Dual-domain models are used to explain anomalous solute transport behavior observed in diverse hydrologic settings and applications, from groundwater remediation to hyporheic exchange. To constrain such models, new methods are needed with sensitivity to both immobile and mobile domains. Recent experiments indicate that dual-domain transport of ionic tracers has an observable geoelectrical signature, appearing as a nonlinear, hysteretic relation between paired bulk and fluid electrical conductivity. Here we present a mechanistic explanation for this geoelectrical signature and evaluate assumptions underlying a previously published petrophysical model for bulk conductivity in dual-domain media. Pore network modeling of fluid flow, solute transport, and electrical conduction (1) verifies the geoelectrical signature of dual-domain transport, (2) reveals limitations of the previously used petrophysical model, and (3) demonstrates that a new petrophysical model, based on differential effective media theory, closely approximates the simulated bulk/fluid conductivity relation. These findings underscore the potential of geophysically based calibration of dual-domain models.