Mass transfer definition

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. 

Tbe mass-transfer coefficients k c and /cf by definition are equal to tbe ratios of tbe molal mass flux Na to tbe concentration driving forces p — Pi) and (Ci — c) respectively. An alternative expression for tbe rate of transfer in dilute systems is given by... 

It is important to understand that when chemical reactions are involved, this definition of Cl is based ou the driving force defined as the difference between the couceutratiou of un reacted solute gas at the interface and in the bulk of the liquid. A coefficient based ou the total of both uureacted and reached gas could have values. smaller than the physical-absorption mass-transfer coefficient /c . 

Tray Efficiencies in Plate Absorbers and Strippers Compn-tations of the nnmber of theoretical plates N assnme that the hqnia on each plate is completely mixed and that the vapor leaving the plate is in eqnihbrinm with the liqnid. In actnal practice a condition of complete eqnihbrinm cannot exist since interphase mass transfer reqnires a finite driving-force difference. This leads to the definition of an overall plate efficiency... 

What this shows is that, from the definition of off-bottom motion to complete uniformity, the effect of mixer power is much less than from going to on-bottom motion to off-bottom suspension. The initial increase in power causes more and more solids to be in active communication with the liquid and has a much greater mass-transfer rate than that occurring above the power level for off-bottom suspension, in which slip velocity between the particles of fluid is the major contributor (Fig. 18-23). 

In general, it is fair to state that one of the major difficulties in interpreting, and consequently in establishing definitive tests of, corrosion phenomena in fused metal or salt environments is the large influence of very small, and therefore not easily controlled, variations in solubility, impurity concentration, temperature gradient, etc. . For example, the solubility of iron in liquid mercury is of the order of 5 x 10 at 649°C, and static tests show iron and steel to be practically unaltered by exposure to mercury. Nevertheless, in mercury boiler service, severe operating difficulties were encountered owing to the mass transfer of iron from the hot to the cold portions of the unit. Another minute variation was found substantially to alleviate the problem the presence of 10 ppm of titanium in the mercury reduced the rate of attack to an inappreciable value at 650°C as little as 1 ppm of titanium was similarly effective at 454°C . 

Now R0 (the shear stress in the fluid at the surface) is equal and opposite to R, the shear stress acting on the surface, —q jQs is by definition the heat transfer coefficient at the surface (h), and (—NA)y=o/ CAjl - CAw) is the mass transfer coefficient ho). Then dividing both sides of equation 12.100 by pu, and of equation 12.101 by u, to make them dimensionless ... 

It is important to appreciate the fact that when two or more reaction rates are to be compared and/or combined, they should be defined in the same manner. For instance, if it is required to combine a mass transfer step and a reaction step, then the rates corresponding to both should be defined in an identical manner. Since the mass transfer rate by definition is the flow of material per unit time normal to a unit surface... 

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... 

The origin of the initial microroughness and the events leading up to its final amplification by mass-transfer limited deposition, have not been clarified definitively (P4a). It has been shown (I9a) that preliminary electropolishing, to assure a smooth surface, does not prevent surface roughness at... 

Depending on the driving force we choose to employ in our analysis, there are several definitions of mass transfer coefficients that may be considered appropriate for use. If we consider an arbitrary interface between a fluid and the external surface of a catalyst particle, we might choose to define a mass transfer coefficient based on a concentration driving force (kc) as... 

We conclude that the Li-poor stars definitely have different evolutionary histories to Li-normal plateau stars. A mass-transfer mechanism may explain the origin of these objects, but irrespective of whether this is the correct explanation, the Li-poor objects cannot be included in studies of Li depletion mechanisms that affect normal single stars. Consequently we conclude that the small (zero ) intrinsic spread in plateau Li abundances inferred by [25] is representative of normal halo stars, and thus signifies at most a small depletion in Li, <0.1 dex by the models of [17]. 

Furthermore, at steady-state, (— rA) is also the rate of mass transfer of A across the exterior film, such mass transfer being in series with the combined intraparticle processes of diffusion and reaction hence, from the definition of kAg,... 

Note that Eq. (3) (respectively Eq. (2)) is in fact the definition of the liquid (gas) film thickness dL (dG), which cannot be measured because it does not really exist. The advantage of this model is its simplicity, its teaching power, and its ability to describe the coupling of mass transfer with chemical reactions sufficiently accurately for most practical cases. 

In many applications, a mean droplet size is a factor of foremost concern. Mean droplet size can be taken as a measure of the quality of an atomization process. It is also convenient to use only mean droplet size in calculations involving discrete droplets such as multiphase flow and mass transfer processes. Various definitions of mean droplet size have been employed in different applications, as summarized in Table 4.1. The concept and notation of mean droplet diameter have been generalized and standardized by Mugele and Evans.[423] The arithmetic, surface, and volume mean droplet diameter (D10, D2o, and D30) are some most common mean droplet diameters ... 

The main goal of this chapter is to review the most widely used modeling techniques to analyze sorption/desorption data generated for environmental systems. Since the definition of sorption/desorption (i.e., a mass-transfer mechanism) process requires the determination of the rate at which equilibrium is approached, some important aspects of chemical kinetics and modeling of sorption/desorption mechanisms for solid phase systems are discussed. In addition, the background theory and experimental techniques for the different sorption/ desorption processes are considered. Estimations of transport parameters for organic pollutants from laboratory studies are also presented and evaluated. 

---