Passive tracers

Dye structures of passive tracers placed in time-periodic chaotic flows evolve in an iterative fashion an entire structure is mapped into a new structure with persistent large-scale features, but finer and finer scale features are revealed at each period of the flow. After a few periods, strategically placed blobs of passive tracer reveal patterns that serve as templates for subsequent stretching and folding. Repeated action by the flow generates a lamellar structure consisting of stretched and folded striations, with thicknesses s(r), characterized by a probability density function, f(s,t), whose... 

In whichever approach, the common denominator of most operations in stirred vessels is the common notion that the rate e of dissipation of turbulent kinetic energy is a reliable measure for the effect of the turbulent-flow characteristics on the operations of interest such as carrying out chemical reactions, suspending solids, or dispersing bubbles. As this e may be conceived as a concentration of a passive tracer, i.e., in terms of W/kg rather than of m2/s3, the spatial variations in e may be calculated by means of a usual transport equation. 

RTD functions for combinations of ideal reactors can be constructed (Wen and Fan 1975) based on (1.6) and (1.7). For non-ideal reactors, the RTD function (see example in Fig. 1.4) can be measured experimentally using passive tracers (Levenspiel 1998 Fogler 1999), or extracted numerically from CFD simulations of time-dependent passive scalar mixing. 

Figure 8.6 Convective dispersal of a passive tracer located at t=0 inside the circle in the upper right corner by the velocity field described by equations (8.3.11).

P 7] The topic has only been treated theoretically so far [28], A mathematical model was set up slip boundary conditions were used and the Navier-Stokes equation was solved to obtain two-dimensional electroosmotic flows for various distributions of the C, potential. The flow field was determined analytically using a Fourier series to allow one tracking of passive tracer particles for flow visualization. It was chosen to study the asymptotic behavior of the series components to overcome the limits of Fourier series with regard to slow convergence. In this way, with only a few terms highly accurate solutions are yielded. Then, alternation between two flow fields is used to induce chaotic advection. This is achieved by periodic alteration of the electrodes potentials. 

Passive tracer particles were placed at selected plans, given in pg]... 

Figure 1.21 Pointcare sections for various periods T = 2, 4 and 6 and h = 2. A passive tracer particle was initially inserted at (x0, y0) = (0,0.01), and its motions were followed by 3000 periods [28] (by courtesy of ACS).

G. I. Taylor s concept of the effective axial diffusion coefficient, which has proved so useful in combining variable axial advection with radial transfer into one parameter, works best when there is no exchange of a passive tracer with the pipe walls. An analogue of his method, which should be applicable when development lengths are large and there is exchange at the wall, has yet to be provided. It would be of great value. 

Buzzi A, D Isidoro M, Davolio S (2003) A case study of an orographic cyclone south of the Alps during the MAP SOP. Q J R Meteor Soc 129 1795-1818 DTsidoro M, Maurizi A, Tampieri F, Tiesi A, Villani MG (2005) Assessment of the numerical diffusion effect in the advection of passive tracer in BOLCHEM. Nuovo Cimento C 28 151-158... 

The simplified sequence of the simulation of a passive tracer within an IFS time-... 

Musgrave D. L. (1985) A numerical study of the roles of subgyre-scale mixing and the western boundary current on homgenization of a passive tracer. J. Geophys. Res. 90(C4), 7037-7043. 

Sundermeyer M. A. and Price J. F. (1998) Lateral mixing and the North Atlantic tracer release experiment observations and numerical simulations of Lagrangian particles and a passive tracer. J. Geophys. Res. 103(C10), 21481-21497. 

Britter, R.E., Caton, F., Di Sabatino, S., Cooke, K.M., Simmonds, P.G., and Nickless, G. (2000) Dispersion of a passive tracer within and above an urban canopy. In Proceedings of the Third Symposium on the Urban Environment, American Meteorological Society. 

