Diffusion of water vapor

Pick s law States that the molecular diffusion of water vapor in a gas without appreciable displacement of the gas is analogous to the conduction of heat, and is governed by a similar type of law. 

Upward diffusion of water vapor through the cold temperatures of the tropopause is very inefficient in fact, the upper limit of cloud formation often occurs at the tropopause. Thus the stratosphere is so dry as to prevent rain formation, and particles and gases have very much longer residence times there than in the troposphere. Stratospheric removal requires diffusion back through the tropopause, which then may be followed by precipitation scavenging. 

Situation Two different strengths of plastic foil are in evaluation for the packaging of a moisture-sensitive product. Information concerning the diffusion of water vapor through such foils is only sparsely available for realistic conditions. To remedy this lack of knowledge, samples of the product are sealed into pouches of either foil type and are subjected to the following tests ... 

The basic assumption for a mass transport limited model is that diffusion of water vapor thorugh air provides the major resistance to moisture sorption on hygroscopic materials. The boundary conditions for the mass transport limited sorption model are that at the surface of the condensed film the partial pressure of water is given by the vapor pressure above a saturated solution of the salt (Ps) and at the edge of the diffusion boundary layer the vapor pressure is experimentally fixed to be Pc. The problem involves setting up a mass balance and solving the differential equation according to the boundary conditions (see Fig. 10). 

Measurement of relative humidity depends on the system used. Systems employing vacuum are usually evacuated prior to introduction of water vapor [29]. For cases in which there is not a gas-forming reaction occurring, measurement of total pressure in the system can be used as a measure of water vapor pressure. Systems in which air is not evacuated require specific measurement of water vapor pressure. (For the latter type of system, caution should be taken to assure that the relative humidity source is in close proximity to the solid, since the diffusion of water vapor through air to the solid is required to maintain a constant relative humidity in the immediate vicinity of the solid.) A wide variety of pressure measuring instrumentation is commercially available with varying accuracy, precision, and cost. 

How does the diffusivity of water vapor in air at 5°C compare with that at 25°C ... 

From a flat surface of water at 20 °C water is vaporizing into air (25 °C, water pressure 15.0 mmHg) at a rate of 0.0041 g cm" h . The vapor pressure of water at 20 °C is 17.5 mmHg. The diffusivity of water vapor in air at the air film temperature is 0.25 cm s". Estimate the effective thickness of the air film above the water surface. 

D — gaseous diffusion coefficient of water through air, 0.208 sq. cm. per second Dm = diffusivity of water vapor in air... 

In contrast, Nafion removes water vapor by a process called perevaporation. Water is absorbed onto the walls of the Nafion, moves through the walls, and evaporates into the sweep gas [30]. As a result, volatile analytes should not be lost through the membrane. The efficiency of removal depends on diffusion of water vapor to the walls of the membrane. When the water vapor load is significantly less than the dew point, the efficiency also improves as the temperature of the dryer is reduced [31]. This membrane separator does not remove organic solvent vapor from the Ar gas stream, but it also does not suffer from loss of volatile analytes. 

The rate of evaporation of water from such an isolated drop, although governed entirely by diffusion, is not governed entirely by diffusion of water vapor. Latent heat must be supplied during evaporation. The drop cools until this heat is conducted in from the air at a rate equalling the outward diffusion of water vapor. There is no other significant heat source since even if the drop were black, the direct radiation contribution of full sunlight would not be important for drops of this size. 

An important conclusion from Fig. 6 is that for a small void, it is immaterial wheter or not the initial void contains pure water or an air/water mixture. The diameters at any particular time during the cure cycle are nearly identical when the initial void diameters under 0.1 atm are the same. An air/water void initially containing pure air has a very large driving force for diffusion of water vapor from the resin to the void during the first few minutes of the cycle. This results in diffusion into the void of a large amount of water vapor (relative to the original amount of dry air in the void). Consequently the mole fraction of water vapor in the air/water void quickly approaches unity, and thereafter the rate of diffusion of water vapor across the interface of the air/water void is nearly the same as that for a pure water void. 

Let us first consider the diffusion of water vapor from a horizontal surface into quiescent air as indicated in Fig. 11-5. At the surface, the partial pressure of the vapor is ps. The vapor pressure steadily drops with a rise in elevation z to the free atmosphere value of px. The molecular diffusion of the water vapor may be written in the form of Eq. (11-13) as... 

