The Stimulus Response Technique

Alternatively, the signal can be injected as a pulse (ideally infinitely narrow so that its width = 0 while its area = 1), the broadening of which is observed when, with a certain delay, the dyed zone has reached the vessel output. The formalized plot of the observed concentrations C versus time is called a C curve, and its shape characterizes the type of flow (Fig. 3.2 ). For plug flow the input and output pulses have the same shape for mixed flow, after an abrupt rise, the color intensity decreases expo- 

The residence time distribution curve (RTD) can be inscribed by its statistical moments, of which the centroid of distribution T and spread of distribution a are the most important numerical values. Thus, for a C curve, the zeroth moment is 

In FIA, the sample throughput and the sample dispersion D are related to the standard deviation of the peak, o. The throughput rate is limited to the maximum value 5max, beyond which excessive carryover will make the estimation of peak height unreliable (see Fig. 2.12). Thus 

The first and second moments can be expressed in either time or volume units. It is important to note that they do not yield useful information 

It comprises the true width of the injected impulse and the true residence time and, therefore, it yields a realistic estimation of the sampling frequency rather than the classical parameters such as N, H, or a, which can be obtained only by injecting an infinitely short impulse, but have the advantage of stringent theoretical evaluation. 

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Thus we see that the stimulus-response technique using a step or pulse input function provides a convenient experimental technique for finding the age distribution of the contents and the residence-time distribution of material passing through a closed vessel. 

To validate the "Single Blade Volume Ou ut Model", the feedstock residence time was also studied experimentally by using the stimulus-response technique. Using scrap tires as feedstock, the residence time in the PDU reactor has been measured, which showed a very good agreement with the model prediction [8]. The experiments for measuring the of wood bark feedstock in the PDU reactor is in preparation. The results will be presented later. 

The physical process of material dispersion is due to the hydrodynamic processes taking place in the flowthrough system and is therefore conveniently investigated by the stimulus response technique, which is based on introduction of a tracer into a flowing stream and on measurement of the dispersion of the tracer as caused by the transport process throughout the system. If the tracer is injected as a zone (stimulus), then the observed... 

Except for the case of an ideal plug flow reactor, different fluid elements will take different lengths of time to flow through a chemical reactor. To be able to predict the behavior of a given piece of equipment as a chemical reactor, one must be able to determine how long different fluid elements remain in the reactor. One does this by measuring the response of the effluent stream to changes in the concentration of inert species in the feed stream called the stimulus-response technique. In this section we discuss the analytical form in which the distribution of residence times is cast, derive relationships of this type for various reactor models, and illustrate how experimental data are treated to determine the distribution function. 

To understand the behavior of the fluidized bed, one can determine the average residence time or the residence time distribution (RTD) from the tracer technique. For instance, RTD in fluidized bed dryer is usually carried out by means of the stimulus-response technique, in which an impulse of solids marked with some appropriate tracer is fed to the dryer and its time of elution and concentration measured at the exit of the dryer. The material of the tracer has to be such that it can be detected and does not react with the substrate material, and its form of application and response are well known (Levenspiel, 1972). 

F g, X15 The stimulus-response technique for investigation of flow dispersion in an electrochemical reactor, (a) Injection of a marker pulse of ions at the reactor inlet followed by cathodic detection of the limiting current at the reactor outlet i. cc (b) Injection ol a marker pulse of KCI at the reactor inlet, followed by conductimetric detection at the outlet The conductance of the KCI electrolyte proportional to... 

The experimental technique used for finding this desired distribution of residence times of fluid in the vessel is a stimulus-response technique using tracer material in the flowing fluid. The stimulus or input signal is simply tracer introduced in a known manner into the fluid stream enter-... 

Fio. 2. Stimulus response techniques commonly used in the study of the behavior of flow systems (L13). 

