Quantifying the dispersion of discrete inclusions in composites using continuum theory

A novel and robust method for quantifying the quality of dispersion of discrete inclusions in a composite was recently introduced. The method quantifies dispersion based on the minimum amount of work required to move the inclusions such that they are in a fully uniform state. As the new dispersion quantification method is founded on a physical thermodynamic framework, it is distinct from previously developed methods that have strictly a mathematical and statistical basis. However, implementation of the new method is computationally expensive for domains consisting of many inclusions. In this paper, the novel dispersion quantification method is recast in terms of continuum mechanics and thermodynamics in order to make use of diffusion models, which makes possible the quantification of dispersion considering domains with many inclusions. To demonstrate the practicality of the new approach, the dispersion of carbon nanofibers in an aqueous solution is analyzed.