Resistance liquid-phase

Of course, condensed phases also exliibit interesting physical properties such as electronic, magnetic, and mechanical phenomena that are not observed in the gas or liquid phase. Conductivity issues are generally not studied in isolated molecular species, but are actively examined in solids. Recent work in solids has focused on dramatic conductivity changes in superconducting solids. Superconducting solids have resistivities that are identically zero below some transition temperature [1, 9, 10]. These systems caimot be characterized by interactions over a few atomic species. Rather, the phenomenon involves a collective mode characterized by a phase representative of the entire solid. 

Hl Height of one transfer unit based on liquid-phase resistance m ft... 

Transfer of material between phases is important in most separation processes in which two phases are involved. When one phase is pure, mass transfer in the pure phase is not involved. For example, when a pure liqmd is being evaporated into a gas, only the gas-phase mass transfer need be calculated. Occasionally, mass transfer in one of the two phases may be neglec ted even though pure components are not involved. This will be the case when the resistance to mass transfer is much larger in one phase than in the other. Understanding the nature and magnitudes of these resistances is one of the keys to performing reliable mass transfer. In this section, mass transfer between gas and liquid phases will be discussed. The principles are easily applied to the other phases. 

Z. 5-25-Y, large huhhles = AA = 0.42 (NG..) Wi dy > 0.25 cm Dr luterfacial area 6 fig volume dy [E] Use with arithmetic concentration difference, ffg = fractional gas holdup, volume gas/total volume. For large huhhles, k is independent of bubble size aud independent of agitation or liquid velocity. Resistance is entirely in liquid phase for most gas-liquid mass transfer. [79][91] p. 452 [109] p. 119 [114] p. 249... 

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 =... 

The liquid-phase rate coefficient is strongly affected by fast chemical reactions and generally increases with increasing reac tion rate. Indeed, the condition for zero hquid-phase resistance m/k-d) imphes that either the equilibrium back pressure is negligible, or that... 

When liquid-phase resistance is important, particular care should be taken in employing any given set of experimental data to ensure that the equilibrium data used conform with those employed by the original author in calculating values of fci or Hi. Extrapolation to widely different couceutratiou ranges or operating conditions should... 

Use of Operating Curve Frequently, it is not possible to assume that = 0 as in Example 2, owing to diffusional resistance in the liquid phase or to the accumulation of solute in the hquid stream. When the back pressure cannot be neglected, it is necessary to supplement the equations with a material balance representing the operating line or curve. In view of the countercurrent flows into and from the differential section of packing shown in Fig. 14-3, a steady-state material balance leads to the fohowing equivalent relations ... 

Solution. For TGE in water, the Henry s law coefficient may he taken as 417 atm/mf at 20°G. In this low-concentration region, the coefficient is constant and equal to the slope of the eqnihhrinm hne m. The solnhility of TGE in water, based on H = 417, is 2390 ppm. Because of this low solnhility, the entire resistance to mass transfer resides in the liquid phase. Thus, Eq. (14-25) may he used to obtain Nql, the nnmher of overall hqnid phase transfer units. 

The traditional design method normally makes use of overall values even when resistance to transfer lies predominantly in the liquid phase. For example, the COg-NaOH system most commonly used for comparing the Kg< values of various tower packings is a liqiiid-phase-controlled system. When the liqiiid phase is controlling, extrapolation to different concentration ranges or operating conditions is not recommended since changes in the reaction mechanism can cause /cl to vary unexpectedly and the overall values do not explicitly show such effects. 

Aside from the lack of an explicitly defined liquid-phase-resistance term, the limitations on the use of Eq. (14-66) are related to the fact that its derivation implicitly assumes that the system is dilute iysM = 1) and that the operating and equilibrium curves are straight lines over the range of tower operation. Also, Eq. (14-66) is strictly vahd only for the temperature and pressure at which the original test was run even though the total pressure pf appears in the denominator. 

The ambiguity of the total pressure effect can be seen by a comparison of the gas-phase- and liquid-phase-controlled cases when the gas phase controls, the liquid-phase resistance is negligible and Kg( = K npf is independent of the total pressure. For this case the coefficient K g< is inversely proportional to the total system pressure as shown in Eq. (14-66). On the other hand, when the liquid phase controls, the correct equation is... 

Table 14-3 presents a typical range of values for chemically reacting systems. The first two entries in the table represent systems that can be designed by the use of purely physical design methods, for they are completely gas-phase mass-transfer limited. To ensure a negligible liquid-phase resistance in these two tests, the HCl was absorbed into a solution maintained at less than 8 percent weight HCl and the NH3 was absorbed into a water solution maintained below pH 7 by the addition of acid. The last two entries in Table 14-3 represent liquid-phase mass-transfer hmited systems. 

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. 

