Diffusion of liquids

The amorphous orientation is considered a very important parameter of the microstructure of the fiber. It has a quantitative and qualitative effect on the fiber de-formability when mechanical forces are involved. It significantly influences the fatigue strength and sorptive properties (water, dyes), as well as transport phenomena inside the fiber (migration of electric charge carriers, diffusion of liquid). The importance of the amorphous phase makes its quantification essential. Indirect and direct methods currently are used for the quantitative assessment of the amorphous phase. 

Porosity bears but little connection to permeability. The permeability is a measure of the rate of diffusion of liquids and gases through the refractory. It is understandable that the... 

Many other methods for separating isotopes have been described. A partial list includes membrane and membrane pervaporation, thermal diffusion of liquids, mass diffusion, electrolysis and electro-migration, differential precipitation, solvent extraction, biological microbial enrichment, and more. Although not discussed in... 

One of the first applications of CMD to a realistic and important system was to study the quantum dynamical effects in water. It was found that, even at 300 K, the quantum effects are remarkably large. This finding, in turn, led us to have to reparameterize the flexible water model (called the SPC/F2 model) in order to obtain good agreement with a variety of experimental properties for the neat liquid. An example of the large quantum effects in water can be seen in Fig. 3 in which the mean-spared displacement correlation function, ( x(t) - x(0) 2) is plotted. (These are new results which are better converged than those in Ref 34.) Shown are the quantum CMD and the classical MD results for the SPC/F2 model. The mean-squared displacement for the quantized version of the model is 4.0 X 10- m s-f while the classical value is 4.0 x 10 m s-f The error in these numbers is about 15%. These results suggest that quantum effects increase the diffusivity of liquid water by a factor of two. 

The thickness of lining depends on the severity of corrosion or erosion. The diffusion of liquids is inversely proportional to the square of the thickness of the lining at a given temperature. That is to say, a 6 mm thickness is four times more resistant than a lining of 3 mm thickness. The speed of diffusion in the temperature range 30-80 deg C is proportional to the temperature increase. The fabricators of vessels are to be informed in advance that the vessel is meant for lining and should be asked to follow the standard procedure for fabrication of equipment meant for rubber lining. 

The critical temperature of pure CO2 is 31°C [7]. For the subcritical range of 31-50°C, the fluid entering the extraction cell will consist of two phases - a liquid methanol phase and a supercritical phase. It has been reported that the diffusivity of liquid is about 10-100 times smaller than that of the supercritical fluid [6] and this implies that the difficulty of mass transfer associated with the former is also magnified by the same factor. In an extraction process, mass transfer occurs during 1) the fluid s penetration of the matrix s pores and 2) the subsequent transport of the analyte (solute) from the matrix into the bulk fluid [6]. The presence of entrained liquid methanol droplets will thus greatly increases the amount of mass transfer resistance present in the system. Such resistance is reduced upon an increase in temperature and this accounts for the rise in extraction efficiency observed in the temperature range of 45-50°C. 

Leading characteristics of five main kinds of reactors are described following. Stirred tanks, fixed beds, slurries, and three-phase fluidized beds are used. Catalyst particle sizes are a compromise between pressure drop, ease of separation from the fluids, and ease of fluidization. For particles above about 0.04 mm dia, diffusion of liquid into the pores and, consequently, accessibility of the internal surface of the catalyst have a minor effect on the overall conversion rate, so that catalysts with small specific surfaces, of the order of 1 m2/g, are adequate with liquid systems. Except in trickle beds the gas phase is the discontinuous one. Except in some operations of bubble towers, the catalyst remains in the vessel, although minor amounts of catalyst entrainment may occur. 

Since the length scales associated with the thermal lens are on the order of 10 to 1000 times the grating constant, their characteristic time scale interferes with polymer diffusion within the grating. Such thermal lensing has been ignored in many FRS experiments with pulsed laser excitation [27,46] and requires a rather complicated treatment. A detailed discussion of transient heating and finite size effects for the measurement of thermal diffusivities of liquids can be found in Ref. [47]. 

Snively, C. M. and Koenig, J. L. (1998) Application of real time mid-infrared FTIR imaging to polymeric systems, diffusion of liquid crystals into polymers. Macromolecules 31, 3753-5. 

The diffusivity of liquids is less than gases by a factor of about 10 5. This was noted in Chapter 2, where some typical diffusion coefficients are given. The slower diffusion in liquids results in slower speeds of analysis in LC and in a significant contribution by the mass transfer term CM in causing zone broadening. 

The environment that causes this kind of corrosion is often rather inert the polymer does not dissolve or swell, but there is some diffusion of liquid or gas, in particular at the surface. If the diffusion rate is small localised plasticization is possible and subsequently deformation is caused by the stresses. This leads to increased plasticization and to the formation of crazes and even of cracks. 

Cohen and Turnbull [87] generalized somewhat the theoretical concepts of the relationship between diffusion and self-diffusion of liquids modelled by assemblies of rigid spheres and obtained on the basis of the theories of Frenkel and Eyring, Fox and Flory [88] and Williams, Landell and Ferry [89] the equation ... 

The most useful index of excessive exposure to lead is a blood-lead analysis, and the majority of methods discussed here are concerned with this measurement. Many of the earlier ETA—AAS methods used little or no sample pretreatment and in almost all cases the variety of matrix interferences encountered necessitated strict control of ETA conditions, and made calibration by standard additions mandatory. The problem of diffusion of liquid blood samples into the graphite atomisers was overcome as an... 

Modeling of diffusion of liquids becomes more complex when the steric effect of molecular exclusion inside the pores is accounted for. Following Kerkhof and Geboers (2005), a distribution coefficient between the pore and free liquid may be defined by... 

For isobaric counter diffusion of liquids, we have the same relation as Eq. (6.242)... 

Liu G, Mackowiak M, Li Y, Jonas J. Rotational diffusion of liquid toluene in confined geometry. J Chem Phys 1991 94 239. 

As a consequence, solvent viscosity is also modified by confinement. Molecular dynamics simulations show that the average viscosity in the pore is greater than that in a bulk liquid at the same temperature by more than 50% for the smaller pores.The local viscosity varies across the pore, showing oscillations as the pore wall is approached for the smaller pores these oscillations persist across the entire width of the pore. Indeed, studies on the diffusion of liquids... 

The diffusivities of gases and liquids typically have magnitudes that are 10 and 10 cm s, respectively. The diffusivity of gases is proportional to and inversely proportional to P, whereas, the diffusivity of liquids is proportional to T and inversely proportional to viscosity jL (may strongly depend on T). 

The protocol used for collecting in-situ spectra is exemplified in part by some representative spectra for LaHY and MSA in figure 1 and 2. a) Freeze l- C-l-butene (mp -185°C) onto catalyst, b) Transfer quickly to spectrometer at -100°C and keep at -100°C for 1-2 hr to allow diffusion of liquid over the sample, c) Raise T to -80°C, for short time, then quickly to -50°C and follow DBI until 90% conversion, d) Raise T in steps taking 8-12 hours to reach 25°C. 

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