Of concentration fluctuations

Figure 5.135. Time-variant turbulent fluctuations of concentration about a mean value C, showing the fluctuation value C, ...

Used in calculation of dosing regimens - the frequency of dosing is adjusted to keep the fluctuation of concentration between doses within acceptable hmits... 

Nucleation is initiated by local fluctuations of concentration within a metastable region. The activation energy of nucleation depends on the value of the interface energy required to create a nucleus. The droplet grows by diffusion of macromolecules into the nucleate domains. The natural form of the phase separation through NG mechanism is the sea-island type. 

A general technique for determining fluxes is to measure the correlation of fluctuations of concentration with those of vertical wind speed, which are due to vertical eddies in the atmosphere (see reference 80 and references cited therein). If a species is emitted from the surface, for example, it is somewhat more concentrated in air parcels moving upward than in those moving downward. To effect this approach requires sensors with at least 1 Hz, and preferably 10 Hz, time response. Presently, such instrumentation is unavailable, except for NO and NOy measurements. Developing such techniques for N20, NO (or NO ), NH3, and HN03 would be desirable. 

As a result of Brownian motion, continual fluctuations of concentration take place on a molecular or small-particle scale. For this reason, the second law of thermodynamics is only valid on the macroscopic scale. 

Although the previous equation signifies the importance of the diffusion characteristics of the reactant species, it cannot be used to describe adequately the rate of the reaction. The reason is that the concept of global concentrations for the riA and ng molecules is meaningless, since a unit volume cannot be conceived due to the local fluctuations of concentrations. Hence, the local concentrations of the reactants determine the rate of the reaction for diffusion-limited reactions. Accordingly, local density functions with different diffusion coefficients for the reactant species are used to describe the diffusion component of reaction-diffusion equations describing the kinetics of diffusion-limited reactions. 

Lombardo and Bell (1991) reviewed stochastic models of the description of rate processes on the catalyst surface, such as adsorption, diffusion, desorption, and surface reaction, which make it possible to account for surface structure of crystallites, spatial inhomogeneities, and local fluctuations of concentrations. Comparison of dynamic MC and mean-field (effective) description of the problem of diffusion and reaction in zeolites has been made by Coppens et al. (1999). Gracia and Wolf (2004) present results of recent MC simulations of CO oxidation on Pt-supported catalysts. 

According to the general definitions of the coil and the globule241, the macromolecule is in the coil state, if the fluctuations of the monomer concentration within the macromolecule are of order of the monomer concentration itself and the correlation radius of the fluctuations of concentration is of order of the macromolecular dimensions while in the globular state the concentration fluctuations are small compared with the concentration and the correlation radius is considerably smaller than the globular dimensions. 

There is a lot of common usage of the terms blend time, mixing time, and circulation time. There are differences in concept and interpretation of these different "times. For any given experiment, one must pick a definition of blend time to be used. As an example, if one is measuring the fluctuation of concentration after an addition of material to the tank, then one can pick an arbitrary definition of blending such as reducing the fluctuations below a certain level. This often is chosen as a fluctuation equal to 5% of the original fluctuation when the feed material is added. This obviously is a function of the size of the probe used to measure these fluctuations, which often is on the order of 500 to 1000 pm. 

C. Gabrielli, F. Huet, R.P. Nogueira, Fluctuations of concentration overpotential generated at gas-evolving electrodes, Electrochimica Acta, Volume 50, Issue 18 (2005) pp3726-3736... 

Zeldovich Ya B 1977 The role of thermal fluctuations of concentration in the kinetics of bimolecular reactions Elektrokhimia 13 677-9... 

Segregation effects are also important for fundamental studies. For each demixing process there is a critical point, near which certain fluctuations of concentration in the mixture become anomalously large. Essentially all the work on the theory of these effects in polymer systems has been based on mean field ideas. However in many cases critical phenomena are now known to be qualitatively different from mean field predictions. One of our tasks in this chapter is to classify the critical points some will be of the mean field type, others will be different. 

We consider here a solution (or melt) with two types of polymer chains, A and B, and a slight incompatibility between A and B. We want to investigate the dynamics of the fluctuations of concentration <1> near the critical point in the one-phase region. Experimentally it will help if we add a fraction of solvent to the AB mixture, thereby decreasing the viscosities and relaxation times. However, for simplicity here we consider [Pg.238]

RG theory predicts that the tricritical theta-point behaviour is mean-field with logarithmic corrections caused by the fluctuations of the infinitely long polymer chain. This prediction is supported by experiments. It means that the Widom variable x plays the same role for polymer solutions as Af /No in the Ginzburg criterion (compare with inequality. (7.18)) at x l the behaviour is critical and dominated by the fluctuations of concentration, while at x 1 the behaviour is tricritical and mean-field (Flory-like). 

Figure 87. Seasonal fluctuation of concentration in leaf litter and in saprophagous and predaceous arthropods in a tulip tree (Liriodendron tulipifera) stand experimentally tagged with Cs. The leaf-litter content of radiocesium increased in September following autunmal leaf drc, but then decreased due to leaching. The higher trophic levels of arthropod consumers also show the changing concentrations of which reflect changes in their food bases. The relative amplitudes of the curves illustrate the decrease in Cs concentrations through arthropod food chains. From Crossley and Reichle (1969).

When a small fluctuation of temperature is introduced to the bed which is in a dynamic steady state of concentration Co, temperature To and the amount adsorbed qo = qo(Cb, To), then by linearizing the equilibrium relation for a small fluctuation around the steady state condition, the basic equations for fluctuations of concentration (C = C — Co), temperature T — T — To) and amount adsorbed (q = q — qo), together with the equilibrium amount adsorbed iq q — qo) can be derived. 

The fluctuation of concentrations is always accompanied by a change in free energy, AG. We now expand AG in terms of Ac around the equilibrium concentration (c) using Taylor s series ... 

With condition 6 G ix 76(p <0 (within the spinodal region), the system is unstable to small fluctuations of concentration. The supersaturated solution starts decomposing through the entire volume simultaneously, without generation of nuclei. The spinodal separation is a kinetic process of a spontaneous formation and continuous growth of another phase in an unstable parent phase,caused by the origination of low-amplitude fluctuations of the composition. As a result, the rapid growth of the second phase proceeds with charac-... 

Classically, the aggregation process is described by the Smolu-chowski equation, which is an irreversible chemical reaction kinetic equation used to treat the aggregation of nonfractal particles. Therefore, the collision takes place between two bodies with small fluctuation of concentration, and is assumed to occur randomly. 

Even if nothing peculiar occurs at this critical concentration (C ) with respect to the solution properties, the medium is the subject of fluctuations of concentration while passing from the dilute regime to the semi-dilute one (Figure 4.10). 

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