Manney, G.L., R.W. Zurek, W.A. Lahoz, R.S. Harwood, J.C. Gille, J.B. Kumer, J.L. Mergenthaler, A.E. Roche, A. O Neill, R. Swinbank, and J.W. Waters, Langrangian transport calculations using UARS data. Part I Passive tracers. J Atmos Sci 52, 3049, 1995a. 

The idea underlying chaotic advection is the observation that a certain regular velocity field,u(x,i) can produce fluid pathlines,x(x, i), which uniformly fill the volume in an ergodic way. The motion of passive tracers is governed by the advection equation ... 

Figure 2a depicts the Poincare section of the continuous flow stirrer when St = 1/4ti, and Re = 0.1. The Poincare sections are obtained by numerically tracking four passive tracer particles initially located at (0.005, -0.5), (0.005, 0.0), (0.005, 0.5) and (0.005, 1.0) during 10 convective time-scales PI/Uhs)- a quasi-periodic motion of the passive tracer particle that is initially located at (0.005, 0.0) results in a regular formation separating the upper and lower halves of the Poincare section. A zoomed image showing this KAM boundary is presented in Fig. 2c. The passive tracer particles initially located at the upper and lower halves of the channel entry cannot pass this global barrier. In addition to this, there are two unstirred zones called void zones surrounded by well stirred zone (chaotic sea) at the bottom half of the Poincare section. A zoomed image of these two void zones can be seen in Fig. 2b.

Figure 3 depicts the FTLE distribution obtained by tracking 4,000 passive tracer particle pairs at the end of ten time periods for the stirring case of St = XHti, Re = 0.01, and A = 0.8. The FTLE has a normal distribution with mean = 0.1 and standard deviation a = 0.03. The... 

V. Artale, G. Boffetta, A. Celani, M. Cencini, and A. Vulpiani. Dispersion of passive tracers in closed basins Beyond the diffusion coefficient. Phys. Fluids, 9 3162-3171, 1997. 

M.C. Jullien, P. Castiglione, and P. Tabeling. Experimental observation of Batchelor dispersion of passive tracers. Phys. Rev. Lett., 85 3636, 2000. 

Ventilation efficiency can be characterized by measured levels of metabolically generated CO2 or by the concentration decay of a passive tracer gas. Sulfur hexafluoride (SF ) is often used for this purpose, and it is introduced into the space under consideration. The faster the decline of SF, the greater the ventilation of the space. 

The concentration profile c(x, y, z, i) of a passive tracer under these flow conditions can be determined using the diffusion-advection equation given below ... 

Maksimovic C. Diffusion of Passive Tracer and Drag Reducing Polymer Solution in a Developing Pipe Flow. Int.Conf. Drag Reduction 84, Bristol. 1984. 

Many of the mixing simulations described in the previous section deal with the modeling of mass transfer between miscible fluids [33, 70-77]. These are the simulations which require a solution of the convection-difliision equation for the concentration fields. For the most part, the transport of a dilute species with a typical diSusion coeflEcient 10 m s between two miscible fluids with equal physical properties is simulated. It has already been mentioned that due to the discretization of the convection-diffusion equation and the typically small diffusion coefficients for liquids, these simulations are prone to numerical diffiision, which may result in an over-prediction of mass transfer efficiency. Using a lattice Boltzmann method, however, Sullivan et al. [77] successfully simulated not only the diffusion of a passive tracer but also that of an active tracer, whereby two miscible fluids of different viscosities are mixed. In particular, they used a coupled hydrodynamic/mass transfer model, which enabled the effects of the tracer concentration on the local viscosity to be taken into account. 

As explained, the main drawback of passive tracer (physical) methods arises if the sampling volume is larger than the smallest segregation scales. Under these circumstances, it is impossible to determine whether the two fluids are mixed or not within the measurement resolution. Several authors [39] have pointed out that the problem of finite sampling volume can be solved by using a fast and irreversible chemical reaction of the type A + B P. If dilute reactant is added to one stream and B to the other, then the amount of chemical product formed is equal to the amount of molecular scale mixing between the two streams at the reaction stoichiometric ratio. This is the reason why chemical methods have been developed. 

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