Topic
Mixture theory
About: Mixture theory is a research topic. Over the lifetime, 616 publications have been published within this topic receiving 19350 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, an axiomatic treatment based on the notion of the power as a linear functional on the space of virtual velocity fields is presented. But the approach is restricted to the case of a single continuum, regarded as a mixture with only one constituent.
Abstract: All previous axiomatic treatments of mixture theory neglected diffusion. In particular, GURTIN & DE LA PENI-tA 1 and OLIVER 2 considered rigid mixtures while WILLIAMS 3 allowed mechanical effects, but without diffusion. The main purpose of this paper is to derive dynamical local equations for the mechanical behavior of a mixture with diffusion; the equations of energy and entropy will be treated in a future paper. 4 With this in mind, I present an axiomatic treatment based on the notion of the power as a linear functional on the space of virtual velocity fields. The norm we use in ~ rules out multipolar interactions, but it is a simple exercise to change the norm in ~ to include multipolar interactions, e.g., to include the velocity gradient. I remark, however, that in this instance one must introduce a normalization condition in order to obtain uniqueness for the force measures. The approach we use, which introduces the concept of force in a very natural manner, also applies without change to the case of a single continuum, regarded as a mixture with only one constituent. I now give a summary of this paper. In Part I I give some preliminary definitions. In Part II the power is introduced. The power will be assumed to be a biadditive, bounded linear functional on 5. With this assumption we are able to represent the power as an integral of the velocity field with respect to a certain measure, which we define to be the force. The total power for a constituent will then be assumed to have a certain invariance property which is a consequence of the principle of objectivity. This assumption will give us the balance of force and moment for a constituent. In Part I I I I introduce some additional assumptions on the force measures #. This, with some smoothness conditions, will give us the existence of a stress tensor for each component of the mixture and the existence of an interaction stress for each pair of distinct components of the mixture. I also derive local balance equations and discuss relevant boundary value problems for the mixture. The equations we get differ from the classical ones, as presented, e.g., by BOWEN. 5
15 citations
TL;DR: SedMix3D as discussed by the authors is a 3D bottom boundary layer model developed from mixture theory to simulate the complex coupled interactions between fluid and sandy sediment on the seafloor.
Abstract: The complex coupled interactions between fluid and sandy sediment on the seafloor are simulated with a three-dimensional bottom boundary layer model (SedMix3D) developed from mixture theory. SedMix3D solves the unfiltered Navier-Stokes equations for a fluid-sediment mixture treated as a single continuum with effective properties that parameterize the fluid-sediment and sediment-sediment interactions including a variable mixture viscosity, a bulk hindered settling velocity, and a shear-induced, empirically calibrated, mixture diffusion term. A sediment flux equation models the concentration of sediment by describing the balance of sediment flux by advection, gravity, and shear-induced diffusion. The grid spacing is on the order of a sediment grain diameter, and simulated flows had maximum free-stream velocities between 20 and 120 cm/s and periods between 2 and 4 s. Modeled ripple geometries ranged from a single ripple to multiple ripples with varying heights, lengths, and steepness. Only noncohesive sedim...
14 citations
TL;DR: In this article, a thermo-chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from a mixture theory including the volume fraction concept.
Abstract: A thermo-chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from a mixture theory including the volume fraction concept. The model consists of an electrically charged porous solid saturated with an ionic solution. Incompressible deformation is assumed. The mixture as a whole is assumed locally electroneutral. Different constituents following different kinematic paths are defined: solid, fluid, anions, cations and neutral solutes. Balance laws are derived for each constituent and for the mixture as a whole. A Lagrangian form of the second law of thermodynamics for incompressible porous media is used to derive the constitutive restrictions of the medium. The material properties are shown to be contained in one strain energy function and a matrix of frictional tensors. A principle of reversibility results from the constitutive restrictions. Existing theories of swelling media should be evaluated with respect to this principle.
14 citations
TL;DR: In this paper, a binary mixture theory is developed for propagation of longitudinal waves in a unidirectional, fibrous composite containing a two-dimensional periodic array of cylindrical fibers of arbitrary cross section.
14 citations
Posted Content•
TL;DR: In this article, the authors extended the consistency of mass conservation and momentum transport to multiphase flow problems including an arbitrary number of immiscible and incompressible fluid phases, and demonstrated that the 2nd law of thermodynamics and consistency of reduction only rely on the properties of the Phase-Field equation.
Abstract: In the present study, we extend the \textit{consistency of mass conservation} and \textit{consistency of mass and momentum transport} to multiphase flow problems including an arbitrary number of immiscible and incompressible fluid phases. These two consistency conditions physically couple the Phase-Field equation, which locates different phases, to the hydrodynamics, and lead to a momentum equation that is Galilean invariant and compatible with kinetic energy conservation, regardless of the details of the Phase-Field equation. After implementing these two consistency conditions, we further illustrate that the 2nd law of thermodynamics and \textit{consistency of reduction} of the entire multiphase model only rely on the properties of the Phase-Field equation. All the consistency conditions are physically supported by the control volume analysis and mixture theory. Then, the multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several new techniques are developed to preserve the physical properties of the model after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the correspondences of numerical operators in the discrete Phase-Field and momentum equations. Equipped with these novel techniques, the scheme is consistent and conservative in the sense that it conserves the mass of each phase and momentum, guarantees the summation of the volume fractions to be unity, and preserves all the consistency conditions, on the fully discrete level and for an arbitrary number of phases. The properties of the scheme are all numerically validated. Numerical applications show that the proposed model and scheme are robust and effective to study complicated multiphase dynamics, especially for those including large-density ratios.
14 citations