Tracer dispersal

In a companion pair of contributions, Mauri and Brenner (1991a,b) introduce a novel scheme for determining the rheological properties of suspensions. Their approach extends generalized Taylor-Aris dispersion-theory moment techniques (Brenner, 1980a, 1982)—particularly as earlier addressed to the study of tracer dispersion in immobile, spatially periodic media (Brenner, 1980b Brenner and Adler, 1982)—from the realm of material... 

G. Guillot, G. Kassab, J.P. Hulin and P. Rigord, Monitoring of tracer dispersion in porous media by NMR imaging, /. Phys. D Appl. Phys., 24 (1991) 763. 

FIGURE 2.9 Averaged diapycnal mixing coefficients according to Equations 2.40 and 2.41. Vertical exchange coefficients estimated by the bulk method in the Baltic Sea (Matthaus, 1990b) at 75 m depth and Axell (1998) at 150 m depth and by dye tracer dispersion at about 300 m depth in the ocean thermocline by Ledwell et al. (1998). 

The bounce-back collision typically employed at fluid-solid boundaries, where fluid particles are turned back in the direction they came from following collision with a solid wall, causes the effective wall position to extend one half lattice unit into the fluid from the solid surface (Stockman et al., 1997). This is not a serious problem for velocity computations in slow flows, but has the potential to be a significant problem for tracer/dispersion simulations. Increasing the number of lattice points inside a flow channel can reduce this error, but is computationally very expensive. 

Charlaix, E., J.P. Hulin, and T.J. Plona. 1987. Experimental study of tracer dispersion in sintered glass porous materials of variable compaction. Phys. Fluids 30 1690-1698. 

Gutfraind, R., I. Ippolito, and A. Hansen. 1995. Study of tracer dispersion in self-affine fractures using lattice-gas automata. Phys. Fluids 7 1938-1948. 

Hulin, J.P., E. Charlaix, T. J. Plona, L. Oger, and E. Guyon. 1988. Tracer dispersion in sintered glass beads with abidisperse size distribution. AlChEJ. 34 610-617. 

Koplik, J., I. Ippolito, and J.P. Hulin. 1993. Tracer dispersion in rough channels A two-dimensional numerical study. Phys. Fluids A 5 1333-1343. 

Schmidt numbers for liquids are about 10, compared to 1 for gases, so molecular diffusion may be the key to the difference. The effect of high velocity near the tube wall might be offset by molecular diffusion in gas tests but not in tests with liquids. Another explanation is that pockets of fluid act as side capacities throughout the bed, and diffusion from these pockets is quite slow in liquids, leading to greater tracer dispersion [30]. 

Field methods are based on tracer dispersion study directly in the natural geologic medium (Figure 3.29). As tracers are utilized either components of the already existing pollution or special components injected with water. Such special components maybe 1) natural components (Br,I or CF) of assigned concentrations 2) artificial compounds of assigned isotope composition of elements (<5D,, H, etc.) 3) radioactive isotopes,... 

Dispersion of fracer maferial through a PFR with axial mixing as compared to the tracer dispersion through an ideal PFR is shown in Figure 3.60. In a PFR with axial mixing of fluid elemenfs, the tracer material injected (as an impulse input) at the reactor inlet spreads in the axial direction while it is being drifted in the flow direction by the bulk flow of the... 

Similar experiments to those using polymer have been conducted using viscous solutions made up of carbon-14-labelled glycerol, with Cl again being used as tracer. In these, it has been found (Sorbie et al, 1987d) that the glycerol and chloride dispersion coefficients are identical within experimental error. Thus, it has been identified that the difference in dispersion coefficient arises from the macromolecular nature of the polymer for the xanthan biopolymer. Similar experimental results on polymer/tracer dispersion behaviour have also been found by Kolodziej (1988). 

Until recently, numerical tools and resources were also underdeveloped relative to the magnitude of the striation measurement problem Poincare sections and tracer dispersion simulations were the primary techniques used to characterize mixing. To reconstruct striation patterns successfully by computational methods, it is necessary to track continuous material lines (i.e., dye blobs) injected in chaotic flows. The difficulty of such a numerical experiment is hidden in one word of the previous sentence continuous. The feasibility of tracking material lines or surfaces numerically was explored by Franjione and Ottino, (Franjione and Ottino, 1987). These authors estimations of time and disk space demands... 

In practical applications we are often interested in the early stages of a mixing process, before the process becomes controlled by diffusion (i.e., when striations reach the length scale of diffusion). Short-term mixing dynamics have been extensively studied in the past by tracer dispersion simulations. Consider the sine flow... 

K. Christensen, A. Corral, V. Frette, J. Feder, and T. Jossang. Tracer dispersion in a self-organized critical system, Phys. Rev. Lett. 77,107-110 (1996). 

The experimental findings of gas flow patterns in fluidized beds (in the interpretation of which it is impossible to separate the effects of the emulsion and the bubble phases) indicate that the overall flow pattern lies between plug flow and complete mixing. Yoshida and Kunii [51] showed that experimental measurements of tracer dispersion may be adequately interpreted in terms of the bubbling bed model through the use of the exchange coefficients between the emulsion and the bubble phases. 

---