Thus as (y) will always be greater than unity, the resistance to mass transfer term in the mobile phase will be, at a minimum, about forty times greater than that in the stationary phase. Consequently, the contribution from the resistance to mass transfer in the stationary phase to the overall variance per unit length of the column, relative to that in the mobile phase, can be ignored. It is now possible to obtain a new expression for the optimum particle diameter (dp(opt)) by eliminating the resistance to mass transfer function for the liquid phase from equation (14). 

Note that H is simply Henry s constant corrected for units. When the solute gas is readily soluble in the liquid solvent, Henry s law constant (H or H ) is small and Kj approximately equals k, and the absorption process is controlled by the gas film resistance. For systems where the solute is relatively insoluble in the liquid, H is large and K( approximately equals k, and the absorption rate is controlled by the liquid phase resistance. In most systems, the solute has a high solubility in the solvent selected, resulting in the system being gas film resistance controlled. 

At n = 1 N-s/m, hj, = 1 m and u = 1 m/s, the value r = AP. Thus, the specific cake resistance equals the pressure difference required by the liquid phase (with a viscosity of 1 N-s/m ) to be filtered at a rate u = 1 m/s for a cake 1 m thick. This hypothetical pressure difference is, however, beyond a practical range. For highly compressible cakes, the value ro reaches 10 m or more. Assuming V = 0 (at the start of filtration) where there is no cake over the filter plate, the equation becomes ... 

At = 1 N-s/m and u = 1 m/s, Rf = AP. This means that the filter plate resistance is equal to the pressure difference necessary for the liquid phase to pass through the filter plate at a rate of 1 m/s. For many filter plates, Rf is typically 10 ° m- . 

The structure of the cake formed and, consequently, its resistance to liquid flow depends on the properties of the solid particles and the liquid phase suspension, as well as on the conditions of filtration. Cake structure is first established by hydrodynamic factors (cake porosity, mean particle size, size distribution, and particle specific surface area and sphericity). It is also strongly influenced by some factors that can conditionally be denoted as physicochemical. These factors are ... 

Filter aids may be applied in one of two ways. The first method involves the use of a precoat filter aid, which can be applied as a thin layer over the filter before the suspension is pumped to the apparatus. A precoat prevents fine suspension particles from becoming so entangled in the filter medium that its resistance becomes exces-sive. In addition it facilitates the removal of filter cake at the end of the filtration cycle. The second application method involves incorporation of a certain amount of the material with the suspension before introducing it to the filter. The addition of filter aids increases the porosity of the sludge, decreases its compressibility, and reduces the resistance of the cake. In some cases the filter aid displays an adsorption action, which results in particle separation of sizes down to 0.1 /i. The adsorption ability of certain filter aids, such as bleached earth and activated charcoals, is manifest by a decoloring of the suspension s liquid phase. This practice is widely used for treating fats and oils. The properties of these additives are determined by the characteristics... 

Note that filter aid selection must be based on planned laboratory tests. Guidelines for selection may only be applied in the broadest sense, since there is almost an infinite number of combinations of filter media, filter aids, and suspensions that will produce varying degrees of separation. The hydrodynamics of any filtration process are highly complex filtration is essentially a multiphase system in which interaction takes place between solids from the suspension, filter aid, and filter medium, and a liquid phase. Experiments are mandatory in most operations not only in proper filter aid selection but in defining the method of application. Some general guidelines can be applied to such studies the filter aid must have the minimum hydraulic resistance and provide the desired rate of separation an insufficient amount of filter aid leads to a reduction in filtrate quality — excess amounts result in losses is filtration rate and it is necessary to account for the method of application and characteristics of filter aids. 

When the cake structure is composed of particles that are readily deformed or become rearranged under pressure, the resulting cake is characterized as being compressible. Those that are not readily deformed are referred to as sem-compressible, and those that deform only slightly are considered incompressible. Porosity (defined as the ratio of pore volume to the volume of cake) does not decrease with increasing pressure drop. The porosity of a compressible cake decreases under pressure, and its hydraulic resistance to the flow of the liquid phase increases with an increase in the pressure differential across the filter media. 

Oxygen transfer rate (OTR) The product of volumetric oxygen transfer rate kj a and the oxygen concentration driving force (C - Cl), (ML T ), where Tl is the mass transfer coefficient based on liquid phase resistance to mass transfer (LT ), a is the air bubble surface area per unit volume (L ), and C and Cl are oxygen solubility and dissolved oxygen concentration, respectively. All the terms of OTR refer to the time average values of a dynamic situation. 

The liquid phase resistance, h] , is considered low when compared to the overall resistance therefore, the should give a reasonable approximation to the overall resistance for the system, because l/U = l/hg + l/h] . 

Increase in mass-transfer rate per unit area. As stated above, agitated gas-liquid contactors are used, in general, when it is necessary to deal with sparingly soluble gases. According to the terminology of the film theory, absorption is then controlled by the liquid resistance, and agitation of the liquid phase could increase the mass-transfer rate per unit area. As will be... 

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