Molecular flow, single-phase

Leaving aside the difficult question of whether this model holds for multiphase flows, we still have the problem of determining in terms of the computed properties of the flow. The reader should appreciate that choosing an effective viscosity for a multiphase flow is much more complicated than just adding a turbulence model as done in single-phase turbulent flows. Indeed, even for a case involving two fluids (e.g., two immiscible liquids) for which the molecular viscosities are constant, the choice of the effective viscosities is not obvious. For example, even if the mass-average velocity defined by... 

These definitions rely upon the molecular mean free path in a single-phase flow, surface tension effects and flow patterns in two-phase flow applications. In recent studies in minichannels the hydraulic diameter ranges from 100 /jm to 2-3 mm. The channel cross sections were either circular or rectangular and much of the research concerned boihng. Commonly, classical correlations have been used with or without modifications to predict flow boihng results in minichannels. However agreement was poor and the need for new correlations was evident. 

FIGURE 14.11 Axial and radial Peclet numbers for single-phase flow of a gas or liquid through a packed bed of spherical particles. The limits of molecular diffusion are shown hy sohd hues that represent Pe = Re Sc Xg/g, where Xg = bed tortuousity =1.4 and Eg = bed voidage = 0.4 (Sherwood et al., 1975). 

The use of microscale reactors is not confined to single-phase systems. Both striated and droplet flows of two-phase liquid mixtures have been studied, as have suspensions of solid particles. It seems that almost any chemistry can be used at the microscale. Effectiveness factors in heterogeneous catalysis will be nearly 1.0 since diffusion distances are so small. As pointed out below, rapid molecular diffusion gives nearly instantaneous cross-channel mixing and may cause significant axial mixing. 

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. 

The PPE/PS mixtures are considered classical examples of miscible polymer blends. Within the accessible range of temperatures, single phase melts have been observed with the size of homogeneity below 20 nm. Dynamic flow behavior of PPE/PS blends, with the molecular weight ratio MW(PS)/MW(PPE) = 1, was studied in a wide range of temperatures and compositions [Prest and Porter, 1972]. The authors assumed additivity... 

Pressure-Driven Single-Phase Gas Flows, Table 2 Molecular weight and dynamic viscosity under standard conditions (po = 101,325 Pa and To = 273.15 K) estimated from a VHS or a VSS model (Data fiorn Bird [2]) with corresponding values of cu and a... 

By definition, miscible polymer blends are single-phase mixtures. Miscibility depends on the molecular weight, concentration, temperature, pressure, deformation rate, etc. Flow of these systems can be compared to that of solutions of low molecular weight, miscible components, or to flow of mixtures of polymeric fractions. Both models are far from perfect, but they serve to illustrate the basic behavior of miscible systems. In the first case one can learn about the effects of the thermodynamic interactions between chemically different components on the flow behavior. In the second case, it is the effect of molecular weight and molecular weight distribution that can be observed. 

Formerly, membrane materials consisted mainly of barrier typ>es, sometimes called permeable or semipermeable, in which the gases flowed into and through the pores and interstices, which were of molecular dimensions for example, measured in angstroms. There is the use of materials similar to molecular-sieve adsorbents, for example. For single-phase liquid systems or solutions, the processes may be referred to by the terms dialysis and osmosis, whereas for gas-liquid, gas-solid, or liquid-solid separations, the terms micro- and ultrafiltration are more appropriate. 

Molecular Dynamics Simulation Method Multiscale Modeling and Numerical Simulations Non-Continuous Approaches Pressure Driven Single Phase Gas Flows Spectral Methods... 

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