Diffusion in gas phase

Mass transfer in a gas-liquid or a liquid-liquid reactor is mainly determined by the size of the fluid particles and the interfacial area. The diffusivity in gas phase is high, and usually no concentration gradients are observed in a bubble, whereas large concentration gradients are observed in drops. An internal circulation enhances the mass transfer in a drop, but it is still the molecular diffusion in the drop that limits the mass transfer. An estimation, from the time constant, of the time it wiU take to empty a 5-mm drop is given by Td = d /4D = (10 ) /4 x 10 = 6000s. The diffusion timescale varies with the square of the diameter of the drop, so... 

Second, we consider the diffuseness in gas-phase spectra.74- 78 An account of those aspects of gas-phase spectra that relate to electronic relaxation is only possible if the other causes of diffuseness are first made clear. We therefore summarize some of the characteristics of vibration-rotation spectra with special reference to a molecule like naphthalene at a vapor pressure of 1 mm76 The Doppler width of each line is 0.022 cm-1 the rotational line spacing can be as small as 0.0004 cm-1, or 50 lines per Doppler width the length of a sequence is 300 cm 1 and the average sequence spacing is 5 cm-1 for anthracene the average sequence spacing... 

This equation predicts that for maximum column performance we must minimize the contribution of each term while still maintaining a constant linear flowrate. The first term accounts for the geometry of the packing, the second for longitudinal diffusion in gas phase, and the third for resistance to mass transfer process. 

Useful simplifications are often made in Equation 2.2. We will use gas-liquid contact as an example, and assume gas-filled homogeneous membrane of high porosity, thin wall, and low tortuosity. Since diffusion in gas phase is generally of three orders of magnitude faster than in liquid phase, one can show that and ka are quite high in this case compared to ki, and so the controlling resistance to mass transfer is in the liquid phase. This means A total is essentially the same as If is constant within the contactor the total mass transfer rate in Equation 2.4 can be approximated for the entire contactor as... 

Table 4.17 Expressions for gas-particle mass transfer n , g, Mq and Haq molecule density of the same substance far from the particle, close to the particle, at particle surface and within the particle (droplet) p — gas partial pressure far from the droplet, c g - aqueous-phase concentration, k - mass transfer coefficient (recalculable into spjecific rate constant) g - gas-phase, aq - aqueous-phase, het - interfadal layer (chemistry), in - interfacial layer (transport), coll - collision, ads — adsorption (surface striking), sol - dissolution, diff -diffusion in gas-phase, des - desorption.

A. molecular diffusivity in gas phase Molecular diffusivity in gas phase may be estimated by the Chapman-Enskog equation. For a mixture of components 1 and 2,... 

The theory for diffusion in gas phase is well developed. The diffusion flux of a component i(Ni) depends on all of the components. According to the Stefan-Maxwell theory, the diffusion flux and concentration gradient are governed by the matrix relation... 

If the gas environment is made of a mixture of gas (with G and possibly G), there is in this field a zone of diffusion of the gases G and G because one is formed and the other one destroyed at the interface. However diffusions in gas phase being, in general, very rapid to those that occur in solid phase, we assume that gas diffusion is not a rate-determining step. 

Kinetic theories of adsorption, desorption, surface diffusion, and surface reactions can be grouped into three categories. (/) At the macroscopic level one proceeds to write down kinetic equations for macroscopic variables, in particular rate equations for the (local) coverage or for partial coverages. This can be done in a heuristic manner, much akin to procedures in gas-phase kinetics or, in a rigorous approach, using the framework of nonequihbrium thermodynamics. Such an approach can be used as long as... 

The cage effect described above is also referred to as the Franck-Rabinowitch effect (5). It has one other major influence on reaction rates that is particularly noteworthy. In many photochemical reactions there is often an initiatioh step in which the absorption of a photon leads to homolytic cleavage of a reactant molecule with concomitant production of two free radicals. In gas phase systems these radicals are readily able to diffuse away from one another. In liquid solutions, however, the pair of radicals formed initially are caged in by surrounding solvent molecules and often will recombine before they can diffuse away from one another. This phenomenon is referred to as primary recombination, as opposed to secondary recombination, which occurs when free radicals combine after having previously been separated from one another. The net effect of primary recombination processes is to reduce the photochemical yield of radicals formed in the initiation step for the reaction. 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

Like the Kolmogorov scale in a turbulent flow, the Batchelor scale characterizes the smallest scalar eddies wherein molecular diffusion is balanced by turbulent mixing.3 In gas-phase flows, Sc 1, so that the smallest scales are of the same order of magnitude as the Kolmogorov scale, as illustrated in Fig. 3.1. In liquid-phase flows, Sc 1 so that the scalar field contains much more fine-scale structure than the velocity field, as... 

In a bulk silica matrix that differs from the silica nanomatrix regarding only the matrix size but has a similar network structure of silica, several kinetic parameters have been studied and the results demonstrated a diffusion controlled mechanism for penetration of other species into the silica matrix [89-93]. When the silica is used as a catalyst matrix in the liquid phase, slow diffusion of reactants to the catalytic sites within the silica rendered the reaction diffusion controlled [90]. It was also reported that the reduction rate of encapsulated ferricytochrome by sodium dithionite decreased in a bulk silica matrix by an order of magnitude compared to its original reaction rate in a homogeneous solution [89], In gas-phase reactions in the silica matrix, diffusion limitations were observed occasionally [93],... 

