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Mixture theory
About: Mixture theory is a research topic. Over the lifetime, 616 publications have been published within this topic receiving 19350 citations.
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18 Mar 2023
TL;DR: In this article , a constitutive theoretical framework considering the chemical activity for saturated porous media is derived from the mixture theory incorporated with the chemical thermodynamics, and the complete swelling constitutive models in the confined compression are established for bentonite.
Abstract: In order to reveal the coupling effect among the chemical activity and the hydraulic seepage as well as the mechanical properties, a constitutive theoretical framework considering the chemical activity for saturated porous media is derived from the mixture theory incorporated with the chemical thermodynamics. First, to highlight the important role of porosity in the hydro-mechanical-chemical multi-field coupling mechanism, the solid strain is divided into the porosity-dependent skeleton strain, the matrix strain and the mass-exchange strain. The stress and strain state variables are determined from the energy-conjugated form of the energy balance equation for establishing constitutive equations. Second, under infinitesimal case, general elastic constitutive equations including the relationship between mass fraction and its chemical potential are expressed by the free energy potential. Plastic model and the constitutive equation of thermodynamic flux and force are derived from the dissipative potential. Finally, under the guide of this theoretical framework, the complete swelling constitutive models in the confined compression are established for bentonite. The corresponding governing equations are formulated for multi-field two-phase saturated porous media. Compared with the experimental data, the proposed model can well reflect the chemical and mechanic coupling characteristics of representative elementary volume in the different NaCl concentrations of solution for saturated bentonite.
TL;DR: In this paper, the volume fraction condition is taken into consideration in deducing the thermodynamic restrictions of mixture theory applying the axiom of dissipation, and the results obtained are consistent for mixtures with or without a compressible phase, and in which the free energy of each phase depends on the densities of all phases.
Abstract: Volume fraction condition is a true constraint that must be taken into consideration in deducing the thermodynamic restrictions of mixture theory applying the axiom of dissipation. For a process to be admissible, the constraints imposed by the volume fraction condition include not only the equation obtained by taking its material derivative with respect to the motion of a given phase, but also those by taking its spatial gradient. The thermodynamic restrictions are deduced under the complete constraints, the results obtained are consistent for the mixtures with or without a compressible phase, and in which the free energy of each phase depends on the densities of all phases.
TL;DR: SedMix3D as mentioned in this paper solves the Navier-Stokes equations for the fluid-sediment mixture with an additional equation describing sediment flux, treating the mixture as a single continuum with effective properties parameterizing the intraand inter-phase interactions with closure relations for the mixture viscosity, diffusion, hindered settling, and particle pressure.
Abstract: The highly turbulent, sediment-laden flow above rippled beds in the wave bottom boundary layer (WBBL) is poorly understood and difficult to quantify mainly because of our failure to understand the fundamental interaction forces driving sediment transport. However, recent advances in high performance computing allow for highly resolved simulations of fluid-sediment dynamics in the WBBL to examine the small-scale fluctuations of boundary layer processes and characterize seabed morphology. A three-dimensional mixture theory model, SedMix3D, solves the unfiltered Navier-Stokes equations for the fluid-sediment mixture with an additional equation describing sediment flux. Mixture theory treats the fluid-sediment mixture as a single continuum with effective properties parameterizing the intraand inter-phase interactions with closure relations for the mixture viscosity, diffusion, hindered settling, and particle pressure. We validate results obtained with SedMix3D using temporally and spatially resolved fluid velocity measurements acquired with a particle image velocimetry (PIV) system in a free-surface laboratory flume. Measured two-dimensional velocity fields are compared to two-dimensional vertical slices from the threedimensional simulation domain. We examine the hydrodynamics of the flow by comparing bulk flow statistics, and swirling strength. In general, results from SedMix3D were in excellent agreement with the observations. We believe SedMix3D captures the essential physics governing two–phase turbulent flow over ripples for the conditions represented by the experiments and should provide us with a powerful research tool for studying the dynamics of seafloor bedforms.
Dissertation•
01 Jan 1997
TL;DR: In this article, the second law of thermodynamics is constructed to allow additional constraint equations which will restrict the form of new parameters, and several existing theories of mechanics are assimilated into a cohesive theory to demonstrate the validity of the mathematical model used to represent mixtures.
Abstract: The analysis of material properties depends upon detailed information of the physical, geometric* and chemical properties of the materials. Relating these properties to a set of mathematical models is the principle objective of mechanics. Mixtures of materials made up of several constituents require special consideration since the constituent behavior must be reconciled with the overall behavior of the mixture. Mathematical models and their validity must be established to represent these materials. This thesis establishes a methodology whereby a logical sequence of considerations may be followed to represent complex mixtures adequately. Several existing theories of mechanics are assimilated into a cohesive theory to demonstrate the validity of the mathematical model used to represent mixtures. A structured development Of the second law of thermodynamics is constructed to allow additional constraint equations which will restrict the form of new parameters. An example of a wOod-snow mixture is used to show how the analysis is to be completed. Laboratory tests were run to use as a means of constructing the values of the new constitutive parameters. Proposed ways of including more constituents and spatial dimensions suggested.
TL;DR: In this article , the authors presented a novel HMG model of fully coupled two-phase fluid transport in a deformable porous media through extending mixture coupling theory which is based on non-equilibrium thermodynamics.
Abstract: Abstract The interactions of gas migration, water transport and mechanical deformation of rocks are significant for geoenergy industry (e.g. Carbon Capture and Storage, radioactive waste disposal); however, the hydro-mechanical-gas coupled model remains a challenge due to the gap between multiple disciplines (e.g. Geomechanics and Geoenergy). This work presents a novel hydro-mechanical framework model of fully coupled two-phase fluid transport in a deformable porous media through extending mixture coupling theory which is based on non-equilibrium thermodynamics. The main difference between the mixture coupling theory approach and other approaches (ex., mechanic's approach) is that the mixture coupling theory uses energy and entropy analysis by utilizing the unbalanced thermodynamics, while the mechanic's approach analyses the stress–strain tensors. The gas free energy has been included in the Helmholtz free energy balance equation. Three main governing equations have been obtained for solid, liquid and gas phases. Benchmark experiments and modelling based on classical continuum mechanics approaches are used to validate the model by comparing the measured data to the simulation results. The results have a good agreement with experimental data, demonstrating that gas migration has a great influence on water transport and deformation of the solids. The novelty of this study is that it is providing a new approach to study the multiphase flow coupling in porous media rather than the classic mechanic’s approach. Article Highlights A Hydro-Mechanical-Gas (HMG) model has been developed using the mixture coupling theory approach. The hydro-mechanical framework equations were established by using non-equilibrium thermodynamic and Darcy law. The model has been validated using published experimental data and the results of other researchers with different approaches.