Continuous fluid phase

Many investigators have studied diffusion in systems composed of a stationary porous solid phase and a continuous fluid phase in which the solute diffuses. The effective transport coefficients in porous media have often been estimated using the following expression ... 

I. Continuous fluid phases with a well-defined interface 1, 2, 3,4, 5,6,... 

II. Continuous fluid phases with complex interfaces and fluid phase interchange none. 

IV. One continuous fluid phase and one discrete fluid phase 10,11,12, 13. 

This regime is characterized by the presence of two continuous fluid phases and an interface which can easily be described. The term separated flows is frequently employed to describe these situations in both horizontal and vertical systems. Some flow patterns in Regime I are advantageous for transferring heat between the tube wall and the fluid mixture or for carrying out two-phase reactions. The special case of laminar-laminar flow is included in this regime, and two studies seem to be of interest, Byers and King (B7) and Bentwich and Sideman (B3). 

This regime is characterized by the presence of one continuous fluid phase and one discrete fluid phase in tubular systems. The existence of the discrete phase generates a large interfacial area per unit tube volume for all flow configurations included in this regime. For that reason, Regime IV is of pragmatic interest when interphase heat and mass transfer are of key importance. 

The Hydrodynamic Theory of fluidized bed stability was proposed by Foscolo and Gibilaro who adapted the stability principle of Wallis. They postulated that a fluidized bed is composed of two interpenetrating fluids. One fluid is the gas phase, and the solids phase is also considered as a continuous fluid phase. In this theory, voidage disturbances in the bed propagate as dynamic and kinetic waves. The stability of the fluidized bed depends upon the relative velocities of these two waves. The velocities of the kinetic wave (ue) and the dynamic wave (nj are ... 

In Chapter 12 we will consider multiphase reactors in which drops or bubbles carry one phase to another continuous fluid phase. In fact, these reactors frequently have a sohd also present as catalyst or reactant or product to create a three-phase reactor. We need the ideas developed in this chapter to discuss these even more complicated reactors. 

Migration (secondary) the movement of the hydrocarbons as a single, continuous fluid phase through water-saturated rocks, fractures, or faults followed by accumulation of the oil and gas in sediments (traps, q.v.) from which further migration is prevented. 

The principles and basic equations of continuous models have already been introduced in Section 6.2.2. These are based on the well known conservation laws for mass and energy. The diffusion inside the pores is usually described in these models by the Fickian laws or by the theory of multicomponent diffusion (Stefan-Maxwell). However, these approaches basically apply to the mass transport inside the macropores, where the necessary assumption of a continuous fluid phase essentially holds. In contrast, in the microporous case, where the pore size is close to the range of molecular dimensions, only a few molecules will be present within the cross-section of a pore, a fact which poses some doubt on whether the assumption of a continuous phase will be valid. 

VestolitGmbH/HuelsAG Ethyl chloride Ethylene and hydrogen chloride Continuous fluid-phase conversion to ethyl chloride with catalyst NA NA... 

When a component of a continuous fluid phase (a liquid solution or a gas mixture) is present in nonuniform concentration, at uniform and constant temperature and pressure and in the absence of external fields, that component diffuses in such a way as to tend to render its concentration uniform. For simplicity, let the concentration of a given substance be a function of only one coordinate x, which we shall take as the upward direction. The net flux Z] of the substance passing upward past a given fixed point Aq (i.e., amount per unit cross-sectional area per unit time) is under most conditions found to be proportional to the negative of the concentration gradient ... 

Photocatalytic reactions are promoted by solid photocatalyst particles that usually constitute the discrete phase distributed within a continuous fluid phase in the reactor. Therefore, at least two phases, that is, liquid and solid, are present in the reactor. The solid phase could be dispersed (SPD) or stationary (SPS) within the reactor. SPD photoreactors may be operated with the catalyst particles and the fluid phase(s) agitated by mechanical or other means. Depending on the means of agitation, the photoreactor resembles that of slurry or fluidized bed reactors. In numerous investigations, an aqueous suspension of the catalyst particles in immersion or annular-type photo reactors has been used. However, the use of suspensions requires the... 

