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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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25 Aug 2015
TL;DR: In this paper, the steady-state saturated flow of an incompressible power-law fluid through a porous channel limited by two impermeable flat plates is modeled using a mixture theory, which considers fluid and porous matrix as superimposed continuous constituents of a binary mixture.
Abstract: The steady-state saturated flow of an incompressible power-law fluid through a porous channel limited by two impermeable flat plates is modeled using a mixture theory, which considers fluid and porous matrix as superimposed continuous constituents of a binary mixture. After some simplifying assumptions, the mechanical model gives rise to a coupled system of ordinary differential equations that is simulated by employing a Runge-Kutta method coupled with a shooting strategy. Despite the strong nonlinearity of the problem, this simple methodology provides stable and accurate results, for both shear-thinning and shear-thickening behaviors.
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TL;DR: This paper considers a class of models for multiphase fluids, in the framework of mixture theory, which contains both the gradient of a hydrostatic pressure generated by an incompressibility constraint and a compressible pressure depending on the volume fractions of some of the different phases.
Abstract: In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility constraint, and the gradient of a compressible pressure depending on the volume fractions of some of the different phases. To approach these systems, we define an approximation based on the \emph{Leray} projection, which involves the use of the \emph{Lax} symbolic symmetrizer for hyperbolic systems and paradifferential techniques. In two space dimensions, we prove its well-posedness and convergence to the unique classical solution to the original system. In the last part, we shortly discuss the difficulties in the three dimensional case.
01 Jan 1988
TL;DR: In this paper, the mixture theory proposed by Murakami and Hegemier is applied to the transient dynamic analysis of elastoplastic fiber reinforced composites, and the resulting semi-discrete equations of motion are then integrated using the explicit method.
Abstract: The mixture theory proposed by Murakami and Hegemier [1] is applied to the transient dynamic analysis of elastoplastic fiber reinforced composites. The model is based on the two scale-asymptotic expansions as described by Bensoussan, Lions and Papanicolaou [2], and Sanchez-Palencia [3]. Equations of motion are obtained from the principle of virtual work, while the appropriate incremental constitutive equations are deduced from Reissner’s [4] mixed variational principle. The finite element method is used for the spatial discretization. The resulting semi-discrete equations of motion are then integrated using the explicit method. The fibers are assumed elastic, while the matrix obeys a von Mises yield criterion with linear hardening. A semi-infinite fiber reinforced composite under a step pressure is considered. Stress profiles show the dispersive nature of the waves in the composite.
01 Jan 1987
TL;DR: In this article, a part of the obtained results is used to give necessary and sufficient condition in order to decide whether a given characteristic function is a factor of another one, or not.
Abstract: In more papers author dealt with a new foundation of the mixture theory of probability distribution functions. In this paper a part of the obtained results is used to give necessary and sufficient condition in order to decide whether a given characteristic function is a factor of another one, or not.
TL;DR: In this article, the authors tackle the ambiguity of the momentum equation formulation in commonly used macroscopic models of two-phase solid/liquid regions, developing during alloy solidification, and compare three different forms of momentum equation and their impact on calculated velocity and temperature fields.
Abstract: Purpose – This paper aims to tackle the problem of some ambiguity of the momentum equation formulation in the commonly used macroscopic models of two‐phase solid/liquid region, developing during alloy solidification. These different appearances of the momentum equation are compared and the issue is addressed of how the choice of the particular form affects velocity and temperature fields.Design/methodology/approach – Attention is focused on the ensemble averaging method, which, owing to its stochastic nature, is a new promising tool for setting up the macroscopic transport equations in highly inhomogeneous multiphase micro‐ and macro‐structures, with morphology continuously changing in time when the solidification proceeds. The basic assumptions of the two other continuum models, i.e. based on the classical mixture theory and on the volume‐averaging technique, are also unveiled. These three different forms of the momentum equation are then compared analytically and their impact on calculated velocity and ...