Diffusivities liquids, calculation

The diffusivity of the vapour of a volatile liquid in air can be conveniently determined by Winkdmann s method in which liquid is contained in a narrow diameter vertical tube, maintained at a constant temperature, and an air stream is passed over the top of the tube sufficiently rapidly to ensure that the partial pressure of the vapour there remains approximately zero. On the assumption that the vapour is transferred from the surface of the liquid to tile air stream by molecular diffusion alone, calculate the diffusivity of carbon tetrachloride vapour in air at 321 K and atmospheric pressure from the experimental data given in Table 10.3. 

Optimization requires that a-rtjl have some reasonably high value so that the wall temperature has a significant influence on reactor performance. There is no requirement that 3>AtlR be large. Thus, the method can be used for polymer systems that have thermal diffusivities typical of organic liquids but low molecular diffusivities. The calculations needed to solve the optimization are much longer than those needed to solve the ODEs of Chapter 6, but they are still feasible on small computers. 

The self-diffusion coefficient calculated for the three body potential is Z) = 1.3 X lO cm /sec. This is to be compared with the experimental value of 2.3 x 10" cmVsec and to the value of 2.25 x 10 cm /sec for the two-body liquid. It could be said that the three-body liquid shows more rigidity in some sense than the two-body liquid. 

In contrast to liquid water, a detailed mechanistic understanding of the physical and chemical processes occurring in the evolution of the radiation chemical track in hydrocarbons is not available except on the most empirical level. Stochastic diffusion-kinetic calculations for low permittivity media have been limited to simple studies of cation-electron recombination in aliphatic hydrocarbons employing idealized track structures [56-58], and simplistic deterministic calculations have been used to model the radical and excited state chemistry [102]. While these calculations have been able to reproduce measured free ion yields and end product yields, respectively, the lack of a detailed mechanistic model makes it very difficult... 

Because some of the reactions involved in establishing equilibrium at the membrane surface are slow compared to diffusion, the calculated concentration gradients formed in the liquid membrane do not have a simple form. The equations for partial reaction rate control have been derived by Ward and Robb [23],... 

In Example 2.1.1 we described the experiments of Carty and Schrodt (1975) who evaporated a binary liquid mixture of acetone(l) and methanol(2) in a Stefan tube. Air(3) was used as the carrier gas. Using an effective diffusivity method calculate the composition profiles. 

Effective diffusivities were used for the calculation of the mass-transfer coefficients. In contrast to the binary Maxwell-Stefan diffusivities, the effective diffusivities were calculated via available procedures in ASPEN Custom Modeler , whereas the Wilke-Chang model was used for the liquid phase and Chapman-Enskog-Wilke-Lee model for the vapor phase [94]. In the full model, computationally intensive matrix operations for the Maxwell-Stefan equations are necessary. The model has been further extended to consider the presence of liquid-liquid separation [110, 111]. 

An assessment of the relative diffusion rates of ionic and molecular species in the PAN-based electrolyte may be made from the diffusion coefficients calculated for ferrocene from cyclic voltammograms. Some data are presented in Table 3.8. The ratio of diffusion coefficients of ferrocene in the PAN-based polymer electrolyte and PC/LiC104 liquid electrolyte at room temperature is the same as that obtained for the conductivity of LiC104 in these electrolytic media. It may be noted here that the ferro-cene/ferrocenium couple has been shown [36] to be useful for the overcharge protection of secondary Li batteries. 

Not only surfactant molecules may diffuse in advance of the wetting front. Spreading of pure liquids by surfaee diffusion of molecules from a micro-doplet over a solid surface was comprehensively studied using microellipso-metric measurements [29-34]. It has been observed that on the top of the first monolayer, a second and subsequent layers form, and the corresponding coefficients of surface diffusion were calculated. For liquid polydimethylsi-loxan (PDMS) on a hydrophobed silicone wafer, coefficients of surface diffusion in the first monolayer grow with decreasing molecular mass M of the PDMS from = A x 10 cm /s for M = 28,400 to 7 x 10 cm /s for M = 6700. Correlation between the values and bulk viscosity of the liquid PDMS have been established. 

See Ballentine 1988.) Pl for several liquid transition metals and for liquid La have been calculated, and the dd contribution to p was found to constitute about 80%-90%. This was due to the fact that the magnitude of n Ef) more than compensated for the reduced d-diffusivity. The calculated value for Pi for La (151 p42-cm) compares reasonably well with experiment (Ballentine and Ham-... 

At the catalyst-electrolyte surface we have gas-phase diffusion, and there can also be additional surface diffusion. In surface diffusion, gas molecules physically or chemically absorb onto a solid surface. If it is physical absorption, the species are highly mobUe. If it is chemisorption and the molecule is more strongly bonded to the specific site, species are not directly mobile but can move via a hopping mechanism. Surface diffusion rates can be measured by direct measurement of the flux of a nonreacting gas across the material surface. The difference between the measured diffusion and predicted Knudsen diffusion is calculated to be the surface diffusion component. Values of the surface diffusion coefficient (Ds) are 10 cm /s in solids and liquids, but these vary widely since surface interaction is involved. Also, Ds is a strong function of temperature and surface concentration. Surface diffusion adds to the overall diffusion but is typically less than one-half of the Knudsen component and so has been mostly neglected in fuel cell analysis. 

At first we tried to explain the phenomenon on the base of the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary [12]. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. We worked out the mathematical description of both gas-vapor diffusion and evaporation-condensation processes in cone s channel. Solving the system of differential equations for evaporation-condensation processes, we ve derived the formula for the dependence of top s (or inner) liquid column growth on time. But the calculated curves for the kinetics of inner column s length are 1-2 orders of magnitude smaller than the experimental ones [12]. 

Figure A3.6.13. Density dependence of die photolytic cage effect of iodine in compressed liquid n-pentane (circles), n-hexane (triangles), and n-heptane (squares) [38], The solid curves represent calculations using the diffusion model [37], the dotted and dashed curves are from static caging models using Camahan-Starling packing fractions and calculated radial distribution fiinctions, respectively [38],...

Experiment diffusion coefficients are scarce and not highly accurate, especially in the liquid phase, leading to prediction methods with marginal accuracy. However, use of the v ues predicted are generally suit le for engineering calculations. At concentrations above about 10 mole percent, predicted values should be used with caution. Diffu-sivities in liquids are lO -lO times lower than those in gases. 

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