The RTD for a flowing fluid is normally obtained by the so-called stimulus-response technique. This technique involves the injection of a tracer at the inlet stream or at some point within a reactor and the observation of the corresponding response at the exit stream or at some other downstream point within the reactor. A suitable flow model can then be selected by matching the experimental RTD curve with that obtained from the mathematical model. This approach implies that a transient analysis of reactor and flow model behavior is necessary. 

The PDU vacuum pyrolysis reactor is a semi-continuous horizontal pilot plant reactor 3 m long with a diameter of 0.6 m and a throughput capacity of about 50 - 200 kg/h, depending on the feedstock treated. The configuration of the PDU reactor is almost the same as that of the industrial reactor, except t t the PDU has smaller agitation blades. Two types of tests have been conducted with this reactor, the cold and the hot runs. In the cold tests, the particle flow behaviour is studied by a stimulus-response technique, under different agitation speeds and feed rates. The hot tests enable the conversion to be determined as a function of the feed rate and the agitation speed. 

The ingenuity of electroanalytical chemists has produced many of these dynamic stimulus-response techniques together with the solution of the associated differential diffusion equations. The complicated picture of electroanalysis that developed as a result has now been slightly clarified by some standardization brought about by the availability of commercial instruments. 

In these models, the interactions between the chemical reaction and the transport processes are described in some more details than in first category. The numerous elementary transport processes are lumped together into some effective terms, using different simplification rules. These models are generally based on the Residence Time Distribution (R.T.D.) of the fluid phases. This formulation is convenient because the R.T.D. can be determined experimentally by well established stimulus-response techniques. The resultant R.T.D. reflects bulk pheno-... 

Cascades of tubular or stirred tank reactors are fairly simple to design as it is usually possible to treat the vessels independently. There do exist complex reactors which were developed empirically and are difficult to analyze from first principles. The transport equations still apply, but the hydrodynamics are too complex to allow modeling from first principles. Residence time measurements are a stimulus-response technique for appraising the hydrodynamics. They provide substantial insight in the performance of complex reactors, particularly when the performance is less than expected. See Nauman [2] or Nauman and Buffham [7] for a description of this technique. 

The system is disturbed by a stimulus and the response of the system to the stimulus is measured. Two common stimulus response techniques are the step input response and the pulse input response see Fig. 11.20. 

Next are the references for the themes of this book. The results are compared to the results of other researchers who use brain mapping techniques like functional magnetic resonance imaging and other methods to investigate the stimulus response pathways within the human brain. 

As noted in the previous discussion, different tissues have varying efficiencies of stimulus-response coupling. However, within a given tissue there may be the capability of choosing or altering the responsiveness of the system to agonists. This can be a useful technique in the study of... 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

The dynamics of the system under study can, in fact, be recovered from a variety of stimulus response tests. These include impulse and step response experiments, and frequency response and cross-correlation techniques. Descriptions of these methods and the interrelationships between them are discussed in many references, see, for instance, refs. 22—25 and Sects. 3.2.1—3.2.4 of this chapter. 

Sensory development Several screening tests that detect overall sensory deficits rely on orientation or the response of an animal to a stimulus. Responses are recorded as present, absent or changed in magnitude (Moser MacPhail, 1989). Another approach to the characterization of sensory function involves the use of reflex modification techniques (Crofton, 1990). Changes in stimulus frequency or threshold required to elicit a reflex or to induce habituation indicate possible changes in sensory function. 

J. C. T. Eijkel, Potentiometric detection and characterization of adsorbed protein using stimulus-response measurement techniques, thesis. University of Twente. Enschede, The Netherlands, ISBN 90-9008615-3, 1995. 

The rigorous but unfortunately mathematically difficult approach to the problem of ionic clouds around moving ions is to seek the asymmetrical distribution functions and then work out the implications of such functions for the electric fields developed among moving ions. A simpler approach will be followed here. This is the relaxation approach. The essence of relaxation analysis is to consider a system in one state, then perturb it slightly with a stimulus and analyze the time dependence of the system s response to the stimulus. (It will be seen later that relaxation techniques are much used in modern studies of the mechanism of electrode reactions.)... 

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