Equation 8.2 shows how the net flux density of substance depends on its diffusion coefficient, Dj, and on the difference in its concentration, Ac] 1, across a distance Sbl of the air. The net flux density Jj is toward regions of lower Cj, which requires the negative sign associated with the concentration gradient and otherwise is incorporated into the definition of Acyin Equation 8.2. We will specifically consider the diffusion of water vapor and C02 toward lower concentrations in this chapter. Also, we will assume that the same boundary layer thickness (Sbl) derived for heat transfer (Eqs. 7.10-7.16) applies for mass transfer, an example of the similarity principle. Outside Sbl is a region of air turbulence, where we will assume that the concentrations of gases are the same as in the bulk atmosphere (an assumption that we will remove in Chapter 9, Section 9.IB). Equation 8.2 indicates that Jj equals Acbl multiplied by a conductance, gbl, or divided by a resistance, rbl. 

We now calculate two extreme values of the stomatal conductance for the diffusion of water vapor through open stomata. We will consider air at 25°C for which Dw is 2.5 x 10-5 m2 s-1 (Appendix I). The stomatal conductance tends to be high when a large portion of the leaf surface area (e.g., nast = 0.02) is occupied by open stomata of relatively short pore depth (e.g., Sst = 20 pm). Using a mean radius of 5 pm, Equation 8.5 predicts that the conductance then is... 

The leaf resistance is in series with that of the boundary layer, Thus the total resistance for the flow of water vapor from the site of evaporation to the turbulent air surrounding a leaf (r al) is 4- (see Fig. 8-5). We now must face the complication created by the two leaf surfaces representing parallel pathways for the diffusion of water vapor from the interior of a leaf to the surrounding turbulent air. We will represent the leaf resistance for the pathway through the upper (adaxial) surface by rj afu and that for the lower (abaxial) surface by r af. Each of these resistances is in series with that of an air boundary layer—and for the upper and the lower leaf surfaces, respectively. The parallel arrangement of the pathways through the upper and the lower surfaces of a leaf leads to the following total resistance for the diffusion of water vapor from a leaf ... 

We next examine a simplified expression for the total water vapor resistance that often adequately describes diffusion of water vapor from the sites of evaporation in cell walls to the turbulent air surrounding a leaf and is useful for considering diffusion processes in general. We will consider the case in which nearly all of the water vapor moves out across the lower epidermis and when cuticular transpiration is negligible. By Equations 8.11 and 8.12, the total resistance then is... 

Figure 8-7. Representative values of quantities influencing the diffusion of water vapor out of an actively transpiring leaf. Conductances are given for the indicated parts of the pathway assuming that water moves out only through the lower leaf surface and ignoring cuticular transpiration.

Figure 8-7 also indicates specific values of the conductances as well as the overall series conductance for the diffusion of water vapor from the sites of evaporation to the turbulent air. The largest drop in water vapor content occurs across the stomatal pores because they have the smallest conductance in the current case. For instance, A7V,S, is equal to which is... 

We will now reconsider the values of the various conductances affecting the diffusion of water vapor through the intercellular air spaces, out the stomata, and across the air boundary layer at the leaf surface. Usually gjas is relatively large, is rarely less than 500 mmol m-2 s-1, but g,s, is generally less than... 

Diffusion of Water Vapor in Newborn Rat Stratum Corneum. Measurement and interpretation of diffusion in heterogenous biological systems such as the stratum corneum are difficult compared with similar measurements for well-defined synthetic polymer systems, but studies of water diflFusion in stratum corneum are essential to a better understanding of those factors which contribute to the barrier function of the corneum. Water diffusion measurements under both equilibrium and non-equilibrium conditions are useful to probe the influence of temperature and other factors on stratum corneum macromolecular structure. 

Severinghaus J. P., Bender M. L., Keeling R. F., and Broecker W. S. (1996) Fractionation of soil gases by diffusion of water vapor, gravitational settling, and thermal diffusion. Geochim. Cosmochim. Acta 60, 1005-1018. 

Due to its practical importance, the diffusion of water vapor in air has been the topic of several studies, and some empirical formulas have been developed for the diffusion coefficient DH,o-ai,- Marrero and Mason (1972) proposed this popular formula (Table 14-4) ... 

SOLUTION The liquid layer on the inner surface of a circular pipe is dried by blowing air through it, The mass transfer coefficient is to be determined. Assumptions 1 The low mass flux model and thus the analogy between heat and mass transfer is applicable since the mass fraction of vapor in the air is low (about 2 percent for saturated air at 300 K). 2 The flow is fully developed, Properties Because of lov/ mass flux conditions, v/e can use dry air properties for the mixture at the specified temperature of 300 K and l atm, for which v = 1.58 X 10 mVs (Table A-15). The mass diffusivity of water vapor in the air at 300 K is determined from Eq. 14-15 to be... 

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