Pores diffusion coefficient

Pore Diffusion When flmd transport through a network of fluid-filled pores inside the particles provides access for solute adsorption sites, the diffusion fliix can be expressed in terms of a pore diffusion coefficient D as ... 

Ruthven (gen. refs.) summarizes methods for the measurement of effective pore diffusivities that can be used to obtain tortuosity factors by comparison with the estimated pore diffusion coefficient of the adsorbate. Molecular diffusivities can be estimated with the methods in Sec. 6. 

There are several correlations for estimating the film mass transfer coefficient, kf, in a batch system. In this work, we estimated kf from the initial concentration decay curve when the diffusion resistance does not prevail [3]. The value of kf obtained firom the initial concentration decay curve is given in Table 2. In this study, the pore diffusion coefficient. Dp, and surface diffusion coefficient, are estimated by pore diffusion model (PDM) and surface diffusion model (SDM) [4], The estimated values of kf. Dp, and A for the phenoxyacetic acids are listed in Table 2. 

Reid, Sherwood and Prausnitz [11] provide a wide variety of models for calculation of molecular diffusion. Dr is the Knudsen diffusion coefficient. It has been given in several articles as 9700r(T/MW). Once we have both diffusion coefficients we can obtain an expression for the macro-pore diffusion coefficient 1/D = 1/Dk -i-1/Dm- We next obtain the pore diffusivity by inclusion of the tortuosity Dp = D/t, and finally the local molar flux J in the macro-pores is described by the famiUar relationship J = —e D dcjdz. Thus flux in the macro-pores of the adsorbent product is related to the term CpD/r. This last quantity may be thought of as the effective macro-pore diffusivity. The resistance to mass transfer that develops due to macropore diffusion has a length dependence of R]. 

If zeolitic diffusion is sufficiently rapid so that the sorbate concentration through any particular crystal is essentially constant and in equilibrium with the macropore fluid just outside the crystal, the rate of mass transfer will be controlled by transport through the macropores of the pellet. Transport through the macropores may be assumed to occur by a diffusional process characterized by a constant pore diffusion coefficient Z)p. The relevant form of the diffusion equation, neglecting accumulation in the fluid phase within the macropores which is generally small in comparison with accumulation within the zeolite crystals, is... 

The magnitude of the diffusion coefficients given in Table I can be compared with a value of 3.3 X 10 5 cm.2/sec. determined experimentally by Stokes (26) for HCl in bulk solution at infinite dilution. The pore diffusion coefficients listed in Table I for HCl vary by a factor of (2 - 4) X 10"2 from that given by Stokes. McNeill and Weiss (15) have indicated that active carbon can be considered as a weak-base anion-exchange sorbent. According to Helfferich (13), diffusion coefficients in such resins can be several orders of magnitude less than the corresponding bulk solution coefficients. The Cl" ion probably limits the rate of diffusion, since its mobility in aqueous solution is much less than that of the H30+ ion. Further evidence to support this conclusion has been obtained in the present work from determinations of pore diffusion... 

Obviously liquid residence time is not an appropriate parameter to describe pore diffusion effects in fluidized bed adsorption. This may be elucidated by assessing particle side transport by a dimensionless analysis. Hall et al. [73] described pore diffusion during adsorption by a dimensionless transport number Np according to Eq. (17), De denoting the effective pore diffusion coefficient in case of hindered transport in the adsorbent pores and Ue the... 

From the gas pressure which includes the partial pressure profile, the temperature profile, and local capillary pressure which is a fvmction of the volume fraction profile and the liquid radius of curvature profile inside the green body, the average stress can be determined. The partial pressure profile is determined by the flux, J, and the effective pore diffusion coefficient, as follows ... 

Pore diffusion coefficient, mVs [Eqs. (16-66), (16-67), (16-69)] Adsorbed-phase (solid, surface, particle, or micropore) diffusion coefficient, mVs [Eqs. (16-70), (16-71)]... 

Note that Eqs. 6.85 and 6.84 are identical, if the pore diffusion coefficient is taken as a lumped concentration dependent parameter that includes pore and surface diffusion ... 

The intraparticle (pore) diffusion coefficient defined in Section 6.2.2.4 may estimated by the Mackie-Meares correlation (Mackie and Meares, 1955) ... 

According to Glueckauf [8,9], in linear chromatography the lumped mass transfer coefficient km in Eq. 10.3 is related to the film mass transfer coefficient, kf, and the pore diffusion coefficient. Dp, by... 

Reaction velocity constant Mass transfer coefficient Pore diffusion coefficient... 

The effectiveness factor can be determined as function of particle geometry L, effective pore diffusion coefficient D and the kinetic constant k. These can be put together in a... 

The entity LW/q depends only on the geometry of the flow path and the flowrate whereas the second entity, called the Materials Property Group, MPG, depends on the rock matrix porosity, the pore diffusion coefficient and the retardation coefficient that is determined by the sorption coefficient. 

When there are j chemical reactions between i species in a mixture, it is possible to constract a Damkohler number for reaction j that is specific to component i. This is necessary because the effective pore diffusion coefficient within a catalytic pellet depends on molecular size. Hence, if reaction j is described by nth-order irreversible chemical kinetics, then the Damkohler number of component i in the reactive gas mixture is... 

It is important to choose component A as the reactant gas of highest molecular weight. Since the effective pore diffusion coefficient of component i is inversely proportional to the square root of its molecular weight, a, effective/ , effective < 1... 

For pores smaller than the mean free path but not small enough to have only Knudsen flow, the diffusion flux in the pore is affected by molecule-wall collisions and molecule-molecule collisions. Considering both types of collisions as resistances to diffusion leads to the following equation for the pore diffusion coefficient ... 

The pore diffusion coefficients in tentacle-based matrices are typically higher as the transport mechanism is not based on free diffusion but most probably on a faster film diffusion principle (Thomas et al, 2012, de Neuville et al, 2012). 

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