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We introduce a novel apparatus designed for stress-controlled rheometers toperform simultaneous rheological and electrical measurements on stronglyconductive complex fluids under shear. By means of a non-toxic liquid metal atroom temperature, the electrical connection to the rotating shaft is completedwith minimal additional mechanical friction, allowing for simultaneous stressmeasurements as low as 1 Pa. We use the capabilities of this design to performan extensive set of rheo-electric experiments on gels formulated fromattractive carbon black particles, at concentrations ranging from 4 to 15% wt.First, experiments on gels at rest prepared with different shear history show arobust power-law scaling between the elastic modulus $G'_0$ and theconductivity $\sigma_0$ 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 experimentsreveal for the first time that plastic events take place in the bulk while theshear rate decreases as a weak power law of time in the early stage of theexperiment. The subsequent evolution of the conductivity and shear rate allowsus to propose a local yielding scenario that is in agreement with previousvelocimetry measurements. Finally, we determine the constitutive rheologicaland electrical behavior of carbon black gels. Corrections first introduced formechanical measurements are carefully extended to electrical measurements toaccurately distinguish between bulk and surface contributions to theconductivity. As an illustrative example, we examine the constitutiverheo-electric properties of five carbon black gels of different grades, anddemonstrate the relevance of the novel rheo-electric apparatus as a versatilecharacterization tool for strongly conductive complex fluids and theirapplications.

Simultaneous rheo-electric measurements of strongly conductive complex fluids