Exchange velocity

Exchange velocity The rate with which one ion is displaced from an ex- changer in favor of another. 

Baffles are a very important part of the performance of a heat exchanger. Velocity conditions in the tubes as well as... 

The self-exchange velocity (SEV), which can be calculated from molecular dynamics simulation, has reproduced the Chemla effect. Fur-... 

Okada et al. have presented a dynamic dissociation model, which is schematically shown in one dimension in Fig. 4. They assumed that the separating motion of a cation (or anion) of interest from the reference anion (cation), which is called the self-exchange velocity,is the electrically conducting process, which will be considered in Section III.7( ) in more detail. The Chemla effect can also be reproduced by the SEV. 

Okada et al. have found that internal mohilities are strongly related to the separating motion of unlike ion pairs defined by the self-exchange velocity, which can be easily calculated from MD simulation ... 

Figure 17. Self-exchange velocities vs. internal mobilities calculated from the same MD runs for pure LiCl and (Li, Cs)Cl mixture(xcs, = 0.90). experimental for u. (Reprinted from Ref 47 with permission of Trans Tech Publications.)...

In environmental systems fluxes are usually expressed as mass per unit area and per time (dimension ML 2 "1) and the occupation numbers as concentrations (dimension ML 3). Then, the constant appearing in the flux expression must have the dimension of a velocity (LT"1). Later we will use the term transfer or exchange velocity and designate it as vA/B or vex to discuss the speed with which mass is moved from subsystem A to subsystem B. To summarize, the mass transfer model takes the form ... 

When comparing Eqs. 19-1 and 19-3, the reader may remember the discussion in Chapter 18 on the two models of random motion. In fact, these equations have their counterparts in Eqs. 18-6 and 18-4. If the exact nature of the physical processes acting at the bottleneck boundary is not known, the transfer model (Eqs. 18-4 or 19-3) which is characterized by a single parameter, that is, the transfer velocity vb, is the more appropriate (or more honest ) one. In contrast, the model which started from Fick s first law (Eq. 19-1) contains more information since Eq. 19-4 lets us conclude that the ratio of the exchange velocities of two different substances at the same boundary is equal to the ratio of the diffusivities in the bottleneck since both substances encounter the same thickness 5. Obviously, the bottleneck model will serve as one candidate for describing the air-water interface (see Chapter 20). However, it will turn out that observed transfer velocities are usually not proportional to molecular diffusivity. This demonstrates that sometimes the simpler and less ambitious model is more appropriate. 

Figure 19.5 In multibox models, the exchange between two fairly homogeneous regions is expressed as the exchange flux of fluid (water, air etc.), Q . Normalization by the contact area, A, yields the exchange velocity vex = QJA. This quotient can be interpreted as a bottleneck exchange velocity vex =...

Estimate the bottleneck exchange velocity, vex, between the upper water volume (epilimnion) and the lower one (hypolimnion) of Greifensee and determine the... 

In the expression for the total exchange velocity across a two-layer bottleneck boundary between different media (Eq. 19-20) the transfer velocity vB is multiplied by the extra factor Kpj. What is AiA/B Can you imagine a scheme in which vA carries an extra factor instead How are the two schemes related ... 

Box 20.1 Influence of Wind Speed Variability on the Mean Air-Water Exchange Velocity of Volatile Compounds... 

Box 20.2 Temperature Dependence of Air-Water Exchange Velocity v(w of Volatile Compounds Calculated with Different Models Overall Air-Water Exchange Velocities... 

All the physics is hidden in the coefficient via/w which, because it has the dimension of a velocity (LT-1), is called the (overall) air-water exchange velocity. Air-water exchange occurs due to random motion of molecules. Equation 20-1 is a particular version of Eq. 18-4 in which the air-water exchange velocity adopts the role of the mass transfer velocity, vA/B. 

Generally, the total exchange velocity, v,a/w, can be interpreted as resulting from a two-component (air, water) interface with phase change. Independently of the chosen model (bottleneck or wall boundary), if we choose water as the reference phase, via/w is always of the form (see Eqs. 19-13 and 19-58) ... 

