Two-phase fluids

The static mixer is also useful for direct contact heat transfer between fluids, two phase contacting, and other useful applications such as mass transfer. 

They considered that cement formation was the result of an acid-base reaction leading to the formation of hydrates by a through-solution mechanism, by nucleation and precipitation from pore fluids. Two phases were found in the matrix, one amorphous and the other crystalline. The crystalline phase was newberyite. Finch Sharp concluded that the amorphous phase was a hydrated form of aluminium orthophosphate, AIPO4, which almost certainly contained magnesiiun. They ruled out a pure AlP04.nH20, for they considered that the reaction could not be represented by the equation... 

Li, J., and Kwauk, M., Particle-Fluid Two-Phase Flow, The Energy-Minimization Multi-Scale Method, Metallurgical Industry Press, Beijing (1994)... 

The EMMS model was first proposed for the hydrodynamics of concurrent-up particle-fluid two-phase flow. Though it is based on a rather simplified physical picture of the complex system (Li, 1987 Li and Kwauk, 1994), it harnesses the most intrinsic complexity in the system, the meso-scale heterogeneity, and this is why it allows better predictions to the critical phenomena in the system which is obscured in other seemingly more comprehensive models. 

Li, J., Multi-Scale Modeling and Method of Energy Minimization for Particle-Fluid Two Phase Flow, Ph.D. thesis (in Chinese), Institute of Chemical Metallurgy, Chinese Academy of Sciences, Beijing (1987). 

Li, J., Tung, Y., and Kwauk, M. Method of energy minimization in multi-scale modelling of particle-fluid two-phase flow, m Circulating Fluidized Bed Technology II (Basu, P., and Large, J. F., eds.), p. 75. Pergamon Press (1988). 

Figure 1 shows the eight principal dependent parameters in a generalized particle-fluid two-phase system, the local state of which can be described by some functional relationship between a dependent parameter vector X(r) in terms of these eight parameters ... 

There are two principal approaches to formulate particle-fluid two-phase flow in fluidized beds the pseudo-fluid model and the two-phase model. 

An appropriate understanding of particle-fluid two-phase flow rests on an adequate analysis of the local hydrodynamics corresponding to the scale of bubbles or clusters, as well as the overall hydrodynamics corresponding to the scale of the retaining vessel. Local hydrodynamics, designated as phases, is rooted in the intrinsic characteristics of particle-fluid systems,... 

This section will first deal with the phases in particle-fluid two-phase flow by developing a mathematical model to quantify local hydrodynamic states. This analysis will reveal the insufficiency of the conditions for the conservation of mass and momentum alone in determining the hydrodynamic states of heterogeneous particle-fluid systems, and calls for a methodology different from what is used in analyzing dilute uniform flow. For this purpose the concept of multi-scale interaction between particles and fluid and the principle of energy minimization are proposed. 

To account for the intrinsic characteristics of particle-fluid two-phase flow in fast fluidization, the particles and the fluid are considered to interact with each other on both a micro-scale and meso-scale level to produce local or meso-scale heterogeneity (phases), and the overall fluid-particle system interacts with the equipment boundaries on a much larger scale to produce macro-scale heterogeneity (regions). 

In effect, such a multi-scale analysis resolves a macro-scale heterogeneous system into three meso- to micro-scale subsystems—dense-phase, dilute-phase and inter-phase. Thus, modeling a heterogeneous particle-fluid two-phase system is reduced to calculations for the three lower-scale subsystems, making possible the application of the much simpler theory of particulate fluidization to aggregative fluidization and the formulation of energy consumptions with respect to phases (dense, dilute and inter) and processes (transport, suspension and dissipation). 

Obviously, the different energy terms characterize different aspects of particle-fluid two-phase flow, among which those related to particle suspension and transport are of importance in analyzing fluid-particle interaction, and, in particular, for identifying system stability ... 

If we consider the set of six equations on mass and momentum conservation on the one hand, and the characteristic energy extrema for stability of the three broad regimes of operation on the other, mathematical modeling for local hydrodynamics of particle-fluid two-phase flow beyond minimum fluidization needs therefore to satisfy the following constraints ... 

While local hydrodynamics of particle-fluid two-phase flow—phases, regimes and patterns—is concerned with its intrinsic stability, of direct engineering significance is its overall hydrodynamics, which deals with its space-dependent characteristics subject to the boundary conditions set by the retaining vessel. For the axisymmetric equipment generally employed in engineering, overall hydrodynamics is resolved into the axial and the radial... 

Chen, A., and Li, J. Particle aggregation in particle-fluid two-phase flow, in Fluidization 94—Science and Technology (the organizing committee of CJF-5, ed.), p. 254. Chemical Industry Press, Beijing, 1994. 

Li, J. Multi-scale modeling and method of energy minimization for particle-fluid two-phase flow," Ph. D. Thesis, Institute of Chemical Metallurgy, Academia Sinica, Beijing (1987). 

Wu, W., Li, J., Yang, L., and Kwauk, M. Critical condition for particle aggregation in particle-fluid two-phase flow, Journal of Engineering Thermophysics (in Chinese) 13,324 (1991). Yang, W. C. Criteria for choking in vertical pneumatic conveying lines, Powder Technology 35, 143 (1983). 

Fig. 3. Sound speed for a large heat-capacity-fluid (C6F14) along the phase boundary (------ single phase fluid,----- two-phase mixture).

Wu B. CFD simulation of gas and non-Newtonian fluid two-phase flow in anaerobic digesters. Water Res 2010 44(13) 3861-74. 

Li J, Kwauk M Particle-fluid two-phase fow energy-minimization multi-scale method, Beijing, 1994, Metallurgy Industry Press. 

In the measurement of solid-fluid two-phase flow we need to discriminate the signals from coarse particles and from fines (i.e., tracer seed). As schematically shown in Fig. 19b, a fine (seed) particle whose diameter... 

For an ordinary fluid two-phase system, minimization of the free energy at constant temperature flrst of all results in the well-known chemical potential condition for diffusive equilibrium with respect to the soluble components present. Furthermore, the mathematical extremum condition for the free energy contains the pressure difference AP across the interface as a parameter. Solving for AP, this condition takes the form of a generalized Laplace equation. Whether or not this equation signifies a stable equilibrium is, however, often a rather complex issue where the detailed system properties may enter in a crucial manner. 

A partial stream of the disperse fluid two-phase system is sucked off by a vertical funnel connected with a glass capillary. The capillary diameter is chosen so, that most of the bubbles are deformed to plugs. These are detected twice by a suitable light sensing means that informs on the length of the plugs. If the plug... 

Temperatuie Parts moving in fluids Two-phase fluids Oxidation, scales... 

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