Temperature fractionation

Calctilated species mole fractions, temperature, and heat-release rate across propane jet diffusion flames in "still" air at a height of 3 mm in... 

The preparation of immiscible polymer blends is another way to disperse a bulk polymer into fine droplets. It has been reported for several polymers that when they are dispersed in immiscible matrices into droplets with average sizes of around 1 pm, they usually exhibit multiple crystallization exotherms in a differential scanning calorimetry (DSC) cooling scan from the melt (at a specific rate, e.g., 10 Cmin ). Frensch et al. [67] coined the term fractionated crystallization to indicate the difference exhibited by the bulk polymer, which crystallizes into a single exotherm, in comparison with one dispersed in a large number of droplets, whose crystallization is fractionated temperature-wise during cooling from the melt. 

Following the description given in the previous section, the detailed chemical system is mapped on two controlling variables the mixture fraction (Z) and a reaction progress variable (c). The mixture fraction describes the mixing of the species and enthalpy, while the progress variable follows the advance of the chemical reaction. Hence, the species mass fractions, temperature, density and species chemical source terms become functions of Z and c. The mixture fraction is defined according to [19] as ... 

The left-hand side of this equation is the extent of reaction the quotient 0ss/0ad on the right-hand side is the fractional temperature rise compared with the maximum possible (adiabatic temperature rise). 

The droplet size and size distribution seems to be controlled by a Fokker-Planck type dynamic rate equilibrium of droplet fusion and fission processes, i.e., the primary droplets are much smaller directly after sonication, but colloidally unstable, whereas larger droplets are broken up with higher probability. This also means that miniemulsions reach the minimal droplet sizes under the applied conditions (surfactant load, volume fraction, temperature, salinity, etc.), and therefore the resulting nanodroplets are at the critical borderline between stability and instability. This is why miniemulsions directly after homogenization are called critically stabilized [19,20]. Practically speaking, miniemulsions potentially make use of the surfactant in the most efficient way possible. 

We start by plotting the temperature rise in the reactor. This is done by integrating the steady-state differential equations that describe the composition and heat effects as functions of the axial position in the reactor. The adiabatic plug-flow reactor gives a unique exit temperature for a given feed temperature. This also means that we get a unique difference between the exit and feed temperatures. The temperature difference has to be less than or equal to the adiabatic temperature rise at a given, constant feed composition. Figure 5.20 show s the fractional temperature rise as a function of the reactor feed temperature for a typical system. 

Equation (5.11) represents a straight line in the diagram of fractional temperature rise versus reactor feed temperature. We show three such lines in Fig. 5.21. All lines intersect the temperature rise curve at least once (at a low temperature not shown in Fig. 5.21). It therefore appears that the reactor FEHE can have one, two, or three steady-state solutions for this particular set of reaction kinetics. Furthermore, the intermediate steady state, in the case of three solutions, is open-loop unstable due to the slope condition discussed in Chap. 4. This was verified by Douglas et al. (1962) in a control study of a reactor heat exchange system. 

Entry Fractionalization Temperature CQ Fractionalization Solvent Molecular Weight (daltons) PDI... 

Despite its great potential, in the near future CFD will not completely replace experimental work or standard approaches currently used by the chemical engineering community. In this connection it is even not sure that CFD is guaranteed to succeed or even be an approach that will lead to improved results in comparison with standard approaches. For single-phase turbulent flows and especially for multiphase flows, it is imperative that the results of CFD analysis somehow be compared with experimental data in order to assess the validity of the physical models and the computational algorithms. In this connection we should mention that only computational results that possess invariance with respect to spatial and temporal discretization should be confronted with experimental data. A CFD model usually gives very detailed information on the temporal and spatial variation of many key quantities (i.e., velocity components, phase volume fractions, temperatures, species concentrations, turbulence parameters), which leads to in-... 

Third, in the system of coordinates with the origin located at the surface of one of the electrodes, the hydrodynamic velocity field is two dimensional. Therefore, prescribing the distributions of hydrodynamic velocity, gas fraction, temperature, and so forth across the I EG, one can integrate the equations of mass, momentum, and energy transfer with respect to the distance between the electrodes. As a result, it is possible to reduce the problem s dimension by a unit. 

Figure 3.23 Aerothermal profiles over the multidisperse droplet layer with N = 3 fractions air temperatures and humidity (dashed) with droplet fractional temperatures 1, 2, 3 ((A) cross-section x = 0,001, (B) x = 0,05, (C) x = 0,10).

A scalar is a quantity associated with a point in space, whose specification requires just one number. For example, the fluid density, mass fraction, temperature, pressure and work are all scalar quantities. Scalars can be compared only if they have the same physical dimensions. Scalars measured in the same system of units are said to be equal if they have the same magnitude and sign. A vector is an entity that possesses both magnitude and direction and obeys certain laws. For example, velocity, acceleration, force are all vectors. Two vectors are equal if they have the same direction and the same magnitude. Moreover, a direction has to be specified in relation to a given frame of reference and this frame of reference is just as arbitrary as the system of units in which the magnitude is expressed. We distinguish therefore between the vector as an entity and its components which allow us to reconstruct it in a... 

Fig. 6.21. Cluster fraction temperature dependences x(T) for LTS (1) and HTS (2). At thermodynamical vitrification temperature V, we have x(T) = x, and the percolated liquid cluster disappears at T < rgh...

Fraction Temperature Range CO Parent (wt%) Peak CO Effusion Wg) MJMn... 

Figure 41. Lifetime of Chaser SD1020 foams in the presence of a California light crude oil ( B ) at various temperatures as a function of the average, initial, emulsified oil volume fraction. Temperature and pressure x, 90 °C, 25 psi +, 120 °C, 45 psi and Q 175 °C, 135 psi. Concentration 0.3 wt% SD1020 and 0.3 wt% NaCl...

The drop in temperature in the last part of the bed may be due to heat loss, and complete conversion probably corresponds to a temperature change of 130°C. Intermediate conversions are based on the fractional temperature rise, except for the last 3 feet of bed, where the temperature is too close to the final value for an accurate estimate of x. 

In view of the fact that the sampling conditions are somewhat less than ideal, time-dependent signals obtained for radicals must be viewed with some caution. The time dependence of the major components, however, should be unaffected by the low Mach number flow through the sampling cone. Subsequent experiments with the 110 cone should provide much more definitive information on radical relative mole fractions, temperature, and perhaps also absolute mole fractions of a number of components. 

Fig. 9.12 a) Configuration of reactive distillation column for hydration of ethylene oxide to ethylene glycol used by Ciric and Miao (1994). b) Equilibrium model calculations for the ethylene glycol process showing column profiles for liquid phase mole fraction, temperature and vapor phase molar flow, c) Nonequilibrium model calculations for the ethylene glycol process for a column of diameter 1.7 m showing the corresponding column profiles. Details of the simulations are available in Baur et al. 

Stream Name Vapour i Phase Fraction Temperature [C]... 

Fig. 16. Comparison of elution fractionation temperatures for linear PE fractions with the calibration curve obtained using preparative TREF fractions from branched PEs [9]. Reprinted with permission...

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