Topic
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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01 Jan 1982
TL;DR: In this paper, the authors examined the classical sedimentation problem in view of the continuum theory of mixture, which offers a rigorous axiomatic framework for the dynamics of two-phase flow.
Abstract: Publisher Summary This chapter examines the classical sedimentation problem in view of the continuum theory of mixture. The mixture theory offers a rigorous axiomatic framework for the dynamics of two-phase flow. This theory for a dilute suspension of small negatively buoyant particles provides a physically sound and intuitively satisfying interpretation of turbulent diffusion. The phenomenon can be identified with a correlation arising from decomposition and averaging applied to the drag interaction term in the momentum balances. The classical sedimentation problem, in which a balance of gravitational settling and diffusive fluxes is posed, is embodied in this theory. This chapter also describes the source of the diffusive flux that balances the gravitational settling flux of negatively buoyant particles in a steady, uniform mean flow.
03 Jan 2022
TL;DR: In this article , a variational energy-based continuum mechanics framework is proposed to model large deformation poroelasticity in a porous medium, which is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on.
Abstract: The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework.
06 Jul 2005
TL;DR: These approaches applied to the Cabernet wine data set of Ashenfelter (1999) prove particularly effective in clustering the wines, accurately classifying many of the wines by location.
Abstract: Normal mixture models are often used to cluster continuous data. However, conventional approaches for fitting these models will have problems in producing nonsingular estimates of the component-covariance matrices when the dimension of the observations is large relative to the number of observations. In this case, methods such as principal components analysis (PCA) and the mixture of factor analyzers model can be adopted to avoid these estimation problems. We examine these approaches applied to the Cabernet wine data set of Ashenfelter (1999), considering the clustering of both the wines and the judges, and comparing our results with another analysis. The mixture of factor analyzers model proves particularly effective in clustering the wines, accurately classifying many of the wines by location.