Mass transfer component

Considering the end regions of the column as well-mixed stages, with small but finite rates of mass transfer, component balance equations can be derived for end stage 0... 

From equation (8) values of the mass transfer component tc k y a/(l-eG) can be estimated from measured values of -Rjj +co un< er mass transfer-limited conditions by using 2 values of k determined from Intrinsic kinetic studies. 

Fig. 2.7 Van Deemter curve (H/u curve). 1=eddy diffusion and flow distribution connponent of band broadening 2 = longitudinal diffusion component—flow-rates at which this diffusion is not a factor of any significance should be used in liquid chromatography 3 = mass-transfer component— the slope of the line is greater for 50 am than it is for 5)am particles 4 = the resultant van Deemter H/ucurve. ...

Where ACi is concentration difference of species i between sample s surface and liquid bulk. In the case that sulfuric acid and sulfurous acid were assumed as the mass-transfer components, their concentrations in the bulk were used for AQ. On the other hand, in the case that limestone and gypsum were assumed as the mass-transfer components, saturation concentrations on the surface were used for AQ. It should be noted that in the case that sulfurous acid was the mass-transfer component, Eq. 5 should be divided by 2 considering Eq. 1. Later, these calculated values will be compared with experimental values. 

This mass transfer step has been extensively studied, primarily through the examination of simple physical transfer processes, such as vaporization or drying. Thus, the mass transfer component of the overall reaction sequence is perhaps the best understood. While it is possible to calculate the rate of mass transfer between a moving gas stream and a solid surface by the simultaneous solution of the appropriate fluid flow and diffusion equations [1, Chapter 17], here we shall adopt a more empirical approach through the use of mass transfer coefficients, although some comments will be made about the way these two approaches may be regarded as complementary. 

Design Procedure. The packed height of the tower required to reduce the concentration of the solute in the gas stream from to acceptable residual level ofjy 2 may be calculated by combining point values of the mass transfer rate and a differential material balance for the absorbed component. Referring to a sHce dh of the absorber (Fig. 5),... 

The term dqljdt represents the overall rate of mass transfer for component / (at time t and distance averaged over a particle. This is governed by a mass transfer rate expression which may be thought of as a general functional relationship of the form... 

Adsorption. In the design of the adsorption step of gas-phase processes, two phenomena must be considered, equiUbrium and mass transfer. Sometimes adsorption equiUbrium can be regarded as that of a single component, but mote often several components and their interactions must be accounted for. Design techniques for each phenomenon exist as well as some combined models for dynamic performance. 

Mass-Transfer Coefficients with Chemical Reaction. Chemical reaction can occur ia any of the five regions shown ia Figure 3, ie, the bulk of each phase, the film ia each phase adjacent to the iaterface, and at the iaterface itself. Irreversible homogeneous reaction between the consolute component C and a reactant D ia phase B can be described as... 

The enhanced rate expressions for regimes 3 and 4 have been presented (48) and can be appHed (49,50) when one phase consists of a pure reactant, for example in the saponification of an ester. However, it should be noted that in the more general case where component C in equation 19 is transferred from one inert solvent (A) to another (B), an enhancement of the mass-transfer coefficient in the B-rich phase has the effect of moving the controlling mass-transfer resistance to the A-rich phase, in accordance with equation 17. Resistance in both Hquid phases is taken into account in a detailed model (51) which is apphcable to the reversible reactions involved in metal extraction. This model, which can accommodate the case of interfacial reaction, has been successfully compared with rate data from the Hterature (51). 

Below about 0.5 K, the interactions between He and He in the superfluid Hquid phase becomes very small, and in many ways the He component behaves as a mechanical vacuum to the diffusional motion of He atoms. If He is added to the normal phase or removed from the superfluid phase, equiHbrium is restored by the transfer of He from a concentrated phase to a dilute phase. The effective He density is thereby decreased producing a heat-absorbing expansion analogous to the evaporation of He. The He density in the superfluid phase, and hence its mass-transfer rate, is much greater than that in He vapor at these low temperatures. Thus, the pseudoevaporative cooling effect can be sustained at practical rates down to very low temperatures in heHum-dilution refrigerators (72). 

Fluid mixing is a unit operation carried out to homogenize fluids in terms of concentration of components, physical properties, and temperature, and create dispersions of mutually insoluble phases. It is frequently encountered in the process industry using various physical operations and mass-transfer/reaction systems (Table 1). These industries include petroleum (qv), chemical, food, pharmaceutical, paper (qv), and mining. The fundamental mechanism of this most common industrial operation involves physical movement of material between various parts of the whole mass (see Supplement). This is achieved by transmitting mechanical energy to force the fluid motion. 

This process has been used for various situations (1—14). Eor the condensation of a single component from a binary gas mixture, the gas-stream sensible heat and mass-transfer equations for a differential condenser section take the following forms ... 

Likewise, the microscopic heat-transfer term takes accepted empirical correlations for pure-component pool boiling and adds corrections for mass-transfer and convection effects on the driving forces present in pool boiling. In addition to dependence on the usual physical properties, the extent of superheat, the saturation pressure change related to the superheat, and a suppression factor relating mixture behavior to equivalent pure-component heat-transfer coefficients are correlating functions. 

In engineering appHcations, the transport processes involving heat and mass transfer usually occur in process equipment involving vapor—gas mixtures where the vapor undergoes a phase transformation, such as condensation to or evaporation from a Hquid phase. In the simplest case, the Hquid phase is pure, consisting of the vapor component alone. 

When the soHd substrate is placed in the bath, the air is displaced by the bath, fl, and the 37T interface is replaced by an SB interface. Similarly, an interface replaces the interface. The equiHbrium free energy values of these new interfaces are not estabHshed immediately but gradually through mass transfer (if there is any mutual solubiHty between F and fl it is assumed that B does not dissolve 3) and through adsorption of dissolved components. When these processes have gone to completion the new relationship is... 

A = effective surface area for heat and mass transfer in m L = latent heat of vaporization at in kj/kg k = mass-transfer coefficient in kg/ (sm kPa) t = mean source temperature for all components of heat transfer in K t = Hquid surface temperature in K p = Hquid vapor pressure at in kPa p = partial pressure of vapor in the gas environment in kPa. It is often useful to express this relationship in terms of dry basis moisture change. For vaporization from a layer of material ... 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

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. 

For the special case of steady-state unidirectional diffusion of a component through an inert-gas film in an ideal-gas system, the rate of mass transfer is derived as... 

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