Tracers heterogeneities

Where Water Hammer Occurs. Water hammer can occur in any water supply line, hot or cold. Its effects can be even more pronounced in heterogeneous or biphase systems. Biphase systems carry water in two states, as a liquid and as a gas. Such a condition exists in a steam system where condensate coexists with live or flash steam in heat exchangers, tracer lines, steam mains, condensate return lines and, in some cases, pump discharge lines. 

His researches and those of his pupils led to his formulation in the twenties of the concept of active catalytic centers and the heterogeneity of catalytic and adsorptive surfaces. His catalytic studies were supplemented by researches carried out simultaneously on kinetics of homogeneous gas reactions and photochemistry. The thirties saw Hugh Taylor utilizing more and more of the techniques developed by physicists. Thermal conductivity for ortho-para hydrogen analysis resulted in his use of these species for surface characterization. The discovery of deuterium prompted him to set up production of this isotope by electrolysis on a large scale of several cubic centimeters. This gave him and others a supply of this valuable tracer for catalytic studies. For analysis he invoked not only thermal conductivity, but infrared spectroscopy and mass spectrometry. To ex-... 

Happel, J. Hnatow, M. A. "The Use of Tracers to Study Heterogeneous Catalysis" New York Academy of Sciences, No. AA9213 1973. 

Typically it took about 160 to 200 seconds to inject a pulse of about 455 kg coarse tracer particles into the bed pneumatically from the coaxial solid feed tube. It can be clearly seen from Figs. 38 to 42 that the tracer particle concentration increases from essentially zero to a final equilibrium value, depending on the location of the sampling port. The steady state was usually reached within about 5 minutes. There is considerable scatter in the data in some cases. This is to be expected because the tracer concentration to be detected is small, on the order of 4%, and absolute uniformity of mixing inside a heterogeneous fluidized bed is difficult to obtain. 

Figure 14.3. Distinction between homogeneous and heterogeneous immunoassay formats. Haptenic analytes are indicated as triangles, and conjugated fluorescent probes are indicated by the letter F. In this hypothetical depiction, the homogeneous immunoassay is quantitated in the original reaction mixture. The heterogeneous immunoassay requires removal of unreacted tracer, further addition of reagents such as an enzyme to release a fluorescent molecule F, followed by quantitation.

The O isotopes show signihcant heterogeneity between the different meteorite classes (Fig. 8a Clayton et al. 1976, 1977). Differences are small, but, each chondrite group has a distinct bulk O isotopic composition. O isotopes also indicate the close ties between the Earth and the Moon. O therefore can be used to identify members of a family that formed from a common reservoir, which is the definition of a tracer. Such differences are also formd between chondrules within the same meteorites related to their size (Gooding et al. 1983). This is a survival of the initial isotopic heterogeneity in already high temperature processed materials like chondrules. 

Fig. 10.3 Photographs of a homogenous, saturated sand pack with seven dye tracer point injections being transported, under a constant flow of 53 mL/min, from left to right times at (a) t=20, (b) t= 105, (c) t= 172, (d) t=255 min after injection. Internal dimensions of the flow cell are 86 cm (length), 45cm (height), and 10cm (width). Reprinted from Levy M, Berkowitz B (2003) Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J Contam Hydrol 64 203-226. Copyright 2003 with permission of Elsevier...

Since hthium and boron isotope fractionations mainly occur during low temperature processes, Li and B isotopes may provide a robust tracer of surface material that is recycled to the mantle (Elhott et al. 2004). Heterogeneous distribution of subducted oceanic and continental crust in the mantle will thus result in variations in Li and B isotope ratios. Furthermore, dehydration processes active in subducdon zones appear to be of crucial importance in the control of Li and B isotope composition of different parts of the mantle. For the upper mantle as a whole Jeffcoate et al. (2007) gave an estimated 8 Li-value of 3.5%o. 

Dispersion in a flow through a porous media occurs due to heterogeneity in the media (i.e., the conductivity of the soil varies with space). This is shown on three levels in Figure 6.15. On the particle scale, a thread of tracer will be split a number of times as it moves through the media. Each split of the tracer thread will move through the media at a speed corresponding to the resistance that it encounters. If you take a number of tracer threads coming out of the media at different times and collected them in an outlet pipe, what you would see at the end of the pipe would be a dispersed... 

The picture is less clear for molecular crystals when the molecules deviate strongly from a globular form. NMR data and tracer diffusion data are then often in disagreement. Diffusion profiles (In c, vs. distance) are found to be curved, which is usually attributed to additional heterogeneous and fast diffusion pathways. For plastic crystals, this could indicate that many of them possess a highly defective structure. Even for the aromatic ring molecule benzene, which forms a non-plastic crystal, one finds a D (NMR)/D (tracer) ratio on the order of 103. This cannot be understood unless one invokes other than bulk lattice mechanisms of diffusion. 

Vicini, P., Bonadonna, R., Lehtovirta, M., Groop, L., and Cobelli, C., Estimation of blood flow heterogeneity in human skeletal muscle using intravascular tracer data Importance for modeling transcapillary exchange, Annals of Biomedical Engineering, Vol. 26, 1998, pp. 764-774. 

The most applied CSTRs are recirculation reactors in heterogeneous catalysis and well stirred vessels in slurry or liquid-phase systems. Injection of a (5-pulse of a tracer should give an exponentially decaying output concentration ... 

Besides the compartment analysis, non-compartment models can be used. One frequently used procedure is the regression method. This method performs a linear regression fit on a voxel basis. The slope image provides information about the trapping of the tracer, while the intercept image reflects the distribution volume of the radiopharmaceutical. Another non-compartment model is based on the calculation of the fractal dimension (FD) (17). FD is a parameter for the heterogeneity and is calculated for the time-activity data of each individual VOI. The values of FD vary from 0 to 2 showing the deterministic or chaotic distribution of the tracer activity. We use a subdivision of 7 x 7 and a maximal SUV of 20 for the calculation of FD. 

This phenomenon has been studied by different combined electrochemical techniques such as -> spectroelec-trochemistry, radioactive -> tracer method, -> electrochemical quartz crystal microbalance, conductivity etc. by varying the experimental parameters, e.g., film thickness, the composition and concentration of the electrolyte solutions, the wait-time at different waiting potentials, and temperature [iii-x]. Several interpretations have been developed beside the ESCR model. The linear dependence of the anodic peak potential on the logarithm of the time of cathodic electrolysis (wait-time) -when the polymer in its reduced state is an insulator -has been interpreted by using the concept of electric percolation [ix]. Other effects have also been taken into account such as incomplete reduction [vii], slow sorp-tion/desorption of ions and solvent molecules [iii-vi], variation of the equilibrium constants of -+polarons and - bipolarons [viii], dimerization [xi], heterogeneous effects [xii], etc. 

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