Mass transfer concentration

Fig. 3. Concentration profiles near an iaterface where the arrow represents the direction of mass transfer, = concentration of C in A-rich phase,...

During interphase mass transfer, concentration gradients will be set up across the interface. The concentration variations in the bulk phases x and y will be described by differential equations whereas at the interface /, we will have jump conditions or boundary conditions. Standart (1964) and Slattery (1981) give detailed discussions of these relations for the transport of mass, momentum, energy, and entropy. It will not be possible to give here the complete derivations and the reader is, therefore, referred to these sources. A masterly treatment of this subject is also available in the article by Truesdell and Toupin (1960), which must be compulsory reading for a serious researcher in transport phenomena. 

Biot number for mass transfer concentration of species i,kmol/m liquid-phase diffusivity,m7ls effective diffusivity within solid or catalyst phase, Damkohler number... 

Enlianced mass transfer concentrate less volatile component. Surface Tension increases... 

Electrochemistry is dominated by the study of species dissolved in solution. The use of a solvent as the reaction medium helps electrochemists to control important reaction conditions such as pH, rate of mass transfer, concentration of reactant, solubility, solvation, etc. Water and organic solvents are the most popular media. However, by using appropriate ionic liquids, reactants and products that are unstable in those media remain stable, and redox reactions that are impossible in water and organic solvents become possible. The reaction environments are markedly wider in some ionic liquids than in other solvent systems. In spite of this, some fundamental electrochemical concepts generally used in conventional solvent systems are not always valid in ionic liquids. 

Figure 21.2 shows a typical polarization curve (or current-voltage curve) of PEMFCs. This curve results from both the anodic HOR and the cathodic ORR reactions. The actual celt voltage is much lower than the ideal celt voltage and the theoretical cell voltage. When the current is drawn from a fuel cell, the actual cell voltage will drop from its ideal due to several types of irreversible losses, as shown in Figure 21.2. The drop is mainly caused by mixed potential and fuel crossover, activation overpotential, ohmic overpotential, as well as mass transfer (concentration) overpotential.

Interfiidal Mass Transfer (Concentration Gradients in the Film) For a first-order reaction and low Re numbers (for a fixed bed Shmin = 3.8), the influence of film diffusion can be neglected, if the following condition is fulfilled (Section 4.7) ... 

Figure 7.1.11. Mass-transfer/concentration profiles in an ion exchange column (a) sections of the column where it is in A form, B form or in mixed AB form (b) concentration profile of the A form of the resin in the column at any time (c) breakthrough behavior at the column bottom, sharp breakthrough and diffuse breakthrough.

The oscillations observed arise as a result of the mass transfer of CTAB (Fig. 3, B). Under mass transfer, concentration gradients build up in the diffusion layer (Pradines et al. 2007). The surfactant concentration in contact with the interface (that determines the corresponding adsorption level) decreases. 

Mass transfer rates may also be expressed in terms of an overall gas-phase driving force by defining a hypothetical equiHbrium mole fractionjy as the concentration which would be in equiHbrium with the bulk Hquid concentration = rax ) ... 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Rate Equations with Concentration-Independent Mass Transfer Coefficients. Except for equimolar counterdiffusion, the mass transfer coefficients appHcable to the various situations apparently depend on concentration through thej/g and factors. Instead of the classical rate equations 4 and 5, containing variable mass transfer coefficients, the rate of mass transfer can be expressed in terms of the constant coefficients for equimolar counterdiffusion using the relationships... 

Equation 28 and its liquid-phase equivalent are very general and valid in all situations. Similarly, the overall mass transfer coefficients may be made independent of the effect of bulk fiux through the films and thus nearly concentration independent for straight equilibrium lines ... 

Rate equations 28 and 30 combine the advantages of concentration-independent mass transfer coefficients, even in situations of multicomponent diffusion, and a familiar mathematical form involving concentration driving forces. The main inconvenience is the use of an effective diffusivity which may itself depend somewhat on the mixture composition and in certain cases even on the diffusion rates. This advantage can be eliminated by working with a different form of the MaxweU-Stefan equation (30—32). One thus obtains a set of rate equations of an unconventional form having concentration-independent mass transfer coefficients that are defined for each binary pair directiy based on the MaxweU-Stefan diffusivities. 

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),... 

Equation 39 can often be simplified by adopting the concept of a mass transfer unit. As explained in the film theory discussion eadier, the purpose of selecting equation 27 as a rate equation is that is independent of concentration. This is also tme for the Gj /k aP term in equation 39. In many practical instances, this expression is fairly independent of both pressure and Gj as increases through the tower, increases also, nearly compensating for the variations in Gj. Thus this term is often effectively constant and can be removed from the integral ... 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

In certain adsorbents, notably partially coked 2eohtes and some carbon molecular sieves, the resistance to mass transfer may be concentrated at the surface of the particle, lea ding to an uptake expression of the form... 

Eor a linear system f (c) = if, so the wave velocity becomes independent of concentration and, in the absence of dispersive effects such as mass transfer resistance or axial mixing, a concentration perturbation propagates without changing its shape. The propagation velocity is inversely dependent on the adsorption equiUbrium constant. 

Adsorption Dynamics. An outline of approaches that have been taken to model mass-transfer rates in adsorbents has been given (see Adsorption). Detailed reviews of the extensive Hterature on the interrelated topics of modeling of mass-transfer rate processes in fixed-bed adsorbers, bed concentration profiles, and breakthrough curves include references 16 and 26. The related simple design concepts of WES, WUB, and LUB for constant-pattern adsorption are discussed later. 

The first assumption in all such physical mass transfer processes is that equiHbrium exists at the interface between the two phases. This assumption implies that, at the interface, the concentration of the gas in the Hquid, is equal to its solubiHty at its partial pressure in the gas phase,Since, for sparingly soluble gases such as oxygen, there is a direct proportionaHty between the two,... 

The rate of mass transfer,/, is then assumed to be proportional to the concentration differences existing within each phase, the surface area between the phases,, and a coefficient (the gas or Hquid film mass transfer coefficient, k or respectively) which relates the three. Thus... 

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... 

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