Liquid phase diffusion

Here, a is the mass accommodation coefficient expressing the probability of a gaseous molecule to stay on the surface when it collides with the particle surface, and Eg, Fsoi, and F xn are conductance corresponding to the gas phase diffusion, liquid phase diffusion and chemical reaction, respectively. When we neglect Eg, and Fsoi + Fjxn are expressed as F s, Eq. (6.2) can be simplified as. 

Activated carbons for use in Hquid-phase appHcations differ from gas-phase carbons primarily in pore size distribution. Liquid-phase carbons have significantly more pore volume in the macropore range, which permits Hquids to diffuse more rapidly into the mesopores and micropores (69). The larger pores also promote greater adsorption of large molecules, either impurities or products, in many Hquid-phase appHcations. Specific-grade choice is based on the isotherm (70,71) and, in some cases, bench or pilot scale evaluations of candidate carbons. 

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. 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

With regard to the liqiiid-phase mass-transfer coefficient, Whitney and Vivian found that the effect of temperature upon coiild be explained entirely by variations in the liquid-phase viscosity and diffusion coefficient with temperature. Similarly, the oxygen-desorption data of Sherwood and Holloway [Trans. Am. Jnst. Chem. Eng., 36, 39 (1940)] show that the influence of temperature upon Hl can be explained by the effects of temperature upon the liquid-phase viscosity and diffusion coefficients. 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

The gas-phase rate coefficient fcc is not affecded by the fact that a chemic reaction is taking place in the liquid phase. If the liquid-phase chemical reaction is extremely fast and irreversible, the rate of absorption may be governed completely by the resistance to diffusion in the gas phase. In this case the absorption rate may be estimated by knowing only the gas-phase rate coefficient fcc of else the height of one gas-phase transfer unit Hq =... 

Equations (13-111) to (13-114), (13-118) and (13-119), contain terms, Njj, for rates of mass transfer of components from the vapor phase to the liquid phase (rates are negative if transfer is from the liquid phase to the vapor phase). These rates are estimated from diffusive and bulk-flow contributions, where the former are based on interfacial area, average mole-fraction driving forces, and mass-... 

D( = diffusion coefficient of solute in liquid g = gravity-acceleration constant h = length of wetted wall kf = mass-transfer coefficient, liquid phase r = mass rate of flow of hqnid. f = viscosity of liquid = density of hqnid... 

High mass-transfer rates in both vapor and hquid phases. Close approach to eqiiilihriiim. Adiabatic contact assures phase eqiiilihriiim, Only moderate mass-transfer rate in liquid phase, zero in sohd. Slow approach to equilibrium achieved in brief contact time. Included impurities cannot diffuse out of solid. Sohd phase must be remelted and refrozen to allow phase equilibrium. 

If the bulk-liquid phase is well mixed and no diffusion occurs in the solid phase, a simple expression relating the solid-phase composition to the frac tion frozen can be obtained for the case in which the distribution coefficient is independent of composition and fraction frozen... 

There have been many modifications of this idealized model to account for variables such as the freezing rate and the degree of mix-ingin the liquid phase. For example, Burton et al. [J. Chem. Phy.s., 21, 1987 (1953)] reasoned that the solid rejects solute faster than it can diffuse into the bulk liquid. They proposed that the effect of the freezing rate and stirring could be explained hy the diffusion of solute through a stagnant film next to the solid interface. Their theoiy resulted in an expression for an effective distribution coefficient k f which could be used in Eq. (22-2) instead of k. 

A pure gas A diffuses into a liquid film where it reacts with B from the liquid phase. Material balances on the two participants are ... 

The reaction mechanisms are quite complicated in these syntheses, the kinetics depending on inter-diffusion rates in neighbouring particles, the formation of transient liquid phases, and in some cases, the vapour transport of a reactant. The presence of the latter can be detected by dre retarding effect of increased pressure in an inert surrounding atmosphere. 

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

Sulfide Stress Cracking) on steels over Rockwell C 22. (4) static stresses. other equipment handling sour gas, oil and/or water wherein H2S and H2O (liquid phase) are present up to about 150 F, where sulfide stress cracking slows down perceptibly. stainless steels with Rockwell hardness over C 22. (4) into crystal structure, exact mechanism uncertain. Sulfur expedites absorption of atomic H into grain structure. (4) if feasible use inhibitors and/or resistant coatings where feasible time or heating up will permit H to diffuse out but will not relieve any areas when H2 has concentrated. 

In suspension processes the fate of the continuous liquid phase and the associated control of the stabilisation and destabilisation of the system are the most important considerations. Many polymers occur in latex form, i.e. as polymer particles of diameter of the order of 1 p.m suspended in a liquid, usually aqueous, medium. Such latices are widely used to produce latex foams, elastic thread, dipped latex rubber goods, emulsion paints and paper additives. In the manufacture and use of such products it is important that premature destabilisation of the latex does not occur but that such destabilisation occurs in a controlled and appropriate manner at the relevant stage in processing. Such control of stability is based on the general precepts of colloid science. As with products from solvent processes diffusion distances for the liquid phase must be kept short furthermore, care has to be taken that the drying rates are not such that a skin of very low permeability is formed whilst there remains undesirable liquid in the mass of the polymer. For most applications it is desirable that destabilisation leads to a coherent film (or spongy mass in the case of foams) of polymers. To achieve this the of the latex compound should not be above ambient temperature so that at such temperatures intermolecular diffusion of the polymer molecules can occur. 

Liquid phase applications account for nearly 80% of the total use of activated carbon. Activated carbon used in liquid phase applications typically have a high fraction of pores in the macropore (>50nm) range. This is to permit the liquid phase molecules to diffuse more rapidly into the rest of the pore structure [15]. 

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