Contact power theory

Contact power theory is an empirical approach relating particulate collection efficiency and pressure drop in wet scrubber systems. The concept is an outgrowth of the observation that particulate collection efficiency in spray-type scrubbers is mainly determined by pressure drop for the gas plus any power expended in atomizing the liquid. Contact power theory assumes that the particulate collection efficiency in a scrubber is solely a fimction of the total power loss for the unit. The total power loss, is assumed to be composed of two parts the power loss of the gas passing through the scrubber, q, and the power loss of the spray liquid during atomization, The gas term can be estimated by... 

Unlike the Johnstone equation approach, this method requires specifying two coefficients. The validity and accuracy of the coefficients available from the literature for the contact power theory equations have been questioned. Some numerical values of a and fi for specific particulates and scrubber devices are provided below. 

The installation of a venturi scrubber is proposed to reduce the discharge of particulates from an open-hearth steel ftimace operation. Preliminary design information suggests water and gas pressure drops across the rubber of S.Opsia and 36.0 in. of H2O, respectively. A liquid-to-gas ratio of 6.0gpm/1000acfm is usually employed with this industry. Estimate the collection efficiency of the proposed venturi scrubber. Assume contact power theory to apply with a and P given by 1.26 and 0.57, respectively. Recalculate the collection efficiency if the power requirement on the liquid side is neglected. 

The JKR model predicts that the contact radius varies with the reciprocal of the cube root of the Young s modulus. As previously discussed, the 2/3 and — 1/3 power-law dependencies of the zero-load contact radius on particle radius and Young s modulus are characteristics of adhesion theories that assume elastic behavior. 

Upon comparison of Eqs. 29 and 36, it is readily apparent that both theories predict the same power law dependence of the contact radius on particle radius and elastic moduli. However, the actual value of the contact radius predicted by the JKR theory is that predicted by the DMT model. This implies that, for a given contact radius, the work of adhesion would have to be six times as great in the DMT theory than in the JKR model. It should be apparent that it is both necessary and important to establish which theory correctly describes a system. 

There have been several theories proposed to explain the anomalous 3/4 power-law dependence of the contact radius on particle radius in what should be simple JKR systems. Maugis [60], proposed that the problem with using the JKR model, per se, is that the JKR model assumes small deformations in order to approximate the shape of the contact as a parabola. In his model, Maugis re-solved the JKR problem using the exact shape of the contact. According to his calculations, o should vary as / , where 2/3 < y < 1, depending on the ratio a/R. 

Viewing things from the perspective of his physical theory of contact electricity, Volta was intrigued by the apparently endless power of the battery to keep the electric fluid in motion without the mechanical actions needed to operate the classical, friction, electrostatic machine, and the electrophorus. He called his batteiy alternately the artificial electric organ, in homage to the torpedo fish that had supplied the idea, and the electromotive apparatus, alluding to the perpetual motion (his words) of the electric fluid achieved by the machine. To explain that motion Volta relied, rather than on the concepts of energy available around 1800, on his own notion of electric tension. He occasionally defined tension as the effort each point of an electrified body makes to get rid of its electricity but above all he confidently and consistently measured it with the electrometer. 

The theory underlying their function is imperfectly understood even after almost a century... although the very nature of these units limits them to small power capabilities, the concept of small-signal behavior, in the sense of the term when applied to junction devices, is meaningless, since there is no region of operation wherein equilibrium or theoretical performance is observed. Point-contact devices may therefore be described as sharply nonlinear under all operating conditions. 

At shorter distances the repulsive forces start to dominate. The repulsive interaction between two molecules can be described by the power-law potential l/rn (n>9) caused by overlapping of electron clouds resulting in a conflict with the Pauli exclusion principle. For a completely rigid tip and sample whose atoms interact as 1/r12, the repulsion would be described by W-l/D7. In practice, both the tip and the sample are deformable (Fig. 3d). The tip-sample attraction is balanced by mechanical stress which arises in the contact area. From the Hertz theory [77,79], the relation between the deformation force Fd and the contact radius a is given by ... 

A number of new ideas have been put forward recently. A X7 enhancement of the generated second harmonic power was obtained by ultraviolet patterning to produce a chirped periodic nonlinear susceptibility on a 60 pm wide channel waveguide [41 ]. A complete analysis of theory and experiment is given, illustrating the potential of this new technique, very competitive with the contact electrode method developed earlier [42], and first introduced without the chirping and with an enhancement factor of about 1.5 to 2 by the same group [43,44]. 

Several authors have observed that log J versus log V plots are straight lines. This result is consistent with the conventional power law (3.42). It is not clear how this result is modified for non-zero Schottky barriers. The J-V characteristics in our theory depend on the value of the constant of integration C. The Schottky barriers 4>b define P 0), and C depends on P 0), where P(0) is the injected charge carrier density at the contact. 

We will not pursue the analysis in detail any further. It does illustrate the power of spherical tensor methods, and one can only shudder at the possibility of developing the theory in a cartesian coordinate system, with direction cosines. We list the final values of the molecular parameters for 14N35C1 in table 10.12. The values of the hyperfine constants may be interpreted semi-empirically in the following way. The outmost pair of electrons occupy a 3 /rT molecular orbital and the Fermi contact constants, given in table 10.12, may be compared with the atomic values [144] of 1811 and 5723 MHz for the nitrogen and chlorine atoms respectively one concludes that the s electron character... 

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