Principle of single-phase

H.E. Exner. Principles of single phase sintering. Reviews on Powder Metallurgy and Physical Ceramics, 1 1-237, 1979. 

Liu, S. Masliyah, J.H. Principles of Single-Phase Flow Through Porous Media in Suspensions, Fundamentals and Applications in the Petroleum Industry, Schramm, L.L. (Ed.), American Chemical Society Washington, 1996, pp. 227-286. 

Principles of Single-Phase Flow Through Porous Media... 

Exner, H.E. (1979) Principles of Single-Phase Sintering, in Reviews on Powder Metallurgy and Physical Ceramics 1, 1-251. Freund Pub. House, Tel-Aviv, Israel. Not just ceramics a very useful review. German, R.M. (1996) Sintering Theory and Practice. Wiley, New York. The standard reference. Not only concerned with ceramics. 

Fig. 15 The newly introduced principle of single amino acid chelators (42, SAAC) which can directly be subjected to automated solid phase peptide syntheses...

The principle of similarity, i.e. the use of dimensionless groups maintained constant in the course of scale-up, has been characterized even in case of single phase catalytic reactor as limited to simple situations in chemical reactor scale-up. If the overall phenomenon is complex, as in most practical cases, more than one dimensionless group should be kept constant, sometimes leading to contradictory demands. This is certainly true in all practical cases of multiphase packed bed reactors, where also the compromise of weighing the particular effect is only of limited value. Therefore, this method in practice cannot be applied for scale-up of multiphase catalytic reactors. 

It is based on the simplified kinetic equation for dilute gases suggested by Bhatnagar et al. [119]. Both approaches will first be described in the context of single-phase flow. In principle, one could also treat a bubble as a void and use an artificial force field as described by Derksen and Van den Akker [124] to impose the boundary conditions at the surface of the bubble. This would permit one to use the single phase LBM to simulate bubble motion in a liquid. 

When two or more reactants are brought together in a single phase, where they will react with each other, it is often not possible to separate the effects of mixing from chemical reaction, either in space or in time. In exceptional cases it may be possible to mix the reactants at a sufficiently low temperature, where no reaction takes place, and heat the mixture until the reaction starts. This may be done in pure batch reactors, but these are rarely applied in industry. In most technical processes chemical reactions are carried out in such a way that at least one of the reactants is introduced into a mixture where the reaction is already taking place. In these situations the rate of the chemical reaction is in principle dependent on the rate of mixing. There are two well known examples of single phase reactors where this applies ... 

In part I most of the fundamental theory of single phase reactive flows is presented. In part II most of the fundamental theory of multiphase reactive flows is presented. In both parts a few numerical model simulation application examples are given to elucidate the link between theory and applications. In part III the chemical reactor equipment to be modeled are described. Several engineering models are introduced and discussed. A survey of the frequently used numerical methods, algorithms, and schemes is provided. A few practical engineering applications of the modeling tools are presented and discussed. The working principles of several experimental techniques employed in order to get data for model validation are outlined. 

Since the kW developed by a 3-0 winding is 50% more than by a 2-0 winding for the same value of stator current /, the economics of this principle is employed in an induction motor for general and industrial use. As standard practice, therefore, in a multi-phase system, only 3-0 induction motors are manufactured and employed, except for household appliances and applications, where mostly single-phase motors are ttsed. 

We attempt here to describe the fundamental equations of fluid mechanics and heat transfer. The main emphasis, however, is on understanding the physical principles and on application of the theory to realistic problems. The state of the art in high-heat flux management schemes, pressure and temperature measurement, pressure drop and heat transfer in single-phase and two-phase micro-channels, design and fabrication of micro-channel heat sinks are discussed. 

These equations assume that the reactor is single phase and that the surroundings have negligible heat capacity. In principle, Equations (14.19) and (14.20) can be solved numerically using the simple methods of Chapters 8 and 9. The two-dimensional problem in r and is solved for a fixed value of t. A step forward in t is taken, the two-dimensional problem is resolved at the new t, and so on. 

When a two- or higher-phase system is used with two or more phases permeable to the solute of interest and when interactions between the phases is possible, it would be necessary to apply the principle of local mass equilibrium [427] in order to derive a single effective diffusion coefficient that will be used in a one-equation model for the transport. Extensive justification of the principle of local thermdl equilibrium has been presented by Whitaker [425,432]. If the transport is in series rather than in parallel, assuming local equilibrium with equilibrium partition coefficients equal to unity, the effective diffusion coefficient is... 

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