Transfer velocity

Powder transfer velocity and mass flow rate are not subject to any maximum values,... 

However, the dry deposition rate for noble gases, tritium, carbon-14, and nonelemental radioiodine is so slow that this depletion mechanism is negligible within 50 miles of the release point. Elemental o radioiodine and other particulates are readily deposited. This transfer can be quantified as a transfer velocity (where concentration transfer velocity = deposition rate). The transfer velocity is proportional to windspeed and, as a consequence, the rate of depositirm is independent of windspeed since concentration in air is inversely proportional to windspeed. 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

Here Ac = Ca - XhCw with Cg and Cw representing the concentrations in the air and water respectively and Kh the Henry s law constant. The parameter K, linking the flux and the concentration difference, has the dimension of a velocity. It is often referred to as the transfer (or piston) velocity. The reciprocal of the transfer velocity corresponds to a resistance to transfer across the surface. The total resistance R — K ) can be viewed as the sum of an air resistance (i a) and a water resistance (Rw). ... 

The parameters fcg and k are the transfer velocities for chemically unreactive gases through the viscous sublayers in the air and water, respectively. They relate the flux density F to the concentration gradients across the viscous sublayers through expressions similar to Equation (42) ... 

The numerical values of the transfer velocity K for the different gases are not well established. Its magnitude depends on such factors as wind speed, surface waves, bubbles and heat transfer. A globally averaged value of K often used for CO2 is about 10 cm/h. Transport at the sea-air interface is also discussed in Chapter 10 for a review see Liss (1983). 

The piston velocity, or gas transfer velocity, is a function of wind speed. There are large differences in the relationships between piston velocity and wind speed, especially at liigher wind speeds (e.g., Liss and Merlivat, 1986 Wannin-khof, 1992). This is the limiting factor for these calculations. 

Figure 2 Variation of the gas transfer velocity with wind speed. The units of transfer velocity are equivalent to the number of cm of the overlying air column entering the water per hour (Taken from Bigg,28 with permission of Cambridge University Press)...

K = oxygen transfer velocity (m s 1, m h 1 or m d 1) a = water-air surface area, A, to volume of water, V (m-1) dm = hydraulic mean depth of the water phase, i.e., the cross-sectional area of the water volume divided by the water surface width (m)... 

Piston velocity The rate at which supersaturated gases are moved from the surface ocean into the atmosphere by molecular diffusion. Transfer velocity. 

With respect to the physical processes, boundaries can be subdivided into just three classes. The distinction will be made according to the nature of the resistance to mass transfer across the boundary. We must recognize that this transfer is usually mediated by random motions. Thus, the resistance is like the inverse of a generalized diffusivity or transfer velocity, since both these quantities have the function of a conductivity (of mass, heat, momentum, etc.). For simplicity, the following discussion will be focused on the diffusion model (Eq. 18-6), although everything which will be said can also be adapted to the transfer model (Eq. 18-4). 

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. 

Since the inverse of the transfer velocity, (vb) , can be interpreted as a transfer resistance, Eq. 19-13 expresses a simple, but very important rule the total resistance of two bottlenecks is equal to the sum of the resistances of the single bottlenecks. This result can be easily generalized to three and more bottleneck zones (see Problem 19.3). 

Eqs. 19-19 and 19-20 represent a powerful tool for the description of multilayer bottleneck boundaries. In fact, the validity of the result extends beyond the special picture of a series of films across which transport occurs by molecular diffusion. Since the transfer velocities, vA and vBKB/A, can be interpreted as inverse resistances, Eq. 19-20 states that the total resistance of a multilayer bottleneck boundary is equal to the sum of the individual resistances. Note that the resistance of the nonreference phase includes the additional factor KBIA. In Problem 19.3, the above result shall be extended to three and more layers. 

In these equations we recognize expressions which by now should have become familiar to us. During the initial phase of the exchange process (t Zcm), boundary concentration and flux at the interface remind us of a (B-side controlled) bottleneck boundary with transfer velocity vbl = Db,/S (see Eq. 19-19). The concentrations on either side are C and CBq=CA/FA/B, where the latter is the B-side concentration in equilibrium with the initial A-side concentration CA. 

Transfer velocity across gaseous boundary layer typically between 0.1 and 1 cm s"1 (up to 5 cm s 1, see Fig. 20.2). Km is the nondimensional liquid/gas distribution coefficient (for air-water interface inverse nondimensional Henry s law coefficient, i.e., Jfr w) with typical values between 10-3 and 103. DA is the molecular gaseous diffusivity, typical size 0.1 cm2s . 

Typical transfer velocity across liquid layer 10"3 cm s 1 (range 10 5 to 10 2 cm s see Section 20.2 and Illustrative Examples 19.3, 19.4). Km is the equilibrium partition coefficient with typical values between 1 and 104 (see Table 19.1). DA is the aqueous molecular diffusivity in pore space (typical size 10"5 cmV) divided... 

The flux across a bottleneck boundary can be expressed either in terms of Fick s first law or by a transfer velocity. Explain how the two views are related. 

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 ... 

Transfer Velocities in Air Deduced from Evaporation of Water Illustrative Example 20.2 Estimating Evaporation Rates of Pure Organic Liquids... 

Transfer Velocities in the Water Phase Deduced from Compounds with Large Henry s Law Constants... 

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