Mass transfer coefficient surface-averaged

The value of the saturation concentration,, is the spatial average of the value determined from a clean water performance test and is not corrected for gas-side oxygen depletion therefore K ji is an apparent value because it is determined on the basis of an uncorrected. A tme volumetric mass transfer coefficient can be evaluated by correcting for the gas-side oxygen depletion. However, for design purposes, can be estimated from the surface saturation concentration and effective saturation depth by... 

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. 

In the Danckwerts model, it is assumed that elements of the surface have an age distribution ranging from zero to infinity. Obtain the age distribution function for this model and apply it to obtain the average, mass Iransfer coefficient at the surface, given that from the penetration theory the mass transfer coefficient for surface of age t is VlD/(7rt, where D is the diffusivity. 

Mass transfer rates from drops are obtained by measuring the concentration change in either or both of the phases after passage of one or more drops through a reservoir of the continuous phase. This method yields the average transfer rate over the time of drop rise or fall, but not instantaneous values. For measurements of the resistance external to the drop this is no drawback, because this resistance is nearly constant, but the resistance within the drop frequently varies with time. The fractional approach to equilibrium, F, is calculated from the compositions and is then related to the product of the overall mass transfer coefficient and the surface area ... 

In this equation. Act is taken as the maximum possible surface tension lowering. Hence for a solute-free continuous phase, Aa is the difference between the interfacial tension for the solvent-free system and the equilibrium interfacial tension corresponding to the solute concentration in the dispersed phase. Equation (10-6) indicates a strong effect of the viscosity ratio k on the mass transfer coefficient as found experimentally (LI 1). For the few systems in which measurements are reported (Bll, Lll, 04), estimates from Eq. (10-6) have an average error of about 30% for the first 5-10 seconds of transfer when interfacial turbulence is strongest. 

In 1951,Danckwerts [4] proposed the surface renewal model as an extension ofthe penetration model. Instead of assuming a fixed contact time for all fluid elements, Danckwerts assumed a wide distribution of contact time, from zero to infinity, and supposed that the chance of an element ofthe surface being replaced with fresh liquid was independent of the length of time for which it has been exposed. Then, it was shown, theoretically, that the averaged mass transfer coefficient at the interface is given as... 

So far we have approximated the external heat and mass transfer coefficients by virtue of an average value however, precise measurements have indicated that the local value may substantially change along the catalyst surface. Moreover, for a highly exothermic reaction a very strong gas phase concentration and temperature gradients may occur so that the pellet is bathed by a nonuniform external field (13, 14). 

The rate parameters of importance in the multicomponent rate model are the mass transfer coefficients and surface diffusion coefficients for each solute species. For accurate description of the multicomponent rate kinetics, it is necessary that accurate values are used for these parameters. It was shown by Mathews and Weber (14), that a deviation of 20% in mass transfer coefficients can have significant effects on the predicted adsorption rate profiles. Several mass transfer correlation studies were examined for estimating the mass transfer coefficients (15, jL6,17,18,19). The correlation of Calderbank and Moo-Young (16) based on Kolmogaroff s theory of local isotropic turbulence has a standard deviation of 66%. The slip velocity method of Harriott (17) provides correlation with an average deviation of 39%. Brian and Hales (15) could not obtain super-imposable curves from heat and mass transfer studies, and the mass transfer data was not in agreement with that of Harriott for high Schmidt number values. 

Single Sphere Model II (Equations 4, 5, 8, 9 and 10 in reference 6) In this model allowance is made for the resistance to mass transfer offered by the surface film surrounding the herb particles. The mass transfer coefficient kf was obtained from correlations proposed by Catchpole et al (8, 9) for mass transfer and diffusion into near-critical fluids. An average of the binary diffusivities of the major essential oil components present was used in calculating kf (these diffusivities were all rather similar because of their similar structures). 

Although diffusion of reacting species can be written in terms of the diffusivity and boundary layer thickness, the magnitude of 8 is unknown. Therefore, the mass-transfer coefficient is normally used. That is, the average molar flux from the bulk fluid to the solid surface is —x direction in Figure 6.2.1)... 

Consider a circular pipe of inner diameter D = 0.015 m whose inner surface is I covered with a layer of liquid water as a result of condensation (Fig. 14-49). In I order to dry the pipe, air at 300 K and 1 atm is forced to flov/ through if with an average velocity of 1.2 m/s. Using the analogy between heat and mass transfer, determine the mass transfer coefficient inside the pipe for fully developed flov/. 

Consider a 15-cm-intemal-diameter, 10 m long circular duct whose interior surface is wet. The duct is to be dried by forcing dry air at 1 atm and 15°C through it at an average velocity of 3 iii/s. Tlie duct passes through a chilled room, and it remains at an average temperature of 15°C at all times. Determine the mass transfer coefficient in the duct. 

Liquid toluene (C iHsCHj) was stored at6.4°C in an open top 20-cm-diameter cylindrical container. Tile vapor pressure of toluene at 6.4°C is 10 nun Hg. A gentle stream of fresh air at 6.4"C and 101.3 kPa was allowed to flow over the open end of the container. The rale of evaporation of toluene into air was measured to be 60 g/day. E.stimaie the concentration of toluene (in g/m ) at exactly 10 nun above the liquid surface. The diffusion coefficient of toluene at 2S° C is D.,a = 0.084 X 10-"inVs. 14-141 In an experiment, a sphere of crystalline sodium. chloride (NaCI) was suspended in a. stirred tank filled with water at 20°C. It-s initial mass was 100 g. In 10 minutes, the mass Of sphere was found to have decreased by 10 percent. The density of NaCl is 2160 kg/ra Its solubility in water at 20°C is 320 kg/m, Use these results to obalin an average value for the mass transfer coefficient. 

Air flows in a 4-cm-diameter wet pipe at 20 C and 1 atm with an average velocity of 4 m/s in order to dry the surface. The Nussell number in this case can be determined from Nu = 0.023Re Pi"- where Ke = 10,550 and Pr = 0.731. Also, the diffusion coefficient of water vapor in air is 2.42 X 10 mVs. Using the analogy between heal and mass transfer, the mass transfer coefficient inside the pipe for fully developed flow becomes... 

The mass transfer coefficient used in this equation should be the average value over the total external particle surface area Ap, including the flat ends of each particle. Hqwever,... 

The average mass transfer coefficient over the surface of area A is... 

Apart from this, each model contains an empirical parameter effective film thickness effective exposure time 0, and effective rate of surface renewals. Consequently, when predicting the average rate of purely physical absorption for large-scale conditions, one cannot expect better results from refined models than from the empirical mass-transfer coefficient first defined by Whitman (W5). 

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