Velocity relative between phases

In reality, the slip velocity may not be neglected (except perhaps in a microgravity environment). A drift flux model has therefore been introduced (Zuber and Findlay, 1965) which is an improvement of the homogeneous model. In the drift flux model for one-dimensional two-phase flow, equations of continuity, momentum, and energy are written for the mixture (in three equations). In addition, another continuity equation for one phase is also written, usually for the gas phase. To allow a slip velocity to take place between the two phases, a drift velocity, uGJ, or a diffusion velocity, uGM (gas velocity relative to the velocity of center of mass), is defined as... 

When two-phase flow is compared to the single-phase case for the same flow rate of an individual phase, it is an experimental fact that the frictional pressure drop will always be higher for two-phase flow. This higher pressure drop may be caused by the increased velocity of the phases due to the reduction in cross-sectional area available for flow, and also to interactions occurring at the extended gas-liquid interface which exists in most of the possible flow patterns. It is equally true that the heat flux will always be higher for two-phase flow than for the same situation in single-phase flow with the same liquid flow rate. On the other hand, mass transfer will depend upon both the extent of the gas-liquid interface and the relative velocity between the two flowing phases. 

Mass transfer between phases Relative phase velocities, C, P, T Important... 

Transfers between phases Temperature, concentration, and relative velocities of phases Indirect... 

The word electrokinetic implies the combined effects of motion and electrical phenomena. Specifically, our interest in this chapter centers on those processes in which a relative velocity exists between two parts of the electrical double layer. This may arise from the migration of a particle relative to the continuous phase that surrounds it. Alternatively, it could be the solution phase that moves relative to stationary walls. 

Relatively, increasing the interface area, i.e.. enhancing the dispersal of a liquid or a solid, is a measure that can be employed widely, and, in fact, has been applied successfully in a number processes, such as spray drying and cooling etc. However, it is also limited to an extent. For example, spray drying can only be applied in the production of powdery products, and excessive dispersion may give rise to difficulties in powder collection etc while spray cooling is only applicable to the cases where moisture increase is permitted. On the other hand, in common equipment systems, the maximum relative velocity between phases is mostly just equal to the terminal velocity, which... 

All the results mentioned above lead to a simple and clear conclusion increasing the relative velocity between phases is one of the most effective approaches to enhance transfer processes. 

In traditional processing devices, increase in relative velocity is limited by various factors. For example, in column equipment the operating velocity must be smaller than that of liquid-flooding the limitation of relative velocity in common gas-solid or liquid-solid suspensions is the terminal velocity, etc. It seems that other approaches must be found in order to raise the relative velocity between phases to higher levels. 

The efforts to search for approaches to raising relative velocity between phases has led to the development and/or application of impinging stream contactors, and also some other devices. 

All the researches, developments, and applications of IS, RPB, and IJ show the extreme importance of increasing relative velocity for enhancing transfer between phases. 

In the impinging streams of gas-liquid systems, high relative velocity between phases and collision between droplets favor surface renewing of droplets, resulting in reduced liquid film resistance and thus increased overall mass transfer coefficient. 

Round the outlets of the nozzles. This region has a very short residence time although its contribution to absorption is not negligible because both the driving force for the reaction s) and the relative velocity between phases are considerably large. 

As mentioned earlier, in gas-continuous impinging streams heat and mass transfer between phases are enhanced efficiently mainly by the following factors (1) Very high relative velocity between phases round the impingement plane, even higher than in common devices by several tens of times (2) Oscillation movement of particles or... 

The state of the dynamic balance between mobile phase processes in every chromatographic column is governed by the flow velocity relative to the fundamental velocity uc, that is, by [16]... 

In previous work [15,17,28] we have evaluated the relation between the flow ratio co, the pore size, and the ionic strength of the solution experimentally, by means of size-exclusion electrochromatography (SEEC). In SEEC the transport rates of the (neutral) macromolecules depend direcdy on co. As in conventional, pressure-driven SEC, the separation in SEEC is based on the differential accessibility of the (stagnant) mobile phase in the pores of the particles for macromolecules of different sizes. However, with increasing pore flow ratio in SEEC, the velocity difference between the mobile-phase fractions inside and outside the particles decreases. The retention ratio x (the retention time relative to a low-molecular-mass marker) for a probe molecule in SEEC is given by... 

Slip, or relative velocity between phases, occurs for vertical flow as well as for horizontal. No completely satisfactory, flow regime-independent correlation for volume fraction or holdup exists for vertical flow. Two frequently used flow regime-independent methods are those by Hughmark and Pressburg AIChE J., 7, 677 [1961]) and Hughmark Chem. Eng. Prog., 58[4], 62 [April 1962]). Pressure drop in upflow may be calculated by the procedure described in Hu mark Ind. Eng. Chem. Fundam., 2, 315-321 [1963]). The mechanistic, flow regime-based methods are advisable for critical applications. 

The term (d e )/(Z)vv ) = dAu/Dy, where Au = (e/v) d, represents the Peclet number for fine-scale drop-turbulence interactions. In the case of larger droplets there is a significant velocity difference between the droplet and the continuous phase then the approach presented in Section 4.2 and employing the relative velocity Reynolds number, Eq. (32), can be used, resulting in the following relation ... 

The Earth s mantle is peridotitic in composition and is significantly depleted in silica relative to primitive chondrites. Seismological evidence shows that the mantle is layered and can be divided into an upper and lower mantle, separated by a transition zone at 400-660 km depth. Above the transition zone the mantle is dominated by olivine and orthopyroxene with minor garnet and clinopyroxene. The lower mantle is made up of phases Mg- and Ca-perovskite and magnesiowustite. Seismic velocity contrasts between the upper and lower mantle are thought to reflect the ph ase transformations between the two and are not related to differences in bulk chemical composition. The lower mantle is separated from the outer core by the D" layer, a hot thermal boundary layer of enigmatic composition. 

VELOCITIES IN DIFFUSION. Several velocities are needed to describe the movements of individual substances and of the total phase. Since absolute motion has no meaning, any velocity must be based on an arbitrary state of rest. In this discussion velocity without qualification refers to the velocity relative to the interface between the phases and is that apparent to an observer at rest with respect to the interface. 

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