The Accommodation Coefficient

Up to this point we have assumed that once a vapor molecule encounters the surface of a particle its probability of sticking is unity. This assumption can be relaxed by introducing an accommodation coefficient a, where 0 a 1. The flux of a gas A to a spherical particle in the kinetic regime is then given by (12.25). 

The transition regime formulas can then be extended to account for imperfect accommodation by multiplying the left-hand side of (11.27) by or. The Fuchs expression in (11.31) becomes 

FIGURE 11.3 Comparison of experimental dibutyl phthalate evaporation data with the theories of Loyalka et al. (1989), Sitarski and Nowakowski (1979) (for z = 15), and the equation of Fuchs and Sutugin (1970). Reprinted from Aerosol Science and Technology, 25, Li and Davis, 11-21. Copyright 1995, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. 

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In the case of polyatomic molecules, one may consider separately the accommodation coefficients for translational and for vibrational energy. Values of the latter, civ, are discussed by Nilsson and Rabinovitch [7]. 

Based on the accommodation coefficient, the slip length is given by... 

If the accommodation coefficient CA is equal or close to unity for liquid metals, as appears most likely for clean systems, then bubble growth in such liquids is little affected by mass transfer effects. It has been illustrated that the growth rate curves for CA = 1 and CA = are not very far apart. 

Thus, as observed (Fig. 24), the heat transfer rate is directly proportional to pressure at low pressure. Note also that the heat transfer rate is independent of the distance separating the two surfaces, as expected by intuition. It was assumed that the accommodation coefficient was the same on each surface. If this assumption is not valid, the expression for a must be modified to the form... 

The accommodation coefficients for OH and HO2 in our model are parameterised as temperature dependent accommodation coefficients (Gratpanche et al., 1996) in Table 3, with no account taken of the surface characteristics. There are a few papers reporting uptake coefficients for both OH and HO2 with lower limits quoted for the HO2 coefficients due to experimental limitations, giving rise to a low confidence in current experimental values for HO2 (Cooper and Abbatt, 1996 Hanson et al., 1992). The impact of reactions on aerosol on HO2 concentrations in the remote atmosphere could be significant if the uptake coefficient was greater than 0.1, and could dominate if it was close to unity (Saylor, 1997). 

Growth of particles by accumulation on existing particles can be classed as two broad processes. If the precursor is supersaturated, growth will occur at a rate limited by vapor diffusion, which depends on the supersaturation, the temperature, the particle size, and the accommodation coefficient at the surface. The proportionality of particle size changes with the ratio of particle diameter to mean free path of the suspending... 

In the creeping flow range, C is equal to the ratio of the terminal velocity to the terminal velocity in continuum flow. The value of C is sensitive to the nature of molecular reflections from the surface of the particle (E5). The accommodation coefficient, o-r, may be interpreted as the fraction of molecules undergoing diffuse reflection, the balance being specularly reflected. Typical values for lie between 0.8 and unity. For near-continuum flow. Basset (B9) showed that... 

The energy exchange between an impinging gas atom or molecule and a surface can be represented by a coefficient, the accommodation coefficient, as defined by Knudsen,11... 

We easily find the dependence of the evaporation rate on superheating by applying the principle of detailed equilibrium. The accommodation coefficient, i.e., the probability that molecules of vapor falling onto the surface of the liquid will stick, we take equal to 1. The number of molecules which evaporate in unit time is equal to the number of molecules which fall in unit time onto the surface at equilibrium pressure which, in turn is equal to the product of half the number n of molecules in a unit volume of vapor and the average velocity cx of the molecules in the direction normal to the surface. 

Another useful parameter is the accommodation coefficient a. The accommodation coefficient is defined by the temperature of the molecules before the impact T), the surface temperature 7 2, and the temperature of the reflected molecules T3 [364] ... 

For an elastic reflection, the mean velocity of the molecules before and after hitting the surface are identical and so are the temperatures T = 7 s. Then a = 0. If the molecules reside a long time on the surface they have the same temperature, after desorption, as the surface T2 = 7 s and a = 1. Thus, the accommodation coefficient is a measure of how much energy is exchanged before a molecule leaves the adsorbent again. 

Equation (4.11) applies provided that the gas phase resistance to the transfer of HTO is limiting. This requires that the accommodation coefficient of molecules at the surface, the solubility, and the liquid phase diffusion, or mixing, within the drop, are all sufficiently high. 

Some radioactive vapours are adsorbed or chemisorbed on surfaces so strongly that the boundary condition is Xo equal to zero. This is also true of particles in the submicrometric size range. The velocity of gas molecules perpendicular to surfaces is of order 100 ms-1, whereas the resistance of the laminar boundary layer to molecular diffusion usually restricts vg to a value of the order 0.1 m s-1 or less. Hence if the accommodation coefficient, the fraction of molecular collisions which entail sorption at the surface, exceeds about 10-3, the surface will act as a perfect sink. 

For the deposition of particles, bounce-off and blow-off, which must be carefully distinguished, may be considered analogous to the accommodation coefficient and to re-evaporation respectively. 

The values of the accommodation coefficient ]3 for the recombination over silver and gold (see Table 6) are probably high enough to be compatible with reaction between mobile adatoms, but the low value for copper is not. Once again, we face the same dilemma posed by recombination over the Group IB metals. 

Methods of detecting adsorbed films, which are of great value as auxiliaries to determinations of the amounts adsorbed, include the measurement of the accommodation coefficient ( 11), of the thermionic... 

The fraction of the atoms or molecules condensing may vary from unity to a very small fraction. The exchange of heat between a gas and a solid is controlled by the fraction of gas molecules which condense, i.e. remain long enough to come into thermal equilibrium with the solid. Much work has been done on the accommodation coefficient , defined as a in the equation... 

We have already mentioned that the temperature-jump effect arises as a result of the failure of the molecules to accommodate to the surface temperature when the mean free path becomes of the order of a characteristic body dimension. The parameter which describes this behavior is called the accommodation coefficient a, defined by... 

Values of the accommodation coefficient must be determined from experiment, and a brief summary of such measurements is given in Table 12-1. 

Accommodation Coefficient Measurements. Recently Lee and Tang (20) have presented measurements of the accommodation coefficients of O3 and SO2 on aqueous solution. In the case of O3 a value of 5 x 10" is reported. It is seen by examination of Figure 9 that an accommodation coefficient of this magnitude is well above the value that would lead to interfacial mass-transport limitation under circumstances of interest, intersecting the O3 line only at pH >6, well... 

Equation (5) indicates that by monitoring the gas concentration change as a function of time, the accommodation coefficient may be deduced using a computer program. However, precautions must be undertaken to satisfy the boundary condition that the surface concentration of the dissolved gas must be negligible at all times. This can be accomplished in principle by agitation and by addition of proper chemical reagents in the aqueous phase to remove the dissolved gas as quickly as it is absorbed. In addition, the system must be operated at sufficiently low pressure so that the gas-phase resistance is much smaller than interfacial resistance. 

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