Author(s): Cass T. Miller; William G. Gray; Christopher E. Kees; Iryna V. Rybak; Brittany J. Shepherd

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Keywords: Averaging theory; continuum mechanics; entropy production rate; mechanistic modelling; porous medium flow; TCAT

Abstract: Understanding the dynamics of wet granular materials is important for a range of applications, including levee safety, beach erosion, and scour around hydraulic structures. Several continuum models have been proposed recently to model the relevant processes for these applications at computationally tractable resolutions, which were derived using mixture theory approaches for granular and aerated flows. The thermodynamically constrained averaging theory is used to formulate a framework for three-phase flow models involving mechanistic conservation and balance principles for a set of entities consisting of phases, interfaces, and a common curve. The derived entropy inequality provides a basis for formulating permissibility conditions on closure relations. An example is provided showing how the entropy inequality derived in this work can be used to examine the closure relations in existing models. Results from this example show that this existing model violates entropy permissibility conditions. Several possible extensions and uses of this foundational work are summarized.

DOI: https://doi.org/10.1080/00221686.2019.1581673

Year: 2019