Separator conditions, 282 calculate values

The crucial question is at what value of <)> is the attraction high enough to induce phase separation De Hek and Vrij (6) assume that the critical flocculation concentration is equivalent to the phase separation condition defined by the spinodal point. From the pair potential between two hard spheres in a polymer solution they calculate the second virial coefficient B2 for the particles, and derive from the spinodal condition that if B2 = 1/2 (where is the volume fraction of particles in the dispersion) phase separation occurs. For a system in thermodynamic equilibrium, two phases coexist if the chemical potential of the hard spheres is the same in the dispersion and in the floe phase (i.e., the binodal condition). 

We have calculated the energy 0 in this way for some polymers and separation conditions (Table 2) and, using the lattice-like model and a slit-like pore, we have found the distribution coefficients, K 1, for these macromolecules as a function of N, D, 0 and 0f 65). It turned out that for such a crude model not only the calculated KJj 1 values were close to the experimental ones, but also, which is especially important, that the chemical nature of the macromolecule, the functional groups and the separation conditions (the mobile phase composition) were correctly accounted for. Two examples of such calculations are given in Figs. 8 and 9. 

With adiabatic combustion, departure from a complete control of m by the gas-phase reaction can occur only if the derivation of equation (5-75) becomes invalid. There are two ways in which this can happen essentially, the value of m calculated on the basis of gas-phase control may become either too low or too high to be consistent with all aspects of the problem. If the gas-phase reaction is the only rate process—for example, if the condensed phase is inert and maintains interfacial equilibrium—then m may become arbitrarily small without encountering an inconsistency. However, if a finite-rate process occurs at the interface or in the condensed phase, then a difficulty arises if the value of m calculated with gas-phase control is decreased below a critical value. To see this, consider equation (6) or equation (29). As the value of m obtained from the gas-phase analysis decreases (for example, as a consequence of a decreased reaction rate in the gas), the interface temperature 7], calculated from equation (6) or equation (29), also decreases. According to equation (37), this decreases t. Eventually, at a sufficiently low value of m, the calculated value of T- corresponds to Tj- = 0, As this condition is approached, the gas-phase solution approaches one in which dT/dx = 0 at x = 0, and the reaction zone moves to an infinite distance from the interface. The interface thus becomes adiabatic, and the gas-phase processes are separated from the interface and condensed-phase processes. 

The relationships between capacity factor, k , and organic modifier concentration in the mobile phase, and the effect of the column temperature on k for the antibiotics studied have been used to define k as a function of T and V (volume fraction) on the basis of a small number of experimental measurements for a given combination of column, organic solvent, and type of antibiotic. From calculated values of k, resolution values, Rs, may be estimated for adjacent band-pairs under all conditions. The method developed enables the optimization of RP-HPLC separations of the p-lactam antibiotics in the absence of difficult theoretical calculations, using a small number of experimental data, including the influence of the organic solvent in the mobile phase (isopropanol) and the column temperature. 

As a result of carried out calculations it was shown, that the HCl accumulation in pore space results in occurrence of gradient both of the concentration, and functionality of vanadium-oxide groups on the depth of separate grain. The value of a given gradient is determined by boundary conditions in equation (7). In Figure 7 the dependencies of... 

A 100 kmol/h stream containing ethylene glycol, furfural, and water is sent to a flash drum where the temperature and pressure are controlled such as to cause separation into two liquid streams and a vapor stream. At these conditions the /(-values are determined as listed below and may be assumed constant within the range of operations. It is required to calculate the product streams flow rates and compositions. 

These data were then transferred to a spreadsheet in a statistical program, where the outputs were ordered from smallest to largest. From the rearranged data, the peak pair resolution was determined by calculating the difference in adjacent mobilities. From this, the minimum peak pair resolution and product peak pair resolution was determined. These values were then used to generate a response surface from which an optimum separation condition could be determined. 

The method of surface-reaction kinetics at a constant separation factor, as developed by Thomas for saturation conditions, is again applied. Values of NR should be calculated for the real or hypothetical saturation step, and for the elution step, by using the methods of Section III, D. An apparent NTU for saturation can be obtained from the calculated value for elution (NR+), by the relation (Ne) pp = NRVr. Where part or all of the resistance is in the fluid phase, (Nr),pp will not be equal to Nr as determined for saturation then, the combined saturation and elution should be described by the geometric mean of these two Na values. 

It is of primary interest in many cases to calculate du/dY at Y = 0. This quantity is proportional to the shear stress and can be used in the absence of separation to calculate the frictional force on a body. More importantly, however, condition (10-120) indicates that separation will occur if du/dY 0 at any point x on the body surface (other than the stagnation point x = 0). Furthermore, the point x where this occurs should provide an estimate of the position of the separation point. To calculate (du/dY)Y=0 from the Blasius series solution, we require numerical values for the second derivative of f (Y) at Y = 0, namely,... 

The Nusselt number for power-law fluids for constant wall heat flux reduces to the newto-nian value of 4.36 when n = 1 and to 8.0 when n = 0. Equation 10.47 is applicable to the laminar flow of nonnewtonian fluids, both purely viscous and viscoelastic, for the constant wall heat flux boundary condition for values of xId beyond the thermal entrance region. The laminar heat transfer results for the constant wall temperature boundary condition were also obtained by the separation of variables using the fully developed velocity profile. The values of the Nusselt number for n = 1.0, Vi, and A calculated by Lyche and Bird [40] are 3.66, 3.95, and 4.18, respectively, while the value for n = 0 is 5.80. These values are equally valid for purely viscous and viscoelastic fluids for the constant wall temperature case provided that the thermal conditions are fully established. 

It is important to realize that the diameters needed for thermodynamic calculations do not necessarily represent a true minimum attainable separation distance between molecules. The objective is rather to determine optimal or effective diameters which give best results when used with a particular method of dealing with the contributions of molecular attraction. In this chapter the effective diameters sought are to be used specifically with the hard-sphere expansion (HSE) conformal solution theory of Mansoori and Leland (3). This theory generates the proper pseudo parameters for a pure reference fluid to be used in predicting the excess of any dimensionless property of a mixture over the calculated value of this property for a hard-sphere mixture. The value of this excess is obtained from a known value of this type of excess for a pure reference fluid evaluated at temperature and density conditions made dimensionless with the pseudo parameters. For example, if Xm represents any dimensionless property for a mixture of n nonpolar constituents at mole fractions xu x2,. . . x -i at temperature T and density p, then ... 

With over 800 times calculations, RPS can find the optimized separation condition for the desired solutes and the system provides numerical values such as mobile phase composition, flow rate, analysis time and resolution attained at that condition, and then RPS draws the idealized chromatogram at the optimized separation condition on the CRT. 

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