Forced-flow separation number

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

As Re increases, skin friction becomes proportionately less and, at values greater than about 20, flow separation occurs with the formation of vortices in the wake of the sphere. At high Reynolds numbers, the size of the vortices progressively increases until, at values of between 100 and 200, instabilities in the flow give rise to vortex shedding. The effect of these changes in the nature of the flow on the force exerted on the particle is now considered. 

Equations of motion presented here were developed for cases of uniform medium velocity and are oversimplified for many other cases regarding aerosols. In addition, evaluation of the equations for the trajectories of aerosol particles is sometimes impossible because of the difficulty in accurately describing the field of flow. Although for laminar flow Eq. 6.6 can be separated into x and y components, with increasing Reynolds number the nonlinearity of the resisting force prevents separation of the vector equation. Fortunately, most aerosol problems can be treated in the low-Reynolds-number regime. 

At very low Reynolds numbers no flow separation occurs. In Chapter 5 the Reynolds number was shown to represent a ratio of inertial and viscous forces. At very low Reynolds numbers the inertial forces are small, and the inertial terms of the momentum equation become negligibly small compared to the viscous terms. Under these conditions the drag force on a sphere of diameter D is found to be... 

The separation characteristics of a considerable variety of other TLC supports were also tested using different dye mixtures (magnesia, polyamide, silylated silica, octadecyl-bonded silica, carboxymethyl cellulose, zeolite, etc.) however, these supports have not been frequently applied in practical TLC of this class of compounds. Optimization procedures such as the prisma and the simplex methods have also found application in the TLC analysis of synthetic dyes. It was established that six red synthetic dyes (C.I. 15580 C.I. 15585 C.I. 15630 C.I. 15800 C.I. 15880 C.I. 15865) can be fully separated on silica high-performance TLC (HPTLC) layers in a three-solvent system calculated by the optimization models. The theoretical plate number and the consequent separation capacity of traditional TLC can be considerably enhanced by using supports of lower particle size (about 5 fim) and a narrower particle size distribution. The application of these HPTLC layers for the analysis of basic and cationic synthetic dyes has also been reviewed. The advantages of overpressured (or forced flow) TLC include improved separation efficiency, lower detection limit, and lower solvent consumption, and they have also been exploited in the analysis of synthetic dyes. 

Flow across a tube produces a series of vortices in the downstream wake formed as the flow separates alternately from the opposite sides of the tube. This alternate shedding of vortices produces alternating forces which occur more frequently as the velocity of flow increases. For a single cylinder the tube diameter, the flow velocity, and the frequency of vortex shedding can be described by the dimensionless Strouhal number ... 

The terms separation number (Kaiser, 1977) and spot capacity (Guiochon et al. 1982 Guiochon and Siouffi, 1982) are both defined as the maximum number of substances that can be completely separated (resolution = 1) on a plate or column. The separation number for linear HPTLC is 10 to 20 and for HPLC is 20 to 40. Guiochon et al. (1982) have shown that the separation number is raised to 100 to 250 for two-dimensional TLC (Chapter 7), and theoretical calculations indicate that under forced flow conditions (Chapter 7), it should be relatively easy to generate spot capacities well in excess of 5(X). 

During the AMD procedure fractions are focused into narrow bands with a typical peak width of about 1 mm, so that separation numbers around 80 over the useable separation distance of 80 mm can be achieved. This makes AMD an attractive alternative to forced flow TLC (OPLC) (1), the main merit of which has to be seen in the extension of the useful separation distance of the layer, in order... 

Characteristics of the air jet in the room might be influenced by reverse flows, created by the jet entraining the ambient air. This air jet is called a confined jet. If the temperature of the supplied air is equal to the temperature of the ambient room air, the jet is an isothermal jet. A jet with an initial temperature different from the temperature of the ambient air is called a nonisother-mal jet. The air temperature differential between supplied and ambient room air generates buoyancy forces in the jet, affecting the trajectory of the jet, the location at which the jet attaches and separates from the ceiling/floor, and the throw of the jet. The significance of these effects depends on the relative strength of the thermal buoyancy and inertial forces (characterized by the Archimedes number). 

The rate of separation of the fragments depends on the functions A r), C(r), Fc> and the fragmentation number, while the rate of rotation depends only on the function B(r). Further, it is apparent that the separation between the fragments increases only when the hydrodynamic force exceeds the binding physicochemical force. The pair of fragments rotates as a material element in an apparent flow with an effective velocity gradient tensor... 

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