Phases, slip between

The volume fraction, sometimes called holdup, of each phase in two-phase flow is generally not equal to its volumetric flow rate fraction, because of velocity differences, or slip, between the phases. For each phase, denoted by subscript i, the relations among superficial velocity V, in situ velocity Vj, volume fraclion Rj, total volumetric flow rate Qj, and pipe area A are... 

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. 

As shown in Section I, very little is known about predicting liquid-liquid flow patterns and calculating pressure drops, holdups, and interfacial areas however, some estimates can be made by assuming no slip between the phases, using... 

In the LHF models, it is assumed that droplets are in dynamic and thermodynamic equilibrium with gas in a spray. This means that the droplets have the same velocity and temperature as those of the gas everywhere in the spray, so that slip between the phases can be neglected. The assumptions in this class of models correspond to the conditions in very thin (dilute) sprays. Under such conditions, the spray equation is not needed and the source terms in the gas equations for the coupling of the two phases can be neglected. The gas equations, however, need to be modified by introducing a mixture density that includes the partial density of species in the liquid and gas phases based on their mass fractions. Details of the LHF models have been discussed by Faeth.l589]... 

If Q and Q2 are the volumetric rates of feed of the light and heavy liquids respectively, on the assumption that there is no slip between the liquids in the bowl and that the same, then residence time is required for the two phases, then ... 

The. Homogeneous Equilibrium Model (HEM) assumes uniform mixing of the phases across the. pipe diameter, no phase slip (mechanical equilibrium), thermal equilibrium between, the..phases and complete vapour/ liquid, equilibrium. "Homogenous" in the context of the HEM refers to the flow in the vent line. 

A system in which the liquid and gas/ vapour phases are uniformly mixed. In pipe flow, "homogeneous" also implies no slip between the phases and complete vapour/ liquid equilibrium (see 9 3 1)... 

Isothermality in this reactor is difficult to maintain however, wall heat transfer is better than for fixed-bed reactors. Salt or sand baths may be required for isothermality. Residence-time distributions for all three phases can be measured accurately. At low velocity, slip between phases is a problem, but more... 

It also must be kept in mind that all consistent two-phase momentum equations should reduce to single-phase equations if there is no slip between the two phases or the volume fraction of dispersed phase is zero. 

When vapour and liquid flow downwards in a vertical tube, the slip between the two phases is reduced because of the buoyancy. This leads to a deterioration in the heat transfer, and according to measurements made by Pujol [4.90] using the refrigerant R113, the heat transfer coefficient adown of the downward flow is smaller by a factor 0.75 than that for upward flow aup... 

This model assumes perfect mixing inside the element, as the particles enter the cell with different concentrations but leave the cell with a homogeneous concentration. Moreover, inertia is neglected, as well as slipping, between the solid and liquid phases. In Eq. (13), the fluxes can be expressed using the following equations ... 

The information of the velocity slip between the particles and gas is important to assist the determination of particle velocity since the isokinetic condition refers to gas phase and, in many cases, only the velocity information of gas phase is available. The general relationship between the particle velocity and gas phase velocity is governed by the momentum equation of particles. For the linear motion of a spherical particle, the governing equation takes the form (Fan and Zhu, 1997)... 

The simplest mechanical design basis possible is a separator with a homogeneous inflow in which gas and liquid are separated, a weir plate to provide suitable safety criteria for the oil phase, and three outlets for the respective (clean) water, oil, and gas phases. The traditional simplified view is to assume plug flow in the liquid and gas phase, and slip between the liquid and gas, thus neglecting inlet effects and the possible slip between oil and water. Furthermore, Stokes law is used for mass transport between the bulk phases (assuming rapid coalescence). This view is depicted in Fig. 6. 

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