Mass-transfer rate measurement

Experimental work was undertaken (G8) to provide the information necessary to permit a test of this theoretical model. The system used bore complete geometrical and chemical similarity to that used by Cooper et al. (C9) so that their mass-transfer rate measurements, along with the average residence-time and power-consumption results determined in the experimental work (see Section II,D), were used to compare the experimental values with the model. 

Janssen and Hoogland (J3, J4a) made an extensive study of mass transfer during gas evolution at vertical and horizontal electrodes. Hydrogen, oxygen, and chlorine evolution were visually recorded and mass-transfer rates measured. The mass-transfer rate and its dependence on the current density, that is, the gas evolution rate, were found to depend strongly on the nature of the gas evolved and the pH of the electrolytic solution, and only slightly on the position of the electrode. It was concluded that the rate of flow of solution in a thin layer near the electrode, much smaller than the bubble diameter, determines the mass-transfer rate. This flow is affected in turn by the incidence and frequency of bubble formation and detachment. However, in this study the mass-transfer rates could not be correlated with the square root of the free-bubble diameter as in the surface renewal theory proposed by Ibl (18). 

Figure 15.22 provides a comparison between the mass transfer rates measured by Modine (1963) and the rates predicted using the different classes of model for the vapor-phase mass transfer process methods based on the multicomponent film model (all of... 

Polypropylene glycol was used as the diluent. The final form of the flat-sheet SLM system had uniform selectivity and good operational stabihty during continuous operation for more than 2 months. Mass-transfer rates measured were five times the values measured usually during the operation of commercially available silicone tubing-based systems [141]. The system developed by the authors had two more advantages. These were the reduced water flux and the minimum sodium ion transfer. The authors measured the partition coefficient of phenol between polypropylene glycol and water, and determined this to be equal to 84. This value increased to 134 if the aqueous phase contained 20% KCI. 

The behavior of drops in the centrifugal field has been studied (211) and the residence times and mass-transfer rates have been measured (212). PodbieHiiak extractors have been widely used in the pharmaceutical industry, eg, for the extraction of penicillin, and are increasingly used in other fields as weU. Commercial units having throughputs of up to 98 m /h (26,000 gal/h) have been reported. 

It can be obtained from the available literature or measured experimentally. If the erosion corrosion rate (ECR) is directly proportional to the mass transfer rate ... 

Mass-transfer rates have been determined by measuring the absorption rate of a pure gas or of a component of a gas mixture as a function of the several operating variables involved. The basic requirement of the evaluation method is that the rate step for the physical absorption should be controlling, not the chemical reaction rate. The experimental method that has gained the widest acceptance involves the oxidation of sodium sulfite, although in some of the more recent work, the rate of carbon dioxide absorption in various media has been used to determine mass-transfer rates and interfacial areas. 

Measurement of the absorption rate of carbon dioxide in aqueous solutions of sodium hydroxide has been used in some of the more recent work on mass-transfer rate in gas-liquid dispersions (D6, N3, R4, R5, V5, W2, W4, Y3). Although this absorption has a disadvantage because of the high solubility of C02 as compared to 02, it has several advantages over the sulfite-oxidation method. For example, it is relatively insensitive to impurities, and the physical properties of the liquid can be altered by the addition of other liquids without appreciably affecting the chemical kinetics. Yoshida and... 

This approach to the problem is purely theoretical, since this model is based on a characteristic stagnant film thickness which is difficult to estimate or to measure. In addition, this model does not give any information as to the value of A, which must be determined separately by some other method. As a result, it is impossible to estimate the total mass-transfer rate in the disperser with the aid of this model only. 

An attempt has been made by Johnson and co-workers to relate such theoretical results with experimental data for the absorption of a single carbon dioxide bubble into aqueous solutions of monoethanolamine, determined under forced convection conditions over a Reynolds number range from 30 to 220. The numerical results were found to be much higher than the measured values for noncirculating bubbles. The numerical solutions indicate that the mass-transfer rate should be independent of Peclet number, whereas the experimentally measured rates increase gradually with increasing Peclet number. The discrepancy is attributed to the experimental technique, where-... 

Many of the earlier studies of mass transfer involved measuring the rate of vaporisation of liquids by passing a turbulent air stream over a liquid surface. In addition, some investigations have been carried out in the absence of air flow, under what have been termed still air conditions. Most of these experiments have been carried out in some form of wind tunnel where the rate of flow of air and its temperature and humidity could be controlled and measured. In these experiments it was found to be important to keep the surface of the liquid level with the rim of the pan in order to avoid the generation of eddies at the leading edge. 

Ammonia is absorbed in a falling film of water in an absorption apparatus and the film is disrupted and mixed at regular intervals as it flows down the column. The mass transfer rate is calculated from the penetration theory on the assumption that all the relevant conditions apply. It is found from measurements that the muss transfer rate immediately before mixing is only 16 pet cent of that calculated from the theory anil the difference has been attributed to the existence of a surface film which remains intact and unaffected by the mixing process. If the liquid mixing process lakes place every second, what thickness of surface film would account for the discrepancy, ... 

Mass Transfer Rates. Mass transfer occurs across the interface. The rate of mass transfer is proportional to the interfacial area and the concentration driving force. Suppose component A is being transferred from the gas to the liquid. The concentration of A in the gas phase is Ug and the concentration of A in the liquid phase is u . Both concentrations have units of moles per cubic meter however they are not directly comparable because they are in different phases. This fact makes mass transfer more difficult than heat transfer since the temperature is the temperature regardless of what phase it is measured in, and the driving force for heat transfer across an interface is just the temperature difference Tg—Ti. For mass transfer, the driving force is not Ug—ai. Instead, one of the concentrations must be converted to its equivalent value in the other phase. 

