Flow regime equilibrium

In order to obtain a qualitative view of how the transition regime differs from the continuum flow or the slip flow regime, it is instructive to consider a system close to thermodynamic equilibrium. In such a system, small deviations from the equilibrium state, described by thermodynamic forces X, cause thermodynamic fluxes J- which are linear functions of the (see, e.g., [15]) ... 

It is recommended by DIERS12,81 that an open test cell with a 2.5 mm diameter x 100 mm long vent is used (see Figure A2.8). This diameter has. been chosen to give the best discrimination between inherently foamy and non-inherently foamy behaviour and relates to the use of a test cell with a diameter of approximately 70 mm. The use of a 100 mm long vent ensures that two-phase flow will flash to equilibrium (see 9.3.1) which simplifies any computer modelling of the test to determine the flow regime. 

Because there are no flows at equilibrium, where the forces are zero,. 7/ (0) = 0. We will explore the regime, not too far from equilibrium, where the higher-order (h.o.) terms can be ignored, giving... 

In Ref. [120] the first time has been reported on flow-induced phase separation in polymer blends. When PS/PVME blends were exposed to shear or extensional flow at lower temperatures, 20 to 30 K below the equilibrium coexistence temperature, phase separation was observed in both flow regimes. As the authors suggest, the stress, rather than the deformation rate, appears to be the most important parameter in flow-induced phase separation. 

For gas-particle flows, fhe mosf obvious manifestation of non-equilibrium behavior is particle trajectory crossing (PTC) at KUp = oo (i.e. no collisions). PTC occurs in the very-dilute-flow regime ( p c 1) and is most easily identified when fhe granular femper-afure is null (Map = c ). An example of PTC is shown in Figure 1.4. The panel on fhe... 

Steady states for flow and for chemistry are different concepts and are often confused steady-state flow means constant directions and magnitudes of velocities steady-state chemistry means constant concentration distributions. Local equilibrium can possibly maintain a chemical steady state for reactive constituents in a transient flow regime (e.g., Ca2+ and HCCTj" in a Karst aquifer). However, if kinetics plays a significant role, e.g., the dissolution rate of feldspars or oxidation of organic carbon, then the chemical state in a transient flow field depends on competing factors of kinetic rates and velocity changes. Thus, chemical steady state may be achieved for some constituents but not others. 

If T terface and Tbuik replace Ca, equilibrium and Ca, bulks respectively, in the definition of the dimensionless profile P, and the thermal diffusiv-ity replaces a. mix. then the preceding equation represents the thermal energy balance from which temperature profiles can be obtained. The tangential velocity component within the mass transfer boundary layer is calculated from the potential flow solution for vg if the interface is characterized by zero shear and the Reynolds number is in the laminar flow regime. Since the concentration and thermal boundary layers are thin for large values of the Schmidt and Prandtl... 

Ejfect of flow regime experienced The speed with which a metal s surface comes to equilibrium with a water, and in some cases the characteristics of the corrosion product which is developed, can depend on the flow regime that it has experienced. At present, the standard sit-and-soak test defines static conditions. However, if this mechanism was thought potentially to be significant, different flow regimes could be incorporated into an ageing procedure to cover this. 

Pressure oscillations as high-density liquid impinges upon hot channel walls were also recognized as a potential problem, not only in the two-phase flow regime, but also at pressures and temperatures higher than critical, since there is no assurance that phase equilibrium w ill always prevail throughout the flow channels. 

The standard convection-diffusion equations rely on the assumption of local thermal equilibrium. For gas flow, this means that a Maxwell-Boltzmann distribution is assumed for the velocity of the particles in the frame-of-reference comoving with the fluid. When gas flow in microreactors at high temperature or low pressure is considered, this assumption may break down. The principle quantity determining the flow regime of gases and deviations from the standard continuum description is the Knudsen number, defined as... 

In the laminar flow regime (/ epboundary layer treatment does not hold. In gaseous phase, mass transfer resistance is not an important step, since, as discussed before, ScRe becomes rather small and fluid phase is considered to be in equilibrium with the surface of the particles in this range. In liquid phase mass transfer, however, because of the magnitude of the Sc number, ScRcp becomes larger than 10 even though Rcp is small and concentration boundary layer on the surface of the particle must be considered. 

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