Negligent distribution

Since the void fraction distribution is independently measurable, the only remaining adjustable parameters are the A, so when surface diffusion is negligible equations (8.23) provide a completely predictive flux model. Unfortunately the assumption that (a) is independent of a is unlikely to be realistic, since the proportion of dead end pores will usually increase rapidly with decreasing pore radius. 

For large molecules, computation time becomes a consideration. Orbital-based techniques, such as Mulliken, Lowdin, and NBO, take a negligible amount of CPU time relative to the time required to obtain the wave function. Techniques based on the charge distribution, such as AIM and ESP, require a sig-nihcant amount of CPU time. The GAPT method, which was not mentioned above, requires a second derivative evaluation, which can be prohibitively expensive. 

Nuclei have many times more mass than electrons. During a very small period of time when the movement of heavy nuclei is negligible, electrons are moving so fast that their distribution is smooth. This leads to the approximation that the electron distribution is dependent only on the fixed positions of nuclei and not on their velocities. This approximation allows two simplifications... 

Foster s neglect of the role of the adsorbed film was unavoidable in the then absence of any reliable information as to the thickness of the film. It is now known that in fact the effect of the film on the calculated result is far from negligible, as will be demonstrated shortly. Since, however, all the methods of calculating pore size distributions involve a decision as to the upper limit of the range to be studied, this question needs to be discussed first. In effect one has to choose a point corresponding to point G in Fig. 3.1, where the mesopores are deemed to be full up. If the isotherm takes the course GH there are no further cores to be considered in any case but if it swings upwards as at GH, the isotherm is usually so steep that the Kelvin-type approach becomes too inaccurate (cf. p. 114) to be useful. 

Flue particles ia a fluidized bed are analogous to volatile molecules ia a Foiling solution. Therefore, the concentration of particles ia the gas above a fluidized bed is a function of the saturation capacity of the gas. To calculate the entrainment rate, it is first necessary to determine what particle sizes ia the bed can be entrained. These particles are the ones which have a terminal velocity less than the superficial gas velocity, assuming that iaterparticle forces ia a dilute zone of the freeboard are negligible. An average particle size of the entrainable particles is then calculated. If all particles ia the bed are entrainable, the entrained material has the same size distribution as the bed material. 

For most commercial voltages and frequencies used in power distribution, the capacitance effects are negligible. At relatively high voltages the current due to capacitance may reach sufficient value to affect the circuit, and insulation for such an appHcation is designed for a moderately low dielectric constant. 

Trajectory models require spatiaUy and temporaUy resolved wind fields, mixing-height fields, deposition parameters, and data on the spatial distribution of emissions. Lagrangian trajectory models assume that vertical wind shear and horizontal diffusion are negligible. Other limitations of trajectory and Eulerian models have been discussed (30). 

Generally, an HT distribution network has a very short length (f), less than 10-15 km. Moreover, the leakage capacitance (C ) for system voltages up to 66 kV is almost negligible. The Ferranti effect is therefore not applicable to a distribution network. 

When dimensional variation is large, its effeets must be ineluded in the analysis of the stress distribution for a given situation. However, in some eases the effeets of dimensional variation on stress are negligible. A simplified approaeh to determine the likely stress distribution then beeomes available. Given that the mean load applied to the eomponent/assembly is known for a partieular situation, the loading stress ean be estimated by using the eoeffieient of variation, C, of the load and the mean value for the stress determined from the stress equation for the failure mode of eoneern. 

Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

The solute is distributed largely over 4-vn plates in the column and thus, as (n) is large, the differential temperature between plates is negligible, and so the heat conducted axially along the column will be very small compared with that conducted radially to the walls and from the system. 

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