Showing papers on "Mixture theory published in 1983"

A Multiphase Mixture Theory for Fluid-Particle Flows

Abstract: Publisher Summary This chapter presents a theory for suspension of particles in fluids based on the continuum theory of multiphase mixtures and it describes the application of the continuum mixture theory to the description of fluid–particle flows. The maximum concentration of particles can occur off the axis of symmetry because of a balance between lift forces and dynamic pressure forces. This provides a possible explanation of the Segre–Silberberg effect in the context of mixture theory. The classical theory of translational Brownian motion is concerned with the random migration of isolated colloidal particles in a suspending fluid. This random motion is a result of the collisions between the particles and the molecules of the fluid, which are undergoing thermal fluctuations. For neutrally buoyant particles, the particle flux, because of the fluctuating velocity field, is the same as that which can be produced by thermodynamic force acting on each particle. This thermodynamic force is equal to the gradient of the chemical potential of the particles.

Theory for deflagration-to-detonation transition (DDT) in granular explosives

Abstract: In this report, we develop a two-phase mixture theory to describe the deflagration-to-detonation transition (DDT) in porous granular explosives. The theory is based on the continuum theory of mixtures and is able to account for both the compressibility of each phase and the compaction of the granular bed. By requiring the model to satisfy the Second Law of Thermodynamics, specific expressions for the exchange of mass, momentum and energy are proposed which are consistent with previously published empirical models. The model is then applied to the problem of DDT in a pressed column of HMX. Numerical results, using the method of lines, are obtained for a representative case of a 5 cm long bed and a grain size of 200 ..mu..m. 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, porosity, gas product equation of state, drag correlation, compaction viscosity and burn rate on the run distance to detonation.

Mixture Theory for Turbulent Diffusion of Heavy Particles

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.

Theory of Pulse Propagation in Fluid-Saturated Porous Layers

Abstract: We have developed a theory for ultrasonic pulses in a porous solid layer immersed in a fluid. Biot's mixture theory is used to describe the constitutive equation of a fluid saturated porous solid. Since fast and slow waves exist in a Biot solid, t here is mode conversion at the interface even at normal incidence and, therefore, the transmission and reflection coefficients are 2 x 2 matrices. We use matrix methods in developing the s olution of the wave propagation problem. A generalized ray expansion algorithm is obtained by using the Gauss-Seidel matrix iterative method. The arrivals of the fast and the slow waves are easily i dentified. A compact computational algorithm is developed using combinatorial analysis and the Cayley-Hamilton theorem. The computed solution is compared with Plona's experiment on pulses originating in water and striking normally at a porous disk. and experiment has been found. Good agreement between theory