Fluid flow, multiphase systems

Di Felice, R., 1994. The voidage function for fluid-particle interaction systems. International Journal of Multiphase Flow, 20, 153-159. 

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. 

The on-line measurement of viscosity under plant conditions poses particular difficulties. This is due to the wide range of viscosities that can occur within a process plant, to the difficulty of obtaining reliable measurements (particularly for non-Newtonian fluids) and to the accuracy that is often required (e.g. better than within 1 per cent for lubricating oils). Variables which can affect the measured viscosity are the temperature, pressure and rate of flow of the sampled stream— quite apart from the normal errors that can occur in any similar instrument (e.g. due to variations in supply voltage and frequency, sample contamination, sample not being representative of the bulk fluid, etc.). Automatic temperature compensation is always required and, in the case of multiphase systems, the difficulty of obtaining a representative sample is considerable (see Section 6.9). In this instance... 

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

The above-described mixers are essentially low-viscosity devices. In many operations where the viscosity is high, when dealing with concentrated multiphase gas-liquid-solid binary or tertiary systems, or when liquid-to-solid phase transformation occurs during mixing, novel equipment designs are needed to intensify the heat/mass transfer processes. The multiphase fluids also represent an important class of materials that have microstructure developed during processing and subsequently frozen-in, ready for use as a product. To deliver certain desired functions, the control of microstructure in the product is important. This microstructure is developed in most cases by the interaction between the fluid flow and the fluid microstructure hence, uniformity of the flow field is important. 

The front-tracking method is only one example of computational tools that can be used in analysis and design of microfluidic systems. The computational methods for multiphase/fluid flows have been matured enough that they can be safely used as a design tool in microfluidics. In addition, they can be also very useful to discover or understand new flow physics emerging from the miniaturization of flow systems. 

The heat transfer characteristics in multiphase systems depend strongly on the hydrodynamics, which vary significantly with particle properties. The particle size, size distribution, and shape affect the particle and fluid flow behavior through particle-fluid and particle-particle interactions. A discussion of the hydrodynamic characteristics of packed and fluidized beds follows. 

An essential element in the progress of research and engineering of multiphase flow systems and specifically particle-fluid flow systems is improved instrumentation for measurements. They make possible validation of basic concepts in the formation, determination of design parameters, and design of systems. 

Further consequences of the yield stress [i.e., the plug flow] are (i) a drastic reduction of the extrudate swell, B = d/d (d is diameter of the extrudate, d that of the die) [see, e.g., Crowson and FoUces, 1980 Utracki et al, 1984], and (ii) significant increase of the entrance-exit pressure drop, Pg (also known as Bagley correction). For single-phase fluids, these parameters have been related to elasticity by molecular mechanisms [Tanner, 1970 Cogswell, 1972 Laun and Schuch, 1989]. However, in multiphase systems, both B and P depend primarily on the inter-domain interactions and morphology, not on deformation of the macromolecular coils. Thus, in multiphase systems [i.e., blends, filled systems, or composites], only direct measures of elasticity, such as that of Nj, or G should be used. It is customary to plot the measure of the elastic component versus that of the shear components, viz., vs. 

Chemical engineers intuitively work under the assumption that to improve the mass-transfer characteristics of a gas-liquid reactor, more energy must be dissipated in the fluids to effect a more vigorous contacting of the fluids. For singlephase flow in turbulent systems, this concept has become known as the Chilton-Colburn analogy. Another example of the coupling of hydrodynamics and mass transfer in multiphase systems is the common correlation of the mass transfer and the power input for stirred-tank reactors. 

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