Discharge curves, theory

A problem with Debye theory and the use of ideal components in the equivalent circuits has been that most dielectrics actually do not follow an exponential discharge curve, but a fractional power discharge curve. This law is called the Curie — von Schweidler s law (Schweidler, 1907). We shall revert to this phenomenon later in Section 9.2.12. 

A graph of discharge coefficient ( m) plotted against dimensionless lift L/D) is known as a flow characteristic. Fig. 9 shows an example of flow characteristics plotted for various pressure ratios relieving from an air receiver, where Pb is the total backpressure at the valve exit port and Pq the reservoir total pressure.According to ideal one-dimensional compressible flow theory, choked flow should occur at pressure ratios below 0.528. In practice, choked flow will occur at lower pressure ratios because of friction losses upstream of the curtain area. Nevertheless, the curves in Fig. 9 are close-together at pressure ratios below 0.333, and have collapsed to almost a single curve for ratios less than 0.25. Other work shows a similar effect. 

The positions on the I-V curve have been useful in determining a inner potential distribution which can be a effective guide in developing the theory of the hybrid mode. During the negative resistance region ((3)-(4))on the I-V curve, the discharge has been observed to look as a ball of fire .3)... 

The theory of Schubert and Neesse points to small cone angle and curved feed inlets for clarification duties where high mass recoveries are required. The authors compared the above correlation with many published experimental results and found the correspondence better for umbrella (or spray) discharge. No flow rate-pressure drop relationship was proposed. 

As you can see, the LTSpice simulation plots the DC current dependency correctly, but the influence of the AC amplitude is distorted. The AC amplitude has a strong influence on the results, which is to be expected according to the theory [8, 9]. The measured curve with 1 A AC amplitude deviates more from the Simulation with 1 A and the curve with 10 mV amplitude is closer to the simulation, for the case without any superposed DC current. This means a better linearity is achieved by continuously adjusting the current amplitude so a maximal voltage response of 10 mV is met. The asymmetric behavior is clearly visible when comparing the curves with the superposed charging and discharging DC currents. In both cases, the measured impedance is smaller than the impedance without any superposed DC current. 

Polarisation curve of some electrode process is described by an equation of the theory of delayed discharge. Build plots, which illustrate the change of the form of the total polarisation curve and partial curves of anode and cathode processes depending on the change of exchange current io and transport factor a. 

Recently, Plonski analyzed the ability of the theory of electromechanical removal of adsorbed anions to fit the experimental initial and steady-state polarization curves of active iron in acid media. Unlike Drazic and Drazic, the author applied the concept of electrochemical dissolution of vulnerable atoms to a mechanism consisting in a slow-discharge hydrogen evolution and a one-step ferrous ion formation. In order to distinguish the possible role of anions from any other interferences, the... 

The formation mechanism of E t was established by analysis of sections of the polarization curves near E st> Figure 1 shows curves for various pH values and Fig. 2 gives their semilogarithmic representation. The curves are closely satisfied by the equations of the retarded discharge theory they give transfer coefficients (a = 0.20, j3 = 0.69) which depend little on the pH value. The exchai e current... 

Frumkin taking 38 y.F jem for the capacity at extreme positive polarization and 20 (j.F/cm for extreme anionic polarization, finds for solutions from 0.1 to 0.0001 N the cuiYes presented in Fig. 7 which are in not too bad accord with the experimental curves of Fig. 9. The large capacities found experimentally for extreme positive and negative polarizations have already been attributed to the non-ideality of the system (discharge through the interface). There remains, however, a certain discrepancy between theory and experiment, especially at low concentrations in the neighbourhood of the isoelectric point, where the experimental capacity is higher (3.9 uF/cm for 0.0001 N solution) than the theoretical one (2.15 txF/cm ). 

Thus, in the upper part of the polarization curve, the hydrogen overpotential is found to depend strongly on the solution composition. This can be explained on the basis of the theory of a slow ordinary discharge or electrochemical desorption. 

This conclusion is in complete agreement with the experimental results. Figure 6.1 shows the S vs n dependence for different solutions, viz. for a surface-inactive electrolyte, and for solutions to which specifically adsorbed anions and cations have been added. It can be seen that the results for different solutions differ considerably. If, however, we assume, in accordance with the usual equations of the theory of slow discharge[1], that the change in overpotential at a constant concentration of H" " ions is exactly equal to the change in the local -potential (the coefficient (1 - a)/a of the ij -poten-tial is equal to unity, since a = 1/2 in the Tafel regions for the investigated solutions), the displacement of one curve with respect to the other by the difference in overpotentials enables us to... 

---