheo-electric experiments on gels formulated from
attractive carbon black particles, at concentrations ranging from 4 to 15% wt.
First, experiments on gels at rest prepared with different shear history show a
robust power-law scaling between the elastic modulus $G'_0$ and the
conductivity $\sigma_0$ of the gels, i.e. $G'_0 \sim \sigma_0^\alpha$, with
$\alpha =1.65 \pm 0.04$ independently of the gel concentration. Second,
conductivity measurements performed simultaneously with creep experiments
reveal for the first time that plastic events take place in the bulk while the
shear rate decreases as a weak power law of time in the early stage of the
experiment. The subsequent evolution of the conductivity and shear rate allows
us to propose a local yielding scenario that is in agreement with previous
velocimetry measurements. Finally, we determine the constitutive rheological
and electrical behavior of carbon black gels. Corrections first introduced for
mechanical measurements are carefully extended to electrical measurements to
accurately distinguish between bulk and surface contributions to the
conductivity. As an illustrative example, we examine the constitutive
rheo-electric properties of five carbon black gels of different grades, and
demonstrate the relevance of the novel rheo-electric apparatus as a versatile
characterization tool for strongly conductive complex fluids and their
applications.
