Tracer Washout Curve

The disposition of a solute in the fluid as it flows through the system is governed by convection and dispersion. The convection takes place with velocity 

These forms relate the dependence on the system characteristics. Equation (8.13) describes the concentration c(z, t) of a solute in a tree-like structure that corresponds to the arterial tree of a mammal. Considering also the corresponding venular tree situated next to the arterial tree and appropriate inflow and outflow boundary conditions, we are able to derive an expression for the spatiotemporal distribution of a tracer inside a tree-like transport network. We also make the assumption that the arterial and venular trees are symmetric, that is, have the same volume V then, the total length is L = V/Ag The initial condition is c(z, 0) = 0 and the boundary conditions are  

The outflow concentration c(L,t) of the above model describes tracer washout curves from organs that have a tree-like network structure, and it is given by an analytic form reported in [328]. 

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A large change in the conductance of the luminal mucosal cell membrane, PS has only a modest effect on tracer washout of tracer preloaded into the intestinal lumen. Fig. 4b. The curve rises more rapidly, but the washout rate is only slightly greater when the conductance is raised 100-fold. 

Buffham, B. A. and H. W. Kropholler. The Washout Curve, Residence Time Distribution and F Curve in Tracer Kinetics. Math. Biosciences 6 (1970) 179. 

These can be solved by classical methods (i.e., eliminate Sout to obtain a second-order ODE in Cout), by Laplace transformation techniques, or by numerical integration. The initial conditions for the washout experiment are that the entire system is full of tracer at unit concentration, Cout = Sout = L Figure 15.7 shows the result of a numerical simulation. The difference between the model curve and that for a normal CSTR is subtle, and would not normally be detected by a washout experiment. The semilog plot in Figure 15.8 clearly shows the two time constants for the system, but the second one emerges at such low values of W t) that it would be missed using experiments of ordinary accuracy. 

When a steady stream of fluid flows through a vessel, different elements of the fluid spend different times within it. The time spent by each fluid element can be identified by an inert tracer experiment, where a pulse or a step input of a tracer is injected into the flow stream, and the concentration of the pulse in the effluent is detected. As the reader may quickly infer, the tracer must leave the PFR undisturbed. On the other hand, a step pulse may give rise to an exponential distribution in a CSTR. In the beginning of this chapter, we already demonstrated that PFR behavior approaches that of a CSTR under infinite recycle. It follows that infinite CSTRs in series behave like a PFR. Thus, we conclude that any nonideal reactor can be represented as a combination of the PFR and MFR to a certain degree. First, let us show a representative pulse response curve for each of the ideal reactors in Figure 3.5. As seen in the figure, the response to a step input of tracer in a PFR is identical to the input function, whereas the response in a CSTR exhibits an exponential decay. The response curves as shown in Figure 3.5 are called washout functions. The input function of the inert tracer concentration [/] can be mathematically expressed as... 

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