Frequency response measurements volume

The frequency response measurements of this particular system are limited by the calculated natural frequency. Volume fluctuations greater than 30 cycles/minute would not be transmitted due to interference by the inertia of the column. If a 10-ft-high column of mercury were used, only frequencies up to 17 cycles/minute could be used. Conversely a mercury column less than 76 cm (30 inches) would not remain stable during system evacuation the column would be uncontrollably upset by atmospheric air flooding the system. The maximum frequency theoretically available with no safety factor is then approximately 34 cycles/minute. 

Many different techniques are available for flow measurement and for recording of respiratory functions or flow parameters in particular (e.g. [115,116]). However, not all methods are appropriate for measurement of inhalation flows, either because they have low frequency responses or they influence the shape of the inspiratory flow curve by a large volume or by the inertia of the measuring instrument (e.g. rotameters). They may also interfere with the aerosol cloud from the inhalation device during drug deposition studies. 

As an alternative approach to conventional uptake measurements, in the frequency response technique [44-48] one follows the response of the sample to a regular periodic perturbation, e.g. a sinusoidal variation of the system volume. Using complex notation, one may write for the time dependence of the system volume,... 

Yasuda and coworkers (46, 47) extended the use of the frequency-response method to heterogeneous catalytic reactions. The input remains the sinusoidal variation of the volume of the reactor, but with a continuous flow of reactants and measurement by mass spectrometer of the response of the concentrations of the products. Yasuda recently reviewed all his work (48). 

As previously described, frequency response data are obtained by varying the volume of the system sinusoidally by means of alternately raising and lowering the mercury column. The frequency of this sinusoidal variation is established and measured by adjusting the variable speed motor and timing the rpm with a stop watch. The pressure versus... 

Equations (A-22) and (A-23) contain a remarkable discovery, namely, that free volume measurements are unnecessary for obtaining meaningful information by the frequency response technique. Heretofore, when... 

In the frequency response method, first applied to the study of zeolitic diffusion by Yasuda [29] and further developed by Rees and coworkers [2,30-33], the volume of a system containing a widely dispersed sample of adsorbent, under a known pressure of sorbate, is subjected to a periodic (usually sinusoidal) perturbation. If there is no mass transfer or if mass transfer is infinitely rapid so that gas-solid mass-transfer equilibrium is always maintained, the pressure in the system should follow the volume perturbation with no phase difference. The effect of a finite resistance to mass transfer is to cause a phase shift so that the pressure response lags behind the volume perturbation. Measuring the in-phase and out-of-phase responses over a range of frequencies yields the characteristic frequency response spectrum, which may be matched to the spectrum derived from the theoretical model in order to determine the time constant of the mass-transfer process. As with other methods the response may be influenced by heat-transfer resistance, so to obtain reliable results, it is essential to carry out sufficient experimental checks to eliminate such effects or to allow for them in the theoretical model. The form of the frequency response spectrum depends on the nature of the dominant mass-transfer resistance and can therefore be helpful in distinguishing between diffusion-controlled and surface-resistance-controlled processes. 

In a recent development of the frequency response technique Bourdin et al. applied the frequency response approach to their IR temperature measurement system [35-37]. In this experiment the volume of the system is perturbed sinusoidally and both the pressure and temperature responses are measured. It was found that the phase differences between the pressure and temperature were more reliable and reproducible than the phase differences between the pressure and the volume. The explanation seems to be that since the quantity of adsorbent is quite small, a small amount of superficial adsorp-... 

In the frequency response technique the volume is periodically increased and decreased in square waves, and the response of the pressure measured and analysed in terms of Fick s laws under equilibrium conditions. It has the twin advantages of being applicable over a wide frequency range and being able to distinguish between independent kinetic processes. As a result, it appears to show close agreement with microscopic processes, because it can resolve the effects on different length scales. 

Frequency Response Analyzers. These instruments are designed measure a voltage ratio, rather than impedance, but can be adapted to measure impedance by the addition of auxiliary components—in the simplest case, a standard resistor. A detailed account of the circuitry, which was included in the first edition of this volume, would be out of place today here it will be dealt with in brief, to illustrate the principles involved. 

Direct Weighing. The direct weighing method of density determination measures the volume and mass of the mixture to give density. Although direct weighing is not considered a field-type instrument, it could serve as a primary calibration standard. Some of the advantages of this method are the simplicity of the equipment, repeatability, good frequency response, and the lack of... 

The size, the velocity, and the solid volume fraction of the bubbles and the solids slugs are reflected in the shape and frequency of the force probe response as shown in Fig. 24. The amplitude of the oscillations is a measure of the solid slug velocity and solid volume fraction. Inside the bubbles, the probe response is nearly flat because of the negligible solids fraction inside the bubble. The spread of the peaks and the length of the flat portions of the probe responses are measures of the size and velocity of the solid slugs and gas bubbles respectively. 

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