At the end of section 3.1 we addressed a common circumstance in gas-phase thermochemical kinetics studies. For many reactions, there is not enough experimental information to determine A //°, and a negligible barrier for the product recombination reaction is often assumed. The same ideas can be applied for reactions in solution When D and E are radicals, it is frequently accepted that the reverse of reaction 3.33 is diffusion controlled and that A // , has a value of 8kJ mol-1. 

The disappeared positive ions might be recombined with electrons in gas phase or diffused to the electrodes and the wall of reactor vessel, where ions was recombined with electrons. These positive... 

For example, if fhe DL is used on the side of fhe cell where fhe fuel or oxidant is in gas phase, then this part can be referred to as gas diffusion layer (GDL). When bofh fhe CL and the DL are mentioned as one component, then the name "diffusion electrode" is commonly used. Because the DL is of a porous nature, it has also been called "diffusion medium" (DM) or "porous transporf layer" (PTL). Sometimes the DL is also referred to as fhe component formed by an MPL and a backing layer. The MPL has also been called the "water management layer" (WML) because one of its main purposes is to improve the water removal inside the fuel cell. In this chapter, we will refer to these components as MPL and DL because these names are widely used in the fuel cell indusfry. 

At present it is universally acknowledged that TTA as triplet-triplet energy transfer is caused by exchange interaction of electrons in bimolecular complexes which takes place during molecular diffusion encounters in solution (in gas phase -molecular collisions are examined in crystals - triplet exciton diffusion is the responsible annihilation process (8-10)). No doubt, interaction of molecular partners in a diffusion complex may lead to the change of probabilities of fluorescent state radiative and nonradiative deactivation. Nevertheless, it is normally considered that as a result of TTA the energy of two triplet partners is accumulated in one molecule which emits the ADF (11). Interaction with the second deactivated partner is not taken into account, i.e. it is assumed that the ADF is of monomer nature and its spectrum coincides with the PF spectrum. Apparently the latter may be true when the ADF takes place from Si state the lifetime of which ( Tst 10-8 - 10-9 s) is much longer than the lifetime of diffusion encounter complex ( 10-10 - lO-H s in liquid solutions). As a matter of fact we have not observed considerable ADF and PF spectral difference when Sj metal lo-... 

For bimolecular second-order reactions and for trimolecular reactions, if the reaction rate is very high compared to the rate to bring particles together by diffusion (for gas-phase and liquid-phase reactions), or if diffusion is slow compared to the reaction rate (for homogenous reaction in a glass or mineral), or if the concentrations of the reactants are very low, then the reaction may be limited by diffusion, and is called an encounter-controlled reaction. 

Both the mass transfer kinetic parameters (diffusion in the phases, D, D j, surface renewal frequency, s) and chemical reaction rate constants (kg, kj) strongly influence enhancement of the absorption rate. The particle size, dp, the dispersed liquid holdup, e and the partition coefficient, H can also strongly alter the absorption rate [42-44,46,48]. Similarly, the distance of the first particle from the gas-liquid interface, 6q is an essential factor. Because the diffusion conditions are much better in the dispersed phase (larger solubility and, in most cases, larger diffusivity, as well) the absorption rate should increase with the decrease of the (5g value. 

Values of diffusivity in gas mixtures at normal temperature and atmospheric pressure are in the approximate range of 0.03-0.3 m- h and usually increase with temperature and decrease with increasing pressure. Values of the liquid phase diffusivity in dilute solutions are in the approximate range of 0.2-1.2 X 10 5 m h , and increase with temperature. Both gas-phase and liquid-phase diffusivities can be estimated by various empirical correlations available in reference books. 

The term A is related to the flow profile of the mobile phase as it traverses the stationary phase. The size of the stationary phase particles, their dimensional distribution, and the uniformity of the packing are responsible for a preferential path and add mainly to the improper exchange of solute between the two phases. This phenomenon is the result of Eddy diffusion or turbulent diffusion, considered to be non-important in liquid chromatography or absent by definition in capillary columns, and WCOT (wall coated open tubular) in gas phase chromatography (Golay s equation without term A, cf. 2.5). 

In general, experimental conditions are such that mass transport of reactants and products is not rate-limiting and the observed rate expressions refer to the true chemical processes in steps (ii)—(iv). The diffusion limitation is likely to be important in liquid phase hydrogenation reactions, particularly when hydrogen has a limited solubility in the liquid phase, and in gas phase hydrogenation where the catalyst is porous and the reaction occurs within the catalyst pores. 

Cdg Concentration of D in gas phase, moles/volume Cdp Concentration of D in crystallite phase, moles/zeolite pore volume Deff Effective diffusion coefficient, (length) 2/time F Volumetric feed rate to reactor, volume/time H Henry s law-type constant relating gas phase mole fraction to crystallite phase mole fraction... 

There is also another concentration gradient, from the catalyst surface into the pores, which can be more severe in gas - liquid-phase systems than in gas-phase systems owing to the much lower diffusivity in liquids than in gases. 

Figure 1.9. The dependence of the boundary profile on the form of the partition isotherm. (Courtesy of John Wiley-Interscience. ) c=concentration (cm 5/mole) of solute in gas phase q=concentration in liquid or adsorbed phase t=time for band to emerge from column (1) se1f-sharpening profile (2) diffuse profile (3) gaussian profile.

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