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Electron transport in complex fluids, biology, and soft matter is a valuable characteristic in processes ranging from redox reactions to electrochemical energy storage. These processes often employ conductor-insulator composites in which electron transport properties are fundamentally linked to the microstructure and dynamics of the conductive phase. While microstructure and dynamics are well recognized as key determinants of the electrical properties, a unified description of their effect has yet to be determined, especially under flowing conditions. In this work, the conductivity and shear viscosity are measured for conductive colloidal suspensions to build a unified description by exploiting both recent quantification of the effect of flow-induced dynamics on electron transport and well-established relationships between electrical properties, microstructure, and flow. These model suspensions consist of conductive carbon black (CB) particles dispersed in fluids of varying viscosities and dielectric constants. In a stable, well-characterized shear rate regime where all suspensions undergo self-similar agglomerate breakup, competing relationships between conductivity and shear rate were observed. To account for the role of variable agglomerate size, equivalent microstructural states were identified using a dimensionless fluid Mason number, Mnf, which allowed for isolation of the role of dynamics on the flow-induced electron transport rate. At equivalent microstructural states, shear-enhanced particle-particle collisions are found to dominate the electron transport rate. This work rationalizes seemingly contradictory experimental observations in literature concerning the shear-dependent electrical properties of CB suspensions and can be extended to other flowing composite systems. [ABSTRACT FROM AUTHOR]

Carbon black suspensions exhibit complex, shear-dependent macroscopic properties that are a consequence of the state of the suspension microstructure. In this work, the shear-induced microstructure of a model, reversible suspension of conductive carbon black in propylene carbonate is measured using simultaneous steady shear rheology and small angle neutron scattering. These experiments provide microstructural evidence for a bifurcation in the rheological properties. We show that the demarcation line for this bifurcation is the inverse Bingham number, Bi−1, which relates the magnitude of the stress response to an applied shear rate to the yield stress of the presheared suspension. At high shear rates where Bi−1 > 1, the suspension flows homogeneously and exhibits a thixotropic response that arises due to the self-similar breakdown of agglomerates with increasing shear rate. Conversely, at low shear rates where Bi−1 < 1, the applied shear drives the densification and growth of these agglomerates. This densification process leads to a gravitationally driven instability resulting in an inhomogeneous volume fraction distribution along the height of the geometry that is a function of both time under shear and shear rate. Under these shear conditions, the suspension exhibits apparent rheopexy, or antithixotropy, where a significant decline in the viscosity is observed with a step down in shear rate. The unique microstructural measurements presented here reconcile many observations in the literature regarding carbon black suspensions, including an apparent shear-thickening behavior, tunability of both the yield stress and elasticity through shear history, and transient macroscopic properties. [ABSTRACT FROM AUTHOR]