The main part of this chapter deals with models for describing via/w as a function of different environmental factors such as wind speed, water temperature, flow velocity, and others. None of these models is able to totally depict the complexity of the processes acting at the surface of a natural water body. Therefore, theoretical predictions of the exchange velocity always meet severe limitations. Nonetheless, two properties stick out from Eqs. 20-1 to 20-3 ... 

The structure of Eq. 20-3 allows us to identify ranges of AA/w for which the transfer velocity, vfa/w, depends on just one of the two single-phase exchange velocities. 

At first sight, there seems to be a basic difference between the two regimes with respect to the influence of Kia/Vl. In the water-phase-controlled regime, the overall exchange velocity, via/w, is independent of Kia/v/, whereas in the air-phase controlled regime v(a/w is linearly related to Ga/w. Yet, this asymmetry is just a consequence of our decision to relate all concentrations to the water phase. In fact, for substances with small Kia/v/ values, the aqueous phase is not the ideal reference system to describe air-water exchange. This can be best demonstrated for the case of exchange of water itself (Kia/V1 = 2.3 x 10 5 at 25°C), that is, for the evaporation of water. 

The total transfer velocities, via/w and v a/w, are plotted in Fig. 20.1 as a function of Kjalvr. Note that these curves give approximate values which are valid if the real exchange velocities are close to the chosen typical values, vaypicaI and v pical. The figure shows nicely that via/w and v a/w, respectively, become independent of Kia/W if that phase is chosen as the reference system which dominates the overall exchange velocity. A more refined picture of the overall transfer velocities will be shown in Fig. 20.7. 

Before looking closer at the experimental information on single-phase exchange velocities, let us briefly examine the assumption that we made regarding the exist-... 

Figure 20.1 Schematic view of the overall air-water exchange velo-city, via/w, as a function of the air-water partition coefficient, Ku/w, calculated from Eq. 20-3 with typical single-phase transfer velocities v,a = 1 cm s"1, vM = 10 3 cm s1. The broken line shows the exchange velocity v a/w (air chosen as the reference system). The upper scale gives the Henry s Law coefficient at 25°C, Km = 24.7 (Lbar mol"1) x Ku/W.

For T = 298 K (25°C) and M( = 78 g mol-1 (benzene), this velocity is 7 x 103 cm s-1. Even if only a small fraction of the molecules, say one out of every thousand, actually penetrates into the other phase and stays there, the molecular exchange velocity is still of the order of 10 cm s. This is much larger than the largest transfer velocities viaAv shown in Fig. 20.1. Hence, the molecular transfer right at the interface is not the limiting step. At the interface equilibrium conditions can be assumed, indeed. 

Let us now analyze the information on air-water exchange velocities which has been gained from observations both in the field and in the laboratory. We are especially interested in those extreme situations which are either solely water-phase or solely air-phase controlled, since they allow us to separate the influences of the two phases. We start with the latter case, the air-phase-controlled exchange. 

For compounds with Kii/Vl larger than about 10 2 the overall air-water transfer velocity is approximately equal to the water-phase exchange velocity viw The latter is related to wind speed uw by a nonlinear relation (Table 20.2, Eq. 20-16). The annual mean of viw calculated from Eq. 20-16 with the annual mean wind speed ul0 would underestimate the real mean air-water exchange velocity. Thus, we need information not only on the average wind speed, but also on the wind-speed probability distribution. 

In the preceding discussion, we presented experimental information on the singlephase air-water exchange velocities. Water vapor served as the test substance for the air-phase velocity v,a, while 02, C02 or other compounds yielded information on v,w. Now, we need to develop a model with which these data can be extrapolated to other chemicals which either belong also to the single-phase group or are intermediate cases in which both via and vlw affect the overall exchange velocity v,a/w (Eq. 20-3). 

One essential assumption is that all substances experience the same film thickness. Therefore, the model predicts that for given conditions the exchange velocities of different compounds, i and j, should be linearly related to their molecular diffusivities ... 

Because the diffusivity ratio, Dia/Dja, is not exactly identical for air and water and since Eq. 20-3 also contains Kia,w, Eq. 20-19 does not hold for the composite (overall) exchange velocity v,Ww. It can be applied to classes of substances which are either solely water-phase- or air-phase-controlled. 

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