Water vapor diffusion coefficient

Here,/is the water vapor flux, C is the saturated water vapor concentration, De is the water vapor diffusion coefficient in air, T is the temperature, and z is a position in the sample. In this study, it was assumed that the water vapor in the snow sample was saturated. Although there were some arguments about water vapor diffusion coefficient in snow and tortuosity dependence, we did not use those values because we have no data on how those values change during dry snow metamorphism. In reality, we think those values probably affect the water vapor flux. 

The saturated water vapor concentration C was calculated from the temperature at each position. The distribution of the water vapor flux was then calculated using the water vapor diffusion coefficient D. Finally, we compared fc and fn and examined the relationship between the water vapor flux and the crystal growth rate. 

The considered radial process in the bentonite annulus is a complicated one with coupled, highly nonlinear flows that involve many things. There are liquid flow and vapor flow as well as conductive and convective heat flow depending on gradients in pressure, water vapor density and temperature. The flow coefficients depend on water properties such as saturation water vapor pressure and dynamic viscosity of water. They also depend on the properties of bentonite water retention curve, hydraulic conductivity and water vapor diffusion coefficient, and thermal conductivity, all of which are functions of degree of water saturation. 

Water vapor diffusion coefficients as functions of time are shown in Fig, 8. Values obtained from (2), (3), and (4) are all shown for comparison. Due to the scatter obtained, coefficients resulting from (2) are shown as a band of values rather than a single curve. Such a coefficient should be a function of the partial pressure gradient across the diffusional boundary layer. However, under the ambient conditions existing during this study, this quantity was essentially constant, and no partial pressure relationship was determined. However, the effect of boundary layer condensation without subsequent adherence to the container surface is illustrated by the data shown in Fig. 8. Equations (2), (3) and (4) pro-... 

Figure 14.2 Water vapor diffusion coefficient versus activity at 40 °C.

The addition of PEOX to PES causes the water vapor diffusion coefficient to decrease in absolute magnitude, but to increase more strongly with activity. This behavior reflects the increased water sorption and the resultant tendency for materials containing PEOX to be plasticized, and overshadows the effect of the decrease in the free volume of dry polymer. The permeability coefficients for blends containing 10% and 20% PEOX were lower than those for PES, because the decrease in the diffusion coefficient was larger than the increase in the equilibrium water solubility. 

Table 4.10. The coefficient Kw (cm2/s) of water vapor diffusion in the atmosphere at a pressure of 1,000 mb as a function of temperature T. From Roll (1968).

To illustrate the system behavior, the ternary mixture 1 = iso-propanol, 2 = water, and 3 = air is considered here. In order to obtain an algebraic solution, both the dif-fusivities of iso-propanol in air and iso-propanol in water vapor were assumed to be approximately the same, which is not far from reality. The liquid phase mass transfer resistance was negligibly small, as will be shown below. The phase equilibrium constants K/,c and Kjrs were calculated with activity coefficients from van Laar s equation. Water vapor diffuses 2.7-fold faster in the inert gas air than iso-propanol. The ratio of the respective mass transfer coefficients kj3 equals the ratio of the respective diffusivities to the power of 2/3rd according to standard convective mass transfer equations Sh =J Re, Sc). 

Zawodzinski et al. [64] have reported self-diffusion coefficients of water in Nafion 117 (EW 1100), Membrane C (EW 900), and Dow membranes (EW 800) equilibrated with water vapor at 303 K, and obtained results summarized in Fig. 36. The self-diffusion coefficients were deterinined by pulsed field gradient NMR methods. These studies probe water motion over a distance scale on the order of microns. The general conclusion was the PFSA membranes with similar water contents. A, had similar water self-diffusion coefficients. The measured self-diffusion coefficients in Nafion 117 equilibrated with water vapor decreased by more than an order of magnitude, from roughly 8 x 10 cm /s down to 5 x 10 cm /s as water content in the membrane decreased from A = 14 to A = 2. For a Nafion membrane equilibrated with water vapor at unit activity, the water self-diffusion coefficient drops to a level roughly four times lower than that in bulk liquid water whereas a difference of only a factor of two in local mobility is deduced from NMR relaxation measurements. This is reasonably ascribed to the additional effect of tortuosity of the diffusion path on the value of the macrodiffusion coefficient. For immersed Nafion membranes, NMR diffusion imaging studies showed that water diffusion coefficients similar to those measured in liquid water (2.2 x 10 cm /s) could be attained in a highly hydrated membrane (1.7 x 10 cm /s) [69]. 

