Coefficient of bulk diffusion

Fig. 8. Determination of the coefficient of bulk diffusion. Extrapolation of the linear part of the curve Ln ag vs. y/t gives the isotopic ratio a of the surface when bulk diffusion starts.

The diffusion of the ions in the bulk will still be done at a distance close to p and thus, we will be able to apply the same calculations as above, replacing by D, the coefficient of bulk diffusion. Thus, the reactivity will be ... 

It may seem curious that Knudsen diffusion coefficients still appear in equations (5.18) and (5.19), which supposedly give the flux relations at the limit of bulk diffusion control. However, inspection reveals that only ratios of these coefficients are effectively present, and from equation (2,11) it follows that... 

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. 

The reaction is carried out in close-loop reactor connected to a mass spectrometer for 1S02, 180160 and 1602 analyses as a function of time [38], The gases should be in equilibrium with the metallic surface (fast adsorption/desorption steps 1 and f ) If the bulk diffusion is slow (step 6) and the direct exchange (step 5) does occur at a negligible rate, coefficients of surface diffusion Ds can be calculated from the simple relationship between the number of exchanged atoms Ne and given by the model of circular sources developed by Kramer and Andre [41] ... 

When surface diffusion is the only process of exchange, ag tends to an equilibrium value a at t - oo. In most cases, after a rapid step of surface diffusion, it can be observed that a% continues slowly decreasing. This phenomenon corresponds to a slow step of bulk diffusion (coefficient l)h). A model of bulk diffusion in spherical grains was developed by Kakioka et al. which led to the following equation [43] ... 

The ratio kpaitl. e/fCpi ile describes the partition coefficient of the diffusing particle between the bulk phase and pore. If electrostatic or hydrophobic interactions are... 

Most chemical compounds are characterised by diffusion of the components across the bulks of their growing layers in the form of atoms or ions. The process of bulk diffusion is described by Fick s laws. The first Fick law relates the flux of atoms of a given component to its diffusion coefficient and concentration gradient in the direction of diffusion at constant surface area of contacting phases ... 

Figure 6. Influence of bulk diffusion coefficient Db on metal deposition profile.

Upward penetration distance (in metres) of radon from a buried source in terms of bulk diffusion coefficient (D ), fraction of radon detectable (N/Nq) and thickness of inactive cover above the source (from Novikov and Kapkov, 1965)... 

One can see that, in the sample bulk, the polymer remains in a rubbery state. On the contrary, in the superficial layer of thickness the polymer vitrifies and thus becomes brittle. Since the coefficient of plasticizer diffusion varies by at least one order of magnitude on both sides of the glass transition, the real gradient will display rather the shape of Fig. 12.10. In such cases, the diffusion front is very abrupt and the sample weight decreases proportionally with time. 

Since the diffusivity of vacancy and atomic coefficient of self-diffusion can be correlated both in the bulk and at the surface. 

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. 

The flux between two lateral walls caused by the nonuniformity of the ion concentration profiles in the layers adjacent to the electrodes is of the same nature as the heat convection arising while the bottom wall is heated [2]. In the latter case a disturbance of the steady state occurs if the Rayleigh number reachs a certain (critical) value (Ra = gPd AT/vx, where P is the coefficient of bulk heat expansion, d is the distance between the walls, AT the increment of temperature, v the dynamic viscosity, and X the thermal diffusivity) the liquid transforms into a new state with a periodic cell structure in such a way that the circulation in the interior of each cell has an opposite direction compared to that of the adjacent one. According to previous evaluations [53] the critical Rayleigh number in the case of lateral rigid walls is about 1700. 

Typical values of diffusion coefficients for bulk diffusion in fluids and effective diffusion in porous media are given in Figure 3.2.29 without consideration of surface and configurational diffusion in porous media (see also values given in Tables 3.1.6 and 3.1.7). 

The sloping solid line shows the reported temperature variation of T2 between 13 K and 17 K for unconstrained solid D2 with an x = 0.33 p-D2 fraction. The dashed curve shows the coefficient of self-diffusion (on the right hand scale) reported for liquid n-H2 at SVP. Liquid D2 diffusion must follow a similar curve. It is probable that the observed temperature variation of T2 for the narrow central DMR component in a-Si D,F (325) reflects the melting of bulk solid and diffusion in dense fluid D2 in microvoids. Either the presence of F produces unusually large voids (which does not seem likely) or else void surfaces are rendered less effective in controlling the relaxation properties of the contained D2 than was the case in a-Si D,H (circles). 

V acrylate the bulk monomer viscosity of the acrylate. Equation 4.15 is an approximation as the diffusion coefficient of a diffusing entity does not only depend upon the viscosity of the medium, but also on the charateristics of the dififusant itself At 50°C, the monomer diffusion coeficient of MMA is relatively well determined and has been found to be equal to 4.11TO m s [36]. The viscosities of MMA, MA, EA and BA, that are needed to estimate a diffusion coefficient for these monomers on the basis of equation 4.15, were calculated according to [37] ... 

Here, Vn is the surface gradient operator. Ns denotes the number of adsorbed components, r, is the adsorption of component i, s is the surface velocity, >f is the coefficient of surface diffusion, and r is the rate of production of component k by interfacial chemical reactions n is the running unit normal to the surface, J, is the subsurface value of the bulk electrodiffusion flux... 

Short-time water diffusion may be characterized by the effective diffusion coefficients and calculated by equation (27) for the total displacement (r ) and for the displacement ((xy) ) parallel to the surface in the time interval 5 ps < t < 15 ps, using d = 3 and d = 2, respectively. and gradually increase with hydration (Fig. 116). The values of are noticeably lower than due to the strong confining effect of a boundary on the displacement in z direction (normally to the surface). This effect is absent for the displacements parallel to the surface and dIq may be compared with the self-diffusion coefficient of bulk water D 4.2 for the water model studied [648] (see... 

We shall see that the diffusion coefficient for bulk diffusion is indeed a function of pressure, temperature, molecular size, and weight. Diffusion is a spontaneous process that is a result of the second law of thermodynamics. The second law of thermodynamics requires that thermodynamic processes proceed in a way that maximizes entropy. This ultimately requires uniform mixing of everything in the universe. When there is nonuniform mixing, diffusion occurs to eliminate concentration gradients and can be written as... 

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 state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

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