Diffusion, generally coefficient

The diffusion of the sulfur molecules in the pores of the catalyst would be assumed to be mainly influenced by molecular diffusion. This type of diffusion generally occurs in the liquid phase. Since the same liquid was used in both the cases, the coefficient of diffusion would be assumed to be the same. 

Solute Diffusion-Dispersion Coefficient. In these studies D was assumed to be constant and not a function of flow velocity. For low flow velocities this assumption seems reasonably valid (23). For the natural rainfall conditons of these studies the flow velocities were generally quite low. In lieu of actual measured D values on the two Maui soils, an estimate of D obtained on a somewhat similar soil on Oahu bv Khan (24) was used in this study. An average value of D = 0.6 cm /hr was measured in the field with a steady water flux of 10 cm/ day. 

The techniques used for restricted and steady-state diffusion generally involve the use of a diaphragm cell. This method has the disadvantage that the cell has first to be calibrated with a system with a known diffusion coefficient, and for systems with relatively slow diffusivities each run may require an inconveniently long time. 

Diffusion coefficients are very much temperature dependent. When the polymer is below the melting point, diffusion generally occurs at an extremely low rate. The polymer, therefore, should be above the melting point to increase the rate of diffusion and with it the devolatilization efficiency. Even when the polymer is in the molten state, the diffusion coefficients can often be increased substantially by increasing the temperature of the polymer melt [11]. Further, when the polymer is in the molten state, surface renewal is possible. This greatly enhances the devolatilization process. The extent of surface renewal is a strong function of the screw... 

Under normal conditions the membrane bilayer is in a fluid state. Membrane proteins can migrate within the plane of the membrane with diffusion coefficients of about 10 cm sec while lipids diffuse with coefficients of about 10 cm sec . Overall behaviour might be considered, therefore, in thermodynamic terms. But generalized deductions relating fluidity of the membrane to enzyme activity are difficult to make for several reasons. For example, motion in a given lipid molecule may include rapid rotations but slow lateral movement. Also, increased disorder in a bilayer may not correlate with increased translational motion. Moreover, all membranes so far examined have shown transbilayer asymmetry while there is evidence in several cases for at least small areas of concentration of certain lipids, i.e. micro-lateral heterogeneity. These sorts of consideration complicate the interpretation of experiments designed to show how the bilayer lipids affect membrane enzyme activities at a molecular level. 

Here (D is the diffusion coefficient and C is the concentration in the general bulk solution. For initial rates C can be neglected in comparison to C/ so that from Eqs. IV-59 and IV-60 we have... 

The dififiision time gives the same general picture. The bulk self-diffusion coefficient of copper is 10"" cm /sec at 725°C [12] the Einstein equation... 

The first thing to notice about these results is that the influence of the micropores reduces the effective diffusion coefficient below the value of the bulk diffusion coefficient for the macropore system. This is also clear in general from the forms of equations (10.44) and (10.48). As increases from zero, corresponding to the introduction of micropores, the variance of the response pulse Increases, and this corresponds to a reduction in the effective diffusion coefficient. The second important point is that the influence of the micropores on the results is quite small-Indeed it seems unlikely that measurements of this type will be able to realize their promise to provide information about diffusion in dead-end pores. 

As a particular case of this result, it follows that the stoichiometric relations are always satisfied in a binary mixture at the limit of bulk diffusion control and Infinite permeability (at least to the extent that the dusty gas equations are valid), since then all the binary pair bulk diffusion coefficients are necessarily equal, as there is only one of them. This special case was discussed by Hite and Jackson [77], and the reasoning set out here is a straightforward generalization of their treatment. 

Before pursuing the diffusion process any further, let us examine the diffusion coefficient itself in greater detail. Specifically, we seek a relationship between D and the friction factor of the solute. In general, an increment of energy is associated with a force and an increment of distance. In the present context the driving force behind diffusion (subscript diff) is associated with an increment in the chemical potential of the solute and an increment in distance dx ... 

The main conclusion to be drawn from these studies is that for most practical purposes the linear rate model provides an adequate approximation and the use of the more cumbersome and computationally time consuming diffusing models is generally not necessary. The Glueckauf approximation provides the required estimate of the effective mass transfer coefficient for a diffusion controlled system. More detailed analysis shows that when more than one mass transfer resistance is significant the overall rate coefficient may be estimated simply from the sum of the resistances (7) ... 

The diffusion of metal ions in vitreous siUca has not been studied as extensively as that of the gaseous species. The alkaU metals have received the most attention because their behavior is important in electrical appHcations. The diffusion coefficients for various metal ions are Hsted in Table 5. The general trend is for the diffusion coefficient to increase with larger ionic sizes and higher valences. 

Orientation sometimes leads to lower permeabiHty values (better barrier properties). Orientation can iacrease packing density, which lowers the diffusion coefficient D it can also iacrease the difficulty of hopping or diffusiag ia a direction perpendicular to the film. In the latter case, movement ia general may be fast, but movement through the film is limited. However, mere stretching does not always lead to orientation of the molecular chains. In fact, stretching can lead to void formation, which iacreases permeabiHty. 

Table 10 contains some selected permeabiUty data including diffusion and solubiUty coefficients for flavors in polymers used in food packaging. Generally, vinyUdene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation whereas the polyolefins are poor barriers. Comparison to Table 5 shows that the large molecule diffusion coefficients are 1000 or more times lower than the small molecule coefficients. The solubiUty coefficients are as much as one million times higher. Equation 7 shows how to estimate the time to reach steady-state permeation t if the diffusion coefficient and thickness of a film are known. 

Figures 4 and 5 show how the diffusion coefficient and solubility coefficient vary for a series of linear esters in low density polyethylene film. The trends are generally tme for other permeants in other films. As the size of the permeant increases, the diffusion coefficient decreases and the solubility coefficient increases. Since the increase in solubility coefficient is larger than the decrease in the diffusion coefficient, the permeability actually increases as the permeant size increases.

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