Measurements Using Liquid-Phase Reactions. Liquid-phase reactions, and the oxidation of sodium sulfite to sodium sulfate in particular, are sometimes used to determine kiAi. As for the transient method, the system is batch with respect to the liquid phase. Pure oxygen is sparged into the vessel. A pseudo-steady-state results. There is no gas outlet, and the inlet flow rate is adjusted so that the vessel pressure remains constant. Under these circumstances, the inlet flow rate equals the mass transfer rate. Equations (11.5) and (11.12) are combined to give a particularly simple result ... 

In the above theory, the interfacial concentrations Coi and Cli are not measurable directly and are therefore of relatively little immediate use. In order to overcome this apparent difficulty, overall mass transfer rate equations are defined by analogy to the film equations. These are based on overall... 

The moving-drop method [2] employs a column of one liquid phase through which drops of a second liquid either rise or fall. The drops are produced at a nozzle situated at one end of the column and collected at the other end. The contact time and size of the drop are measurable. Three regimes of mass transport need to be considered drop formation, free rise (or fall) and drop coalescence. The solution in the liquid column phase or drop phase (after contact) may be analyzed to determine the total mass transferred, which may be related to the interfacial reaction only after mass transfer rates have been determined. 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

In Ref. 30, the transfer of tetraethylammonium (TEA ) across nonpolarizable DCE-water interface was used as a model experimental system. No attempt to measure kinetics of the rapid TEA+ transfer was made because of the lack of suitable quantitative theory for IT feedback mode. Such theory must take into account both finite quasirever-sible IT kinetics at the ITIES and a small RG value for the pipette tip. The mass transfer rate for IT experiments by SECM is similar to that for heterogeneous ET measurements, and the standard rate constants of the order of 1 cm/s should be accessible. This technique should be most useful for probing IT rates in biological systems and polymer films. 

Electrochemical measurements of mass-transfer rates by the limiting-current technique have been employed with increasing frequency in the last 20 years. This chapter offers a discussion of the underlying principles, conditions of validity, and selected applications. 

Since current can be measured with ease and precision, the limiting-current technique provides a convenient and, under certain conditions, accurate method for measuring mass-transfer rates. The conditions for valid measurement and correct interpretation of limiting currents are discussed in the following sections. 

In principle, the accuracy with which mass-transfer rates may be measured is limited by the precision with which the limiting-current plateau or inflection point can be read. Furthermore, the electrode area, the current... 

Mass-transfer rates from limiting-current measurements in well-supported solutions should invariably be correlated with ionic and not with molecular diffusivities. The former can be calculated from limiting-current measurements, for example, at a rotating-disk electrode. 

Investigations on mass-transfer rates along planar electrodes (F2, H3) in which the rate of increase of current, or of cell voltage, was varied systematically from one measurement to the other revealed that the time taken for attaining the limiting current influenced the limiting-current curve. This unsteady-state effect was noticeable both in the quality of definition of the... 

Of considerable interest is the use of small isolated electrodes, in the form of strips or disks embedded in the wall, to measure local mass-transfer rates or rate fluctuations. Mass-transfer to spot electrodes on a rotating disk is represented by Eqs. (lOg-i) of Table VII. Analytical solutions in this case have to take account of curved streamlines. Despic et al. (Dlld) have proposed twin spot electrodes as a tool for kinetic studies, similar to the ring-disk electrode applications of disk and ring-disk electrodes for kinetic studies are discussed in several monographs (A3b, P4b). In fully developed channel or pipe flow, mass transfer to such electrodes is given by the following equation based on the Leveque model ... 

Overall mass-transfer rates at a sphere in forced flow, and mass-transfer rate distribution over a sphere as a function of the polar angle have been measured by Gibert, Angelino, and co-workers (G2, G4a) for a wide range of Reynolds numbers. The overall rate dependence on Re exhibited two distinct regimes with a sharp transition at Re = 1250. Local mass-transfer rates were deduced from measurements in which the sphere was progressively coated by an insulator, starting from the rear. 

By substituting the well-known Blasius relation for the friction factor, Eq. (45) in Table VII results. Van Shaw et al. (V2) tested this relation by limiting-current measurements on short pipe sections, and found that the Re and (L/d) dependences were in accord with theory. The mass-transfer rates obtained averaged 7% lower than predicted, but in a later publication this was traced to incorrect flow rate calibration. Iribame et al. (110) showed that the Leveque relation is also valid for turbulent mass transfer in falling films, as long as the developing mass-transfer condition is fulfilled (generally expressed as L+ < 103) while Re > 103. The fundamental importance of the Leveque equation for the interpretation of microelectrode measurements is discussed at an earlier point. 

Of particular interest are measurements on a vibrating sphere in forced flow by Gibert and Angelino (G3) because of the careful experimental execution and wide range of frequencies and Re numbers investigated. Below a certain critical frequency, the mass-transfer rate to the sphere is not affected by vibration. 

In work by Okada et al. (03) on a rotating-disk flow, Eqs. (10a) and (10b) in Table VII, the electrolyte was completely enclosed between the rotating disk and the counterelectrode. Mass transfer was measured at the rotating as well as at the stationary disk, and the distance between disks was varied. At low rotation rates, the flux at the rotating disk was higher than predicted by the Levich equation, Eq. (la) in Table VII. The flux at the stationary disk followed a relation of the Levich type, but with a constant roughly two-thirds that in the rotating-disk equation. 

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