Multiphasic systems

In principle, there is no limit to the number of phases that can be used to conduct a chemical process. Triphasic processes have been shown to have some 

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Another approximation, one of the most enduring empirical correlations in multiphase systems, is the Richardson-Zaki correlation for a single particle in a suspension (3) ... 

Whereas the production flow charts of inorganic pigments appear to be simple, the actual processes can be very compHcated. Many pigments are not pure chemical compounds, but can be multiphase systems contaminated with various impurities and modifiers. Because pigments are fine powders, the physical properties are as critical to their appHcation performance as are the chemical properties. 

The foUowiag criterion of phase equUibrium can be developed from the first and second laws of thermodynamics the equUibrium state for a closed multiphase system of constant, uniform temperature and pressure is the state for which the total Gibbs energy is a minimum, whence... 

It is presumed ia this statement that equUibrium ia a multiphase system implies uniformity of T and P throughout aU phases. In certain situations, eg, osmotic equUibrium, pressure uniformity is not required, and equation 212 is then not a useful criterion. Here, however, it suffices. 

If the T and P of a multiphase system are constant, then the quantities capable of change are the iadividual mole numbers of the various chemical species / ia the various phases p. In the absence of chemical reactions, which is assumed here, the may change only by iaterphase mass transfer, and not (because the system is closed) by the transfer of matter across the boundaries of the system. Hence, for phase equUibrium ia a TT-phase system, equation 212 is subject to a set of material balance constraints ... 

Citric acid is utilized in a large variety of food and industrial appHcations because of its unique combination of properties. It is used as an acid to adjust pH, a buffer to control or maintain pH, a chelator to form stable complexes with multivalent metal ions, and a dispersing agent to stabilize emulsions and other multiphase systems (see Dispersants). In addition, it has a pleasant, clean, tart taste making it useful in food and beverage products. 

Thermoplastic elastomers are often multiphase compositions in which the phases are intimately dispersed. In many cases, the phases are chemically bonded by block or graft copolymerization. In others, a fine dispersion is apparentiy sufficient. In these multiphase systems, at least one phase consists of a material that is hard at room temperature but becomes fluid upon heating. Another phase consists of a softer material that is mbberlike at RT. A simple stmcture is an A—B—A block copolymer, where A is a hard phase and B an elastomer, eg, poly(styrene- -elastomer- -styrene). 

For the analysis heat and mass transfer in concrete samples at high temperatures, the numerical model has been developed. It describes concrete, as a porous multiphase system which at local level is in thermodynamic balance with body interstice, filled by liquid water and gas phase. The model allows researching the dynamic characteristics of diffusion in view of concrete matrix phase transitions, which was usually described by means of experiments. 

Note that filter aid selection must be based on planned laboratory tests. Guidelines for selection may only be applied in the broadest sense, since there is almost an infinite number of combinations of filter media, filter aids, and suspensions that will produce varying degrees of separation. The hydrodynamics of any filtration process are highly complex filtration is essentially a multiphase system in which interaction takes place between solids from the suspension, filter aid, and filter medium, and a liquid phase. Experiments are mandatory in most operations not only in proper filter aid selection but in defining the method of application. Some general guidelines can be applied to such studies the filter aid must have the minimum hydraulic resistance and provide the desired rate of separation an insufficient amount of filter aid leads to a reduction in filtrate quality — excess amounts result in losses is filtration rate and it is necessary to account for the method of application and characteristics of filter aids. 

J. Tiaden, B. Nestler, H. J. Diepers, I. Steinbach. Physica D 115 11, 1998 G. J. Schmitz, B. Nestler. Simulation of phase transitions in multiphase systems, peritectic solidification of YBaCuO-superconductors. Mater Sci Eng B 53 11, 1998. 

W. K. Chui, J. Glimm, F. M. Tangerman, H. Zhang, V. Prasad. A parallel algorithm for multizone, multiphase systems with application to crystal growth. J Cryst Growth 750 534, 1997. 

Lithiated carbons are mostly multiphase systems. Hence, the determination of chemical diffusion coefficients for Li1 causes experimental problems because the propagation of a reaction front has to be considered. 

Analyzing the behavior of filled polymers, as any other heterophase systems, two aspects should be distinguished. First, these are the properties of such systems, i.e. their inherent characteristics, independent of a measuring method if, of course, the measurements are correct (to select criteria of correctness of an experiment, carried out with multiphase systems, seems to be an independent and by no means a simple problem). Second, this is a manifestation of these properties when heterophase systems flow in channels of different geometrical form. Behind all this stands the basic applied problem—finding out how the properties of filled polymers, appearing during their flow, affect the properties of finished articles. 

The mechanisms by which this interaction occurs may be divided into two distinct groups (S4) first, the hydrodynamic behavior of a multiphase system can be changed by the addition of surface-active agents, and, as a result, the rate of mass transfer is altered secondly, surface contaminants can interfere directly with the transport of matter across a phase boundary by some mechanism of molecular blocking. 

Chapter 5 Flow of Multiphase Systems (gas- liquid, liquid-solids, gas-solids)... 

The flow problems considered in previous chapters are concerned with homogeneous fluids, either single phases or suspensions of fine particles whose settling velocities are sufficiently low for the solids to be completely suspended in the fluid. Consideration is now given to the far more complex problem of the flow of multiphase systems in which the composition of the mixture may vary over the cross-section of the pipe or channel furthermore, the components may be moving at different velocities to give rise to the phenomenon of slip between the phases. 

Multiphase systems containing solids, liquids and gases. 

Hewitt, G, F. tn Handbook of Multiphase Systems. G, Hetsroni ed. (McGraw-Hill, New York, 1982). 2-25. 

Multiphase systems, solids, liquids and gases 181 Multiple stage pumps, vacuum producing 365 Multistage compression 353 ----number of stages 354... 

Energy and natural resources processing. NSF should sustain its support of basic research in complex behavior in multiphase systems, catalysis, separations, dynamics of solids transport and handling, and new scale-up and design methodologies. 

Example 4.2 used the method of false transients to solve a steady-state reactor design problem. The method can also be used to find the equilibrium concentrations resulting from a set of batch chemical reactions. To do this, formulate the ODEs for a batch reactor and integrate until the concentrations stop changing. This is illustrated in Problem 4.6(b). Section 11.1.1 shows how the method of false transients can be used to determine physical or chemical equilibria in multiphase systems. 

We have considered thermodynamic equilibrium in homogeneous systems. When two or more phases exist, it is necessary that the requirements for reaction equilibria (i.e., Equations (7.46)) be satisfied simultaneously with the requirements for phase equilibria (i.e., that the component fugacities be equal in each phase). We leave the treatment of chemical equilibria in multiphase systems to the specialized literature, but note that the method of false transients normally works quite well for multiphase systems. The simulation includes reaction—typically confined to one phase—and mass transfer between the phases. The governing equations are given in Chapter 11. 

Martin, O. and Averous, L. 2001. Polyjlactic add) Plasticization and properties of biodegradable multiphase system. Polymer 42 6209-6219. 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

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