Laminar mechanisms

Striation thickness Average distance between adjacent interfaces of materials to be mixed by a laminar mechanism. 

A related concept is that of laminar mechanisms, introduced by Sinanoglu (1975), Sinanoglu and Lee (1978), and Lee and Sinanoglu (1981). These mechanisms can be constructed a priori (i.e., without regard to a specific set of mechanism steps) given the number of catalysts involved. Sellers (1971, 1972) also presented procedures for construction of a priori mechanisms for certain chemical systems. In both these instances of mechanism construction, the focus was the a priori enumeration of potential pathway shapes, without regard to the specific reactions permitted by the system. These techniques are thus not applicable to the synthesis of pathways or mechanisms from a given set of reaction steps. 

Lee, L.-S., and Sinanoglu, O., Reaction mechanisms and chemical networks—Types of elementary steps and generation of laminar mechanisms. Z. Phys. Chem. 124, 129-160 (1981). 

From the above the maximum stable drop size can be estimated. There will be smaller drops, but in theory no drops larger than this. No data on distribution as yet exist for laminar breakup. Figure 7-28 compares drop size by laminar mechanisms with those calculated for turbulent flow. Smaller droplets are expected for laminar versus turbulent flow at the same energy dissipation rate. 

The Standard covers bar, plates, sheets, strip, structural shapes rolled stock, pipes, sheets with laminar coating and strip of carbon, alloyed and electrical steels and sets up nondestructive magnetic method of mechanical and service properties and microstructure control. 

Mechanical Properties. The stain resistance of paints is directly related to their porosity. Therefore fillers that help to reduce porosity, ie, those with low surface areas, wide size distribution, and laminar shapes, contribute to stain resistance. 

The criterion of maintaining equal power per unit volume has been commonly used for dupHcating dispersion qualities on the two scales of mixing. However, this criterion would be conservative if only dispersion homogeneity is desired. The scale-up criterion based on laminar shear mechanism (9) consists of constant > typical for suspension polymerization. The turbulence model gives constant tip speed %ND for scale-up. 

Fig. 30. Mechanism for laminar blending in Kenics static mixer (a) after one element, (b) two elements, (c) three elements, (d) four elements, and (e) five...

Thickness of the laminar layer is deterrnined both by the need to reproduce fine detail in the object and by the penetration depth of the actinic laser light into the monomer bath (21,76). There is thus a trade-off between precision of detail in the model and time required for stereohthography, ie, the number of layers that have to be written, and an optimum Light-absorbing initiator concentration in the monomer bath corresponding to the chosen layer thickness. Titanocene-based initiators, eg, bis-perfluorophenyltitanocene has been recommended for this apphcation (77). Mechanistic aspects of the photochemistry of titanocenes and mechanisms of photoinitiation have been reviewed (76). 

TurbulentPremixedFlames. Combustion processes and flow phenomena are closely coimected and the fluid mechanics of a burning mixture play an important role in forming the stmcture of the flame. Laminar combusting flows can occur only at low Reynolds numbers, defined as... 

Turbulent Diffusion FDmes. Laminar diffusion flames become turbulent with increasing Reynolds number (1,2). Some of the parameters that are affected by turbulence include flame speed, minimum ignition energy, flame stabilization, and rates of pollutant formation. Changes in flame stmcture are beHeved to be controlled entirely by fluid mechanics and physical transport processes (1,2,9). 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

Example 4 Plnne Poiseuille Flow An incompressible Newtonian fluid flows at a steady rate in the x direction between two very large flat plates, as shown in Fig. 6-8. The flow is laminar. The velocity profile is to he found. This example is found in most fluid mechanics textbooks the solution presented here closely follows Denn. 

For laminar flow of power law fluids in channels of noncircular cross section, see Schecter AIChE J., 7, 445 48 [1961]), Wheeler and Wissler (AJChE J., 11, 207-212 [1965]), Bird, Armstrong, and Hassager Dynamics of Polymeric Liquids, vol. 1 Fluid Mechanics, Wiley, New York, 1977), and Skelland Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). 

Concentration and temperature differences are reduced by bulk flow or circulation in a vessel. Fluid regions of different composition or temperature are reduced in thickness by bulk motion in which velocity gradients exist. This process is called bulk diffusion or Taylor diffusion (Brodkey, in Uhl and Gray, op. cit., vol. 1, p. 48). The turbulent and molecular diffusion reduces the difference between these regions. In laminar flow, Taylor diffusion and molecular diffusion are the mechanisms of concentration- and temperature-difference reduction. 

First, a mechanism is assumed whether completely mixed, plug flow, laminar, with dispersion, with bypass or recycle or dead space, steady or unsteady, ana so on. Then, for a differential element of space and/or time the elements of a conservation law. 

The second important mechanism in filtration is that of settling. From Stoke s law of laminar particle settling, the settling velocity of a particle is given by ... 

The mechanism of flame propagation into a stagnant fuel-air mixture is determined largely by conduction and molecular diffusion of heat and species. Figure 3.1 shows the change in temperature across a laminar flame, whose thickness is on the order of one millimeter. 

What are the mechanisms by which slow, laminar combustion can be transformed into an intense, blast-generating process This transformation is most strongly influenced by turbulence, and secondarily by combustion instabilities. A laminar-flame front propagating into a turbulent mixture is strongly affected by the turbulence. Low-intensity turbulence will only wrinkle the flame front and enlarge its surface area. With increasing turbulence intensity, the flame front loses its more-or-less smooth, laminar character and breaks up into a combustion zone. In an intensely turbulent mixture, combustion takes place in an extended zone in which... 

At first glance, the science of vapor cloud explosions as reported in the literature seems rather confusing. In the past, ostensibly similar incidents produced extremely different blast effects. The reasons for these disparities were not understood at the time. Consequently, experimental research on vapor cloud explosions was directed toward learning the conditions and mechanisms by which slow, laminar, premixed combustion develops into a fast, explosive, and blast-generating process. Treating experimental research chronologically is, therefore, a far from systematic approach and would tend to confuse rather than clarify. 

We recall from our earlier discussion of chaos in one-dimensional continuous systems (see section 4.1) that period-doubling is not the only mechanism by which chaos can be generated. Another frequently occurring route to chaos is intermittency. But while intermittency in low dimensional dynamical systems appears to be constrained to purely temporal behavior [pomeau80], CMLs exhibit a spatio-temporal intermittency in which laminar eddies are intermixed with turbulent regions in a complex pattern in space-time. 

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