Microscale fluid turbulence is, by deflnition, present only when the continuous fluid phase is present. The coefficients Bpv describe the interaction of the particle phase with the continuous phase. In contrast, Bpvf models rapid fluctuations in the fluid velocity seen by the particle that are not included in the mesoscale drag term Ap. In the mesoscale particle momentum balance, the term that generates Bpv will depend on the fluid-phase mass density and, hence, will be null when the fluid material density (pf) is null. In any case, Bpv models momentum transfer to/from the particle phase in fluid-particle systems for which the total momentum is conserved (see discussion leading to Eq. (5.17)). 

Capillary rarefaction. The continuous fluid phase filling the porous space between deformed bubbles has a common concave boundary with these bubbles. It follows that the local pressure Pi in the liquid phase is less than the pressure Pg in the gaseous phase and these variables are related by... 

Pore Size. If aggregated particles make up a continuous phase, and the voids are filled with a continuous fluid phase, an important characteristic is the (average) pore size, i.e., the width of the channels between particles. This applies to powders and to particle gels. The pore size greatly affects... 

Milk is heterogeneous, consisting of a continuous fluid phase and fat droplets which can be visualized microscopically. It is a heterogeneous mixture of liquids since its contents are both visualizable and variable in composition. 

Continuous fluid phases with a well-deflned interface. This case, not particularly the most important, is nonetheless convenient to start with since the interface between phases formed by vertical annular flow without droplets gives us an area for mass transport that is easy to determine."... 

All of these materials conduct by virtue of ionic mobility in a continuous fluid phase and they are solid by virtue of the continuous polymer phase. 

In the area of chemical engineering there is a big variety of apparatus and reactors in which a stagnant or moving dispersed phase (fluid or solid particles) is surrounded by a moving or nonmoving continuous fluid phase. In Table 3.4-1 some examples are presented. 

Observations are unaffected by refraction at the fluid interface for measurements in the continuous fluid phase, but they are affected if the velocity is determined in the discrete phase (velocity field inside microdrops). Image resolution close to the microchannel walls and in the proximity of the fluid interface is limited by reflections and aperture effects, regions that should be masked before performing the cross-correlation. Several pPIV results have been obtained in segmented gas-liquid flows [50,80,86[. For steady or periodic flows, two-dimensional velocity... 

Q. Volumetric flow rate of the continuous fluid phase (m)... 

Table 7. Heterophase Polymerization Techniques with Continuous Fluid Phases... 

It has been shown in section 4.7.1 that there is quite a variety of three-phase systems that are used for carrying out chemical reactions. The large number of possible configurations that are used in practice all have in common that there is one continuous fluid phase (mostly a liquid, sometimes a gas), that separates the two other phases. In most cases the "isolated phases are dispersed, but one or both of them could also be continuous. Two situations can be distinguished (see section 4.7.1) ... 

Particles, whether solid or fluid, are usually dispersed within a fluid. The fluid phase that contains the particles is referred to as the continuous phase, sinee it is possible to move throughout that phase while remaining within it. The gap between the density of the particles, denoted by p, and the density /y of the eontinuous fluid phase is a key parameter of the particulate media under consideration, because this gap either intervenes directly in the study of mechanical separation (as in the case of gravitational or centrifugal separation or in fluidization) or because the mechanical stabihty of a deposited granular medium depends on it. The third essential parameter is the size > of the particles. The processes considered in this chapter are associated with a flow of the continuous fluid phase. The dynamic viscosity, of the continuous fluid phase is, therefore, also a parameter to be taken into account. Lastly, for fluid particles, the flow of the continuous phase generates a flow inside the fluid particles and, in that case, it is also necessary to introduce the dynamic viscosity inside the dispersed fluid particles. 

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