The transverse diffusion coefficient I) can be expressed by the porosity of wood V, the transverse bound water diffusion coefficient Dbt of wood and the vapor diffusion coefficient... 

Water evaporates from a strangely shaped surface into a flowing stream of hydrogen (15 m/sec, 38 C, 1 atm). Heat transfer studies for air flowing past a similarly shaped object at a superficial mass velocity of 21.3 kg/m sec show that h = 2.3G , where h is the heat transfer coefficient and G is the mass velocity. Find the water evaporation rate into the hydrogen if hydrogen-water vapor diffusivity is 0.775 cm /sec. 

In gases, this penetration distance is much larger than in other phases. For example, the diffusion coefficient of water vapor diffusing in air is about 0.3 cm /sec. In 1 second, the diffusion will penetrate 0.5 cm in 1 minute, 4 cm and in 1 hour, 30 cm. 

Water Transport. Two methods of measuring water-vapor transmission rates (WVTR) ate commonly used. The newer method uses a Permatran-W (Modem Controls, Inc.). In this method a film sample is clamped over a saturated salt solution, which generates the desired humidity. Dry air sweeps past the other side of the film and past an infrared detector, which measures the water concentration in the gas. For a caUbrated flow rate of air, the rate of water addition can be calculated from the observed concentration in the sweep gas. From the steady-state rate, the WVTR can be calculated. In principle, the diffusion coefficient could be deterrnined by the method outlined in the previous section. However, only the steady-state region of the response is serviceable. Many different salt solutions can be used to make measurements at selected humidity differences however, in practice,... 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Chemical Boiling Point C Desnity gm/cm Viscosity cP is-c Water Solubi- lity rag/L Vapor Pressure nun Hg Diffusion Coefficient, cnP/day ... 

It should be recognized that all plastic materials over a time period allow a certain amount of water vapor, organic gas, or liquid to permeate the thickness of the material. It is only a matter of degree of permeation between various materials used as barriers against vapors and gases. It has been found that the permeability coefficient is a function of the solubility coefficient and diffusion coefficient. The process of permeation is explained as the solution of the vapor into the incoming surface of the barrier, followed by diffusion through the barrier thickness, and evaporation on the exit side. 

The level of vapor movement in the unsaturated zone is much less important than transport in liquid form. However, this might not be true if the water content of the soil is very low or if there is a strong temperature gradient. The movement of vapor through the unsaturated zone is a function of temperature, humidity gradients, and molecular diffusion coefficients for water vapor in the soil. 

DWi = diffusion coefficient of water in air Xw = mole fraction of water vapor in air at a point x... 

Transport of the herbicides by vapor diffusion on moist soil was shown to be directly related to vapor pressure and inversely related to water solubility. Transport of the herbicides by leaching was shown to be inversely related to the Freundlich adsorption coefficient which in turn was directly related to the octanol/water partition coefficient and inversely related to water solubility (16). 

Frey, G., P.K. Hopke and J. Stukel, Effects of Trace Gases and Water Vapor on the Diffusion Coefficient of Polonium-218, Science 211 480-481 (1981). 

NAPL will migrate from the liquid phase into the vapor phase until the vapor pressure is reached for that liquid. NAPL will move from the liquid phase into the water phase until the solubility is reached. Also, NAPL will move from the gas phase into any water that is not saturated with respect to that NAPL. Because hydraulic conductivities can be so low under highly unsaturated conditions, the gas phase may move much more rapidly than either of the liquid phases, and NAPLs can be transported to wetter zones where the NAPL can then move from the gas phase to a previously uncontaminated water phase. To understand and model these multiphase systems, the characteristic behavior and the diffusion coefficients for each phase must be known for each sediment or type of porous media, leading to an incredible amount of information, much of which is at present lacking. 

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