Mass transfer drops

In general, the half-wave potential is dependent on the rate of mass transfer (drop time at the DME [158]) and is only not so for reversible reactions. If we consider that just the species Ox exists in bulk solution, then it is fairly easy to show that eqn. (126) may be rewritten as... 

In a fuel cell, as the cell current becomes high, which indicates the electrochemical reaction rate on the electrode surface is fast, the mass transfer rate of the reactants is not fast enough to provide enough reactants to the electrode surface. Depletion of reactants at the electrode surface leads to a drop in cell voltage. The calculation of the cell voltage drop in this part is difficult, and a semi-empirical equation is usually used to estimate the mass transfer drop. The most popular expression for the mass transfer drop is... 

If both the substances have the same specific heat capacities, the term for mass transfer drops out of the equation. However in all other cases it does not assume a negligible value. In particular for substances such as water vapour and air, the specific heat capacities are so different that the mass transfer term cannot be removed. In addition it should be recognised that the energy equation agrees with that for pure substances when the specific heat capacities of the two components are equal and when no chemical reactions occur. 

A previous paper by Ryu and Oldshue treated an example where the final cell concentration was changed from 10 to 12 to 20 g//, and the oxygen mass transfer dropped from 10 to 8.3 to 6.4 mols oxygen/MJ. 

In addition to the fundamental parameters of selectivity, capacity, and mass-transfer rate, other more practical factors, namely, pressure drop characteristics and adsorbent life, play an important part in the commercial viabiUty of a practical adsorbent. 

Values of the mass-transfer coefficient k have been obtained for single drops rising (or falling) through a continuous immiscible Hquid phase. Extensive Hterature data have been summarized (40,42). The mass-transfer coefficient is often expressed in dimensionless form as the Sherwood number ... 

The values of k and hence Sb depend on whether the phase under consideration is the continuous phase, c, surrounding the drop, or the dispersed phase, d, comprising the drop. The notations and Sh are used for the respective mass-transfer coefficients and Sherwood numbers. 

Table 1. Equations for Liquid-Liquid Mass Transfer in Single Drops ...

Although the adsorption of surfactants tends to reduce mass-transfer coefficients by suppressing drop circulation, a sharp increase in mass transfer... 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

In industrial equipment, however, it is usually necessary to create a dispersion of drops in order to achieve a large specific interfacial area, a, defined as the interfacial contact area per unit volume of two-phase dispersion. Thus the mass-transfer rate obtainable per unit volume is given as... 

In many types of contactors, such as stirred tanks, rotary agitated columns, and pulsed columns, mechanical energy is appHed externally in order to reduce the drop si2e far below the values estimated from equations 36 and 37 and thereby increase the rate of mass transfer. The theory of local isotropic turbulence can be appHed to the breakup of a large drop into smaller ones (66), resulting in an expression of the form... 

The role of coalescence within a contactor is not always obvious. Sometimes the effect of coalescence can be inferred when the holdup is a factor in determining the Sauter mean diameter (67). If mass transfer occurs from the dispersed (d) to the continuous (e) phase, the approach of two drops can lead to the formation of a local surface tension gradient which promotes the drainage of the intervening film of the continuous phase (75) and thereby enhances coalescence. It has been observed that d-X.o-c mass transfer can lead to the formation of much larger drops than for the reverse mass-transfer direction, c to... 

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. 

Flow Past Bodies. A fluid moving past a surface of a soHd exerts a drag force on the soHd. This force is usually manifested as a drop in pressure in the fluid. Locally, at the surface, the pressure loss stems from the stresses exerted by the fluid on the surface and the equal and opposite stresses exerted by the surface on the fluid. Both shear stresses and normal stresses can contribute their relative importance depends on the shape of the body and the relationship of fluid inertia to the viscous stresses, commonly expressed as a dimensionless number called the Reynolds number (R ), EHp/]1. The character of the flow affects the drag as well as the heat and mass transfer to the surface. Flows around bodies and their associated pressure changes are important. 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

TABLE 5-25 Mass-Transfer Correlations for Drops and Bubbles... 

Fits some, but not all, data. Low mass transfer rate. = mean molecular weight of dispersed phase tf= formation time of drop. k[, i = mean dispersed liquid phase M.T. coefficient kmole/[s - m" (mole fraction)]. 

TABLE 5-26 Mass-Transfer Correlations for Particles, Drops, and Bubbles in Agitated Systems... 

---