Tracer substances

This is the basic differential equation governing the transport of a dilute tracer substance along a pipe. Being a partial differential equation, its solution, which gives the concentration C as a function of z and /, will be very much dependent on the boundary conditions that apply to any particular case. 

A. Fick, Ann. Phys. (Leipzig) 170, 50 (1855). He actually set up his two laws for the temporal spreading of the concentration of a tracer substance, not for the probability. The first evolution equation for a probability was the Boltzmann equation [L. Boltzmann Vorlesungen tiber Gastheorie I (J. A. Barth, Leipzig, 1896)], following Maxwell s theory of gas kinetics. 

By means of the multivariate cross-correlation function, transport rates in streams can be calculated from natural compound concentrations in water without adding any tracer substances. 

Krantis A. (1983) Hypothermia-induced reduction in the permeation of radiola-belled tracer substances across the blood-brain barrier. Acta Neuropathol. 60, 61-69. 

Endogenous compounds can administered exogenously in place of tracer substances. This has been done for the dog using creatinine (Sapirstein et al. 

Equilibrium dialysis is used in a number of examples to analyse the ratio of lipid-bound to free analyte. Kramer et al. (1998) described the use of equilibrium dialysis by separating the liposome suspension and the water phase by a semi-permeable membrane. The analyte is dissolved in the water compartment of the system and diffuses into the liposome compartment. If equilibrium is reached, the remaining concentration of the analyte in the water compartment is determined by means of a quantification method (mainly HPLC or LCMS, fluorescence techniques) and the partition coefficient is calculated. Kramer et al. (1997) used a radio tracer substance as analyte to quantify the compound in both compartments using liquid scintillation counting. 

FIGURE 3-17 Dispersion of a pulse of a tracer substance in a sand column experiment. Note the parallel between this and the corresponding dispersion of a tracer in a flowing river (Fig. 2-4). The same equation, with a correction factor for porosity in the case of the sand column, describes both situations. However, the physical processes responsible for the Fickian transport differ mechanical dispersion dominates in the sand column, while turbulent diffusion and the dispersion associated with a nonuniform velocity profile dominate in the river. 

FIGURE 3-28 Breakthrough curves for three cases (a) a pulse input of a conservative tracer substance that is not retarded (b) a pulse input of a substance that moves through the porous medium with a retardation factor of three and (c) a pulse input of a substance that is retarded, but for which sorption to the solid phase is either not a linear function of dissolved concentration or not at local equilibrium. Case (c) exhibits tailing (i.e., the breakthrough curve is asymmetrical—skewed toward longer times). 

The overall retention time tR ] of a retained component i is the sum of the deadtime to and the net retention time tR net. The net retention time represents the time during which a substance is adsorbed onto the surface of the adsorbent. As t0 depends heavily on the tracer substance used for its determination the calculation of the net retention time is very difficult. Therefore, this book always refers to the overall retention time, when the term retention time is used. This is in accordance with international convention. 

Both the capacity factor and the net retention time depend on the nature of the tracer substance, which is used to determine to- Therefore only k values that are based on experiments with the same tracer substance should be directly compared and used to calculate selectivities. 

Practical determination of the porosities often suffers some difficulties. The most common method for determining the total porosity is the injection of a non-retained, pore-penetrating tracer substance (grey and small black circles in Fig. 2.5). In normal phase chromatography, toluene or 1,3,5-tri-tert-butylbenzene are often used, while in reversed phase chromatography uracil is the component of choice. 

I Surveillance, i.e. source screening and preliminary site characterisation. Media sediments (biota). Methodologies normalisation for grain size (2-3) and sorptive components (4) sample drying (2-3) and digestion (2-3). Additional tools tracer substances, isotopic and congener patterns (4) (bio)accumulation on organic matrices (4) and chemometric evaluation (3). 

Cardiac output in a human can be determined using a mass balance on a tracer substance in the blood. 

Historically, the most often used mixing measures are based on the spatial variance of the concentration of a tracer substance. The most common of these measures is the intensity of segregation introduced by Danckwerts [6], which is defined as... 

This can be seen by performing one of a number of possible tracer experiments. Imagine a stirred-flow reactor at the stationary state through which flows a dilute water solution of a tracer substance. Its concentration c is the same at inlet and outlet. At time < = 0, the feed is replaced by pure water at the same volumetric flow rate V. How is the concentration of tracer in the reactor or in the effluent going to change with time Again a material balance gives simply ... 

The simplest form of tracer technique involves tracking the tracer or just measuring the tracer content in a sample. In these applications the tracer substance usually represents a larger amount of material, so by observing the tracer the bulk behavior can be studied. A homogeneity measurement can be achieved by measuring the tracer content of several samples. In medical work the presence or absence of the tracer in some location may be significant. 

When a specialized transport process is involved, this may be characterized by performing a sequence of studies at different constant levels of non-tracer mother substance while determining the transport rate for tracer, which has a linear transport at each one of these constant levels. The linear transport rate, PS, is influenced by the concentration of the mother substance in a particular way, namely that there is competition between the non-tracer and tracer substances for transport a high concentration of non-tracer mother substance reduced the value of PSp. obtained via the modeling analysis (Bassingthwaighte, 1982),... 

To find out the effective number of compartments that corresponds to the horizontal equipment of Fig. 7.38, tracer experiments were conducted. After a prescribed time at steady operating conditions a granular tracer substance was added to the solid feed stream. Samples were taken at the discharge of the plant at defined time intervals and analyzed by means of pH measurement after dissolution in de-mineralized water. The pH value of the solution corresponds to the concentration of tracer, and can be used to calculate residence time curves. Measurements were carried out for the two already mentioned total gas flow rates of 500 and 700 m h under otherwise the same conditions (mass flow rate of solids 20 kg h , bed mass 25 kg, tracer mass 5 kg, test duration 140-150 min). 

The RTD of a chemical reactor can be determined by using tracer substances and, consequently, by tracing every volume element that passes through the reactor. We attempt to determine the length of the time the volume elements reside in the reactor. In other words, we attempt to determine the RTD of the species. 

St-Pierre et al. (2007) developed a residence-time distribution method based on the injection and subsequent detection of a tracer substance. The time required for the tracer pulse to travel between the injection and detection points defines an average residence time. Because the reactant flow rate is known, the free volume of the cell can be determined. Measurements performed in the absence and the presence of liquid water allow determination of the volume occupied by liquid water. 

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