Mixture theory

About: Mixture theory is a(n) research topic. Over the lifetime, 616 publication(s) have been published within this topic receiving 19350 citation(s).

A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials

Abstract: In this paper, a two-phase mixture theory is presented which describes the deflagration-to-detonation transition (DDT) in reactive granular materials. The theory is based on the continuum theory of mixtures formulated to include the compressibility of all phases and the compaction behavior of the granular material. By requiring the model to satisfy an entropy inequality, specific expressions for the exchange of mass, momentum and energy are proposed which are consistent with known empirical models. The model is applied to describe the combustion processes associated with DDT in a pressed column of HMX. Numerical results, using the method-of-lines, are obtained for a representative column of length 10 cm packed to a 70% density with an average grain size of 100 μm. The results are found to predict the transition to detonation in run distances commensurate with experimental observations. Additional calculations have been carried out to demonstrate the effect of particle size and porosity and to study bed compaction by varying the compaction viscosity of the granular explosive.

A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems—I. Model formulation

Abstract: Semi-empirical laws and microscopic descriptions of transport behavior have been integrated with principles of classical mixture theory to obtain a set of continuum conservation equations for binary, solid-liquid phase change systems. For a restricted, yet frequently encountered, class of phase change systems, the continuum equations have been cast into forms amenable to clear physical interpretation and solution by conventional numerical procedures.

Flow of variably fluidized granular masses across three‐dimensional terrain: 1. Coulomb mixture theory

Abstract: Rock avalanches, debris flows, and related phenomena consist of grain-fluid mixtures that move across three-dimensional terrain. In all these phenomena the same basic forces govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics and deposits. To predict motion of diverse grain-fluid masses from initiation to deposition, we develop a depth-averaged, three-dimensional mathematical model that accounts explicitly for solid- and fluid-phase forces and interactions. Model input consists of initial conditions, path topography, basal and internal friction angles of solid grains, viscosity of pore fluid, mixture density, and a mixture diffusivity that controls pore pressure dissipation. Because these properties are constrained by independent measurements, the model requires little or no calibration and yields readily testable predictions. In the limit of vanishing Coulomb friction due to persistent high fluid pressure the model equations describe motion of viscous floods, and in the limit of vanishing fluid stress they describe one-phase granular avalanches. Analysis of intermediate phenomena such as debris flows and pyroclastic flows requires use of the full mixture equations, which can simulate interaction of high-friction surge fronts with more-fluid debris that follows. Special numerical methods (described in the companion paper) are necessary to solve the full equations, but exact analytical solutions of simplified equations provide critical insight. An analytical solution for translational motion of a Coulomb mixture accelerating from rest and descending a uniform slope demonstrates that steady flow can occur only asymptotically. A solution for the asymptotic limit of steady flow in a rectangular channel explains why shear may be concentrated in narrow marginal bands that border a plug of translating debris. Solutions for static equilibrium of source areas describe conditions of incipient slope instability, and other static solutions show that nonuniform distributions of pore fluid pressure produce bluntly tapered vertical profiles at the margins of deposits. Simplified equations and solutions may apply in additional situations identified by a scaling analysis. Assessment of dimensionless scaling parameters also reveals that miniature laboratory experiments poorly simulate the dynamics of full-scale flows in which fluid effects are significant. Therefore large geophysical flows can exhibit dynamics not evident at laboratory scales.

Mechanics of Mixtures

Abstract: Kinematics partial stress and total stress balance laws and the entropy inequality constitutive theory steady state problems diffusing singular surface wave propagation in solids infused with fluids epilogue some results from differential geometry status of Darcy's law within the context of mixture theory a brief discussion of a mixture of immiscible fluids.

A two-fluid model for avalanche and debris flows

Abstract: Geophysical mass flows—debris flows, avalanches, landslides—can contain O (10 6 –10 10 )m 3 or more of material, often a mixture of soil and rocks with a significant quantity of interstitial fluid. These flows can be tens of meters in depth and hundreds of meters in length. The range of scales and the rheology of this mixture presents significant modelling and computational challenges. This paper describes a depth-averaged ‘thin layer’ model of geophysical mass flows containing a mixture of solid material and fluid. The model is derived from a ‘two-phase’ or ‘two-fluid’ system of equations commonly used in engineering research. Phenomenological modelling and depth averaging combine to yield a tractable set of equations, a hyperbolic system that describes the motion of the two constituent phases. If the fluid inertia is small, a reduced model system that is easier to solve may be derived.