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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, ${\mathit{Mn}}_f$, 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. 

The microstructural link to the rheology of carbon black suspensions has recently become clear as a result of advances in computational and experimental methods. This understanding reveals the important role of the restructuring, build-up, and break-up of carbon black agglomerates in simple shear, rationalized by a dimensionless balance of the hydrodynamic forces acting to break the agglomerates apart against the cohesive forces holding them together (i.e., the Mason number). The Mason number not only can predict the origin of reversible thixotropy seen in carbon black suspensions observed at higher shear intensities, but can also be used to rationalize the evolution of microstructure at lower shear intensities. This review focuses on carbon black suspension behavior, but the insights derived from carbon black suspensions are broadly applicable to a diverse class of soft matter including colloidal gels relevant to a variety of applications. 

Radio-frequency (RF) heating of thermosetting epoxies is an agile method to decouple the extrudability of epoxy resins from their buildability for additive manufacturing. Through this method, the resin is extruded in the liquid state at the early stages of curing. Then, an RF applicator induces a rapid and uniform increase in temperature of the resin, accelerating the solidification of the printed feature. Understanding the evolution of the resin's RF heating response as it cures is therefore critical in meeting the demands of additive manufacturing. In this work, we show that the high-frequency dielectric loss, determined using in situ rheo-dielectric measurements, of both neat and carbon nanotube (CNT) filled resins is correlated to the heating response at different temperatures throughout curing. Furthermore, we show that the presence of CNTs within the resin augments the heating response and that their dispersion quality is critical to achieving rapid heating rates during the cure.