Continuum modeling of particle suspension conductivity

Abstract

A suspension of network-forming, electrically conductive particles imparts electrical conductivity to an otherwise insulating medium. This effect can be used to great effect in many industrial applications. The ability to describe these networks and to predict their physical properties is a key step in designing systems that rely on these properties. In addition, many times these networks are suspended in a flowing fluid, which disrupts existing networks and forms new ones. The extra layer of complexity introduced by flow requires more sophisticated tools to model the effect on the network and its properties. In the first chapter, we derive a model for the full, tensorial effective conductivity of a particle particle network as a function of a local tensor description of the particle network, the "fabric tensor." We validate our model against a large number of computer-generated networks and compare its performance against an analogous existing model in the literature. We show that the model accurately predicts the isotropic magnitude, deviatoric magnitude, and deviatoric direction of a particle network. In the second chapter, we set out to model the effects of flow on a particle network. We propose two frame-indifferent constitutive equations for the evolution of the fabric tensor. We perform conductivity measurements of real flowing carbon black suspensions and fit our models to the results by using the conductivity model derived in chapter 1. We find that our models are able to reproduce out-of-sample experimental results with a high degree of accuracy.