Micro-inertial formulations of complex materials flow models

Abstract Traditionally microscopic inertia is neglected in deriving the evolution of microstructure within complex fluid systems. We are interested in investigating how to modify existing traditional (micro-dissipative) models to account for micro-inertia. For that, we apply the Single Generator Bracket Formalism of NonEquilibrium Thermodynamics (SGBF-NET) [A. N. Beris and B. J. Edwards, Thermodynamics of Flowing Systems with Internal Microstructure , New York, Oxford University Press, 1994] to examine the mathematical structure of such models, starting from the description of a simplified, unconstrained, dynamic model for nematic liquid crystals. We explore this topic in an area where first-principles micro-inertia models have been developed in the past to be confident on the structure and form of the final equations. We then examine critically the connection within the SGBF-NET description between the micro-inertial and micro-dissipative (traditional) versions of the same model. This comparison allows us to infer rules within the framework of SGBF-NET connecting micro-inertia models to their traditional micro-dissipative equivalents. We then illustrate the application of these rules to dilute emulsions, an area where independent theoretical evidence, based on both experiments and microscopic simulations, is available. We conclude with the inference of the form that micro-inertia models are expected to have for viscoelastic flows.