Longitudinal effect

Van Deemter considered peak dispersion results from four spreading processes that take place in a column, namely, the Multi-Path Effect, Longitudinal Diffusion, Resistance to Mass Transfer in the Mobile Phase and Resistance to Mass Transfer in the Stationary Phase. Each one of these dispersion processes will now be considered separately... 

Input of thermal energy by effective longitudinal conduction... 

The last point is about equivalent spins (or like spins as the two protons of the water molecule). Referring to Solomon equations (see (13)), we can notice that, because of this equivalence, the effective longitudinal relaxation rate is obtained by adding the cross-relaxation rate to the specific longitudinal relaxation rate ... 

Berthelot, J.M., Cupcic, A. and Brou, K.A. (1993). Stress distribution and effective longitudinal Young s modulus of unidirectional discontinuous fiber composites. J. Composite Mater. 27, 1391-1425. 

The flame velocity in porous media is determined by the effective longitudinal thermal conductivity, which strongly depends on the velocity of the gas. Quenching of the flame as the cold wall is approached and the resulting incompleteness of combustion of the fuel material have been the subject of investigation in many recent studies, both theoretical and experimental. In particular, the question of flame propagation in a mixture of methanol and air has been considered theoretically,10 and the incomplete combustion of hydrocarbon mixtures was studied experimentally.11... 

The approach to analysis of biaxial extension of melts in the simulation of the sleeve inflation process was developed by Pirson and Petrie in 1966-1970 with the use of ideas of the thin shell theory which allows to substitute sleeve film by flat film in analysis. The problem was formulated more accurately and completely and solved in works by Han et al. The author made several conclusion the velocity of material extension changes in the main direction of sleeve motion while effective longitudinal viscosity may increase, decrease, or remain constant depending on the nature of material and the range of strain velocities under consideration longitudinal viscosity of the material at fixed process parameters decreases with temperature rise (the behavior of longitudinal velocity is described more strictly above, in Sect, 2.2.6). 

In addition to the induced magnetic field, the migration rate can greatly influence the NMR signal intensity and linewidth. Unlike in LC, the rate of migration of each band in CE is characteristic of electrophoretic mobility and so each move past the detector at different rates. The effective longitudinal (7ie(f) and transverse relaxation (T a) times of NMR nuclei in a flow system can be related to the residence time of the analyte (x) in the detector and the relaxation times (7 b 7 2) under static conditions [45] ... 

The problem of a proper calculation of the barrier-crossing frequency, in such cases, was described by Hynes [200] t, may be used in Vp calculations of a strongly adiabatic reactions. For weakly adiabatic reactions, the effective longitudinal relax-... 

Increasing the flow rate decreases the effective longitudinal relaxation time, which allows shorter repetition delays Ir. However, at the same time the effective transverse relaxation rate increases, leading to line broadening. 

Roth et al. [1988] recast the expression for the effective longitudinal conductivity in terms of spatial frequency, k (rad/m). This approach has two advantages. First, the temporal and spatial behaviors are both described using frequency analysis. Second, a parameter describing the size of a specific piece of tissue is not necessary the spatial frequency dependence becomes a property of the tissue, not the measurement. The expression for the DC effective longitudinal conductivity is... 

This behavior can be understood in terms of the dynamic longitudinal compliance of a polymer, shown in eqn [22]. Much as the static longitudinal fluctuations correspond to an effective longitudinal spring constant, ... 

The picture involved in the one-dimensional dispersion model is the onedimensional process of flow in a tube. There is a flow velocity in direction z, which, in the ideal case, is constant over the reactor cross section %. Because of molecular diffusion, turbulent convection, and the parabolic velocity profile that results from boundary friction (roughness, s), there are large deviations from a uniform flow front. The effective longitudinal dispersion coefficient... 

Figure 18.7 Effective longitudinal piezoelectric coefficient dss and dielectric permittivity 33 for various PZT compositions. The curves are calculated for a single crystal using a phenomenological approach, and shown in comparison with experimental data for a PZTceramic sample. From Ref [36. ...

It is convenient to describe NMR experiments in the rotating frame, and hence, in the following, only the static rf component will be taken into account. The rotating fiame frequency is kept close to the Larmor frequency of the nuclei in the sample. If the rotating frame frequency exactly matches a given resonance frequency, then the effective longitudinal field will be zero in that frame. 

Table 5.1 Four possibilities of piezoelectric effect - longitudinal, transversal, longitudinal shear and transversal shear...

Ad = The longitudinal displacement demand at the abutment from elastic analysis Ajff = The effective longitudinal abutment displacement at idealized yield... 

The dispersion model is an alternative to the tanks-in-series model. This model formally characterizes mass transport in the radial and axial direction as a one-dimensional process in terms of an effective longitudinal dHTusivity Dax that is superimposed on the plug flow. The dimensionless group Dax/(Mf) is called the dispersion number, and the reciprocal value is the Bodenstein number Bo. Calculation of the conversion is possible by equations based on Da and Bo. 

The first general approach to a realistic operative model of TBR consists in a combination of mass balances for all the independent components, one balance for each component for each phase present. The number of balances needed is reduced, of course, in the case of irreversible reactions. Mass balances must take into account methods of feeding the reactor, interphase mass transfer, chemical kinetics, catalyst wetting and effectiveness, longitudinal and radial dispersion, etc. sometimes part of the data is obtained from the boundary or the initial conditions. When necessary, the model should include a heat balance and also a momentum balance. Balances can be written for the reaction ... 

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