Liquids diffusivities

There is also a traffic between the surface region and the adjacent layers of liquid. For most liquids, diffusion coefficients at room temperature are on the order of 10 cm /sec, and the diffusion coefficient is related to the time r for a net displacement jc by an equation due to Einstein ... 

Egelstaff P A 1962 Neutron soattering studies of liquid diffusion Adv. Phys. 11 203-32... 

Liquid Diffusivity Liquid diffiisivities are in general not as accurately predicted as vapor diffiisivities, and specialized methods have been developed. References to each method determined to be accurate are given, but only the most common methods will be presented. 

For prediction of the liquid diffusivity of a solute in a pair of mixed solvents, the method of Tang and Himmelblau, Eq. (2-161), is recommended. 

Liquid Diffusion The movement of liquids by diffusion in soUds is restricted to the equihbrium moisture content below the point of atmospheric saturation and to systems in which moisture and solid are mutually soluble. The first class apphes to the last stages in the diying of clays, starches, flour, textiles, paper, and wood the second class includes the diying of soaps, glues, gelatins, and pastes. 

Diffusion equations mav also be used to study vapor diffusion in porous materi s. It should be clear that aU estimates based on relationships that assume constant diffusivity are approximations. Liquid diffusivity in sohds usually decreases with moisture concentration. Liquid and vapor diffusivity also change, and material shrinks during diying. 

Q/d-) experimental where = average experimental value of liquid diffusivity, mVh. 

Dl = liquid diffusivity, ft /hr andj are constants given in Table 9-41. 

Kassner used a rotating disc, for which the hydrodynamic conditions are well defined, to study the dissolution kinetics of Type 304 stainless steel in liquid Bi-Sn eutectic. He established a temperature and velocity dependence of the dissolution rate that was consistent with liquid diffusion control with a transition to reaction control at 860 C when the speed of the disc was increased. The rotating disc technique has also been used to investigate the corrosion stability of both alloy and stainless steels in molten iron sulphide and a copper/65% calcium melt at 1220 C . The dissolution rate of the steels tested was two orders of magnitude higher in the molten sulphide than in the metal melt. 

Diffusion and Permeation Testing 23.4.4.1 Kinetics of Liquid Diffusion Tests... 

Some Pressure Effects on Liquid Diffusion Coefficients and Equilibrium... 

Rubber swelling modifies the liquid/solid work of adhesion. Wo, because in addition to the initial liquid/solid interactions, liquid diffusion into the solid produces supplementary liquid/liquid interactions, hquid molecules having passed through the liquid/solid interface. Therefore, to the initial work of adhesion in the absence of swelling, Wq, an additional term corresponding to a fraction of the cohesion energy of the liquid, 2y, should be added. If / is the time of diffusion, the work of adhesion at /, Wo(t), can then be expressed as... 

Equation (1) consists of various resistance terms. l/Kj a is the gas absorption resistance, while 1/ K,a corresponds to the maleic anhydride diffusion resistance and l/i k represents the chemical reaction resistance. The reaction rate data obtained under the reaction conditions of 250°C and 70 atm were plotted according to equation (1). Although catalytic reaction data with respect to time on stream were not shown here, a linear correlation between reaction rate data and catalyst loading was observed as shown in Fig. 2. The gas absorption resistance (1/ a) was -1.26 h, while the combined reaction-diffusion resistance (lJK,a + 1 T]k) was determined to be 5.57 h. The small negative value of gas absorption resistance indicates that the gas-liquid diffusion resistance was very small and had several orders of magnitude less than the chanical reaction resistance, as similarly observed for the isobutene hydration over Amberlyst-15 in a slurry reactor [6]. This indicates that absorption of malei c anhydride in solvent was a rapid process compared to the reaction rate on the catalyst surface. 

We have seen that particle sizes of 100-150 y in classical LC lead to slow and inefficient columns. The reason for this is related to the slow diffusion of molecules in the liquid state (e.g., gaseous diffusion coefficient 10 liquid diffusion coefficients). 

Monitoring of the oxygen pressure during reaction indicated that the rate of conversion of glycerol to glyceric acid under basic conditions (see section 3.3) was limited by oxygen mass transfer. All other reactions were free from gas-liquid diffusion control but this does not exclude the possible limitation by intra-porous diffusion. 

In the pores of the electrodes, practically no natural convection of the liquid takes place. Reactants dissolved in the liquid can be supplied in two ways from the external surface to the internal reaction zones (and reaction products transported away in the opposite direction) (1) by diffusion in the motionless liquid diffusion electrode),... 

The enzyme catalysed epoxidation of alpha-olefins like 1-octene with oxygen to the optically active epoxide provides an interesting example of a four-phase system (de Bont et al., 1983). The hold-up of the organic phase may be 2-4 % and the presence of biosurface active agents leads to the creation of a large liquid-liquid interfacial area the liquid droplet size becomes smaller than the gas-liquid diffusion film thickness. 

Experimental values for the more common systems can be often found in the literature, but for most design work the values will have to be estimated. Methods for the prediction of gas and liquid diffusivities are given in Volume 1, Chapter 10 some experimental values are also given. 

The equation developed by Wilke and Chang (1955), given below, can be used to predict liquid diffusivity. This equation is discussed in Volume 1, Chapter 10. 

WILKE, C. R. (1949) Chem. Eng. Prog. 45, 218. Estimation of liquid diffusion coefficients. 

The AIChE design manual recommends the Wilke and Chang (1955) equation for liquid diffusivities and the Wilke and Lee (1955) modification to the Hirschfelder, Bird and Spotz equation for gas diffusivities. 

Leakage through a synthetic liner is controlled by Fick s first law, which applies to the process of liquid diffusion through the liner membrane. The diffusion process is similar to flow governed by Darcy s law except that it is driven by concentration gradients and not by hydraulic head. Diffusion rates in membranes are very low in comparison with hydraulic flow rates even in clays. In synthetic liners, therefore, the factor that most influences liner performance is penetrations. Synthetic liners may have imperfect seams or pinholes, which can greatly increase the amount of leachate that leaks out of the landfill. 

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