Showing papers on "Mixture theory published in 1992"

A comparative analysis of two land surface heterogeneity representations

Abstract: Two contrasting representations of land surface variability used in general circulation models (GCMs) are compared through an analysis of their corresponding surface energy balance equations. In one representation (the 'mixture' approach), different vegetation types are assumed to be homogeneously mixed over a grid square, so that the GCM atmosphere sees near-surface conditions pertaining to the mixture only. In the second representation (the 'mosaic' approach), different vegetation types are viewed as separate 'tiles' of a grid-square 'mosaic', and each tile interacts with the atmosphere independently. The mosaic approach is computationally simpler and in many ways more flexible than the mixture approach. Analytical solutions to the linearized energy balance equations and numerical solutions to the nonlinear equations both demonstrate that the mixture strategy, when applied to two coexisting vegetation types that differ only in canopy transpiration resistance, promotes both total turbulent flux and latent heat flux relative to the mosaic strategy. The effective differences between the strategies, however, are small over a wide range of conditions. In particular, the strategies are effectively equivalent when the transpiration resistances of the different vegetation types are of the same order of magnitude.

Mathematical analysis of a two-phase continuum mixture theory

Abstract: In this paper, we study the mathematical structure of a continuum reactive mixture model of the combustion of granular energetic materials. We obtain and classify the wave fields associated with this description. This analysis shows that this system of hyperbolic equations becomes degenerate when the relative flow is locally sonic. We derive the corresponding Riemann invariants and construct simple wave solutions. We also discuss special discontinuous solutions of the system of equations. For fixed upstream conditions, different downstream states are possible when the relative velocities exceed the speed of the sound gas.

Flow of viscous fluids through a porous deformable matrix

Abstract: A self-contained account of mixture theory is presented as a framework for describing the flow of fluids, liquids and gases, through a porous deformable matrix, incorporating both mechanical and thermal effects. The theory comprises the conservation laws of mass, momentum and energy for each constituent and the mixture properties which describe the interactions between constituents. Mass transfer between constituents which arises during phase change and chemical reactions influences both conservation laws and mixture properties. An analysis of discontinuity conditions at a singular surface is presented, which would be needed, for example, to describe an advancing phase-change front. Details are presented for the flow of viscous fluids through a thermoelastic matrix undergoing infinitesimal deformation, a common model for underground reservoirs. The interactions of immiscible and miscible fluids are discussed. An essential ingredient is the relation between partial physical variables defined as mean values over mixture elements, and intrinsic variables defined with respect to the constituent elements.

Phenomenological models of viscoplastic, thixotropic, and granular materials

Abstract: A simple constitutive framework is used to review some phenomenological models for solid-fluid mixtures. Several successful descriptions of viscoplasticity assume that stress is proportional to a normalized deformation rate. The modulus in this constitutive equation evolves with time for thixotropic materials. This approach is used in most models based on scalar measures of structure. Such measures are determined by an evolution equation that is insensitive to rate reversals during shear flow. This behavior appears to be characteristic of inelastic materials such as an aqueous solution of bentonite. However, the same solution with guargum does not exhibit this response due to elasticity induced by the polymer. Models for granular media extend this constitutive framework by including compressibility effects and a scalar measure of particle interactions. The effect of fluid viscosity on particle interactions is incorporated using a mixture theory approach. Pipe flow of viscoplastic materials and shear flow of granular media are analyzed using boundary conditions that allow slip at solid surfaces.

Modeling of shock-induced chemical reactions in powder mixtures ii: continuum mixture theory

Abstract: This paper discusses a re-examination of the VIR model1 using continuum mixture theory. The continuum theory used is that developed extensively at Sandia National Laboratories for the description of granular explosives. The analysis shows that both formulations produce essentially identical constitutive equations except the distribution of energy due to pore collapse. The difference was attributed to the use of phase pressure for the description of species energy conservation equation in the continuum theory.