Step function input

Distortion is the ratio of final current level to initial current level during transit of the stress pulse from a step-function input. 

For small values of the dispersion parameter one may take advantage of the fact that equation 11.1.37 takes the shape of a normal error curve. This implies that for a step function input a plot of (C — Cq)/(Cq — Co) or F(t)... 

For this model (Eqs. 14.2 and 14.50), Thomas [23] derived an analytical solution in the case of a step function input, i.e., of a breakthrough curve in frontal analysis. This solution can be written in dimensionless form using the following transformation suggested by Hiester and Vermeulen [9,23]. This transformation uses the parameters defined in Eqs. 14.8a to 14.8 d x, Td, K, Req, Ngy, N/y) and... 

Fig. 6-3 Response to a step-function input (a) apparatus for input-response studies, (b) step-function input, (c) response in effluent...

Equation (6-3) shows that the C/Q response to a step-function input gives the RTD function J ff) directly. This approach provides a simple experimental procedure for measuring the RTD for an actual reactor. 

The characteristics of uniform velocity profile and no axial mixing in a plug-flow reactor require that the residence time be a constant, 9 = VjQ. The curve for response to a step-function input is as shown in Fig. 6-5. From Eq. (6-3), the response curve is equal to J 9). Then J 9) = 0 for 6 < VjQ and J 9) = 1 for 0 > VjQ. The input and response curve for a pulse input would correspond to narrow peaks at 0 = 0 and 0 = VjQ, as shown in Fig. 6-6 (solid lines). The response curve, according to Eq. (6-7), is proportional to J 9). 

For an ideal stirred-tank reactor (C/Co)step can be calculated by applying Eq. (3-1) for a step-function input. The third term is 2ero, since there is no reaction. At a time 0 after the tracer concentration in the feed is increased to Cq the other terms in Eq. (3-1) give... 

Solution Figure 6-1 Oo describes a step-function input of tracer of concentration Cq for a series of ideal stirred-tank reactors. A mass balance on the j reactor in a series of n is, according to Eq. (3-1),... 

Response measurements to a step-function input are made for a reaction vessel. The following data are obtained for a given volumetric flow rate ... 

The flow patterns in a reactor are to be investigated by determining the residencetime distribution. Below are the results obtained for the concentration of tracer in the eflluent after introduction of a step function input at a concentration of 0.05 M. 

Consider the solution for the transient response of the dispersion model to a step-function input in concentration as given in Figure 5.23 for the particular case of Np = 10 and R = 0.1. Is the transient response of a comparable CSTR series model the same ... 

Establish the equations for the concentration response to a step function input in concentration, uniform across the radius, using the generalized model. 

If the interaction were instantaneous and without mass-transfer rate limitations, then we would have a simple transmission of whatever input of adsorbate that was admitted to the bed, with the input function at the exit of the bed at a time equal to the residence time in the bed. A step-function input is shown in Curve A. More commonly, we have breakthrough curves such as B in Figure 9.1, there the mass transport and/or adsorption processes are not infinitely rapid, or C in the figure, where rates are slow and even some reversible reaction may occur. 

Lee, T.V. Rothstein, D., and Madey, R., Moment analysis of time-dependent transmission of step-function input of radioactive gas through adsorber bed, Sep. Sci. Technol., 21(6), 689-700 (1986). 

Equation (12.6.2-14) is valid for any input. Of particular interest is the output response to a step function input of tracer, INPUT(0) = U(0). In the case of a unit step input, (12.6.2-14) gives ... 

Switching Method. Sharp step functions or slow-rising sawtooth electrical pulses are applied to a ferroelectric specimen and the total switching current is measured as a function of time. For step-function inputs the resultant current pulse is a measure of the nucleation and growth of reversal domains, while for slow sawtooth inputs the current is usually a series of small pulses analogous to Barkhausen pulses in ferromagnetics. The results provide information regarding domain sizes and incremental volumes swept up by the jerky movement of domain walls. 

FIGURE 15.1 One-dimensional column experiment (a) Sketch of the column device (b) step-function input of tracer and (c) Relative tracer concentration at column outlet and the effect of advection, diffusion, and dispersion. (After Freeze, A.R. and Cherry, J.A. 1979. Groundwater, Upper Saddle River, Prentice Hall, NJ.)... 

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