Temperature effects mass transfer

Reaction rates typically are strongly affected by temperature (76,77), usually according to the Arrhenius exponential relationship. However, side reactions, catalytic or equiHbrium effects, mass-transfer limitations in heterogeneous (multiphase) reactions, and formation of intermediates may produce unusual behavior (76,77). Proposed or existing reactions should be examined carefully for possible intermediate or side reactions, and the kinetics of these side reactions also should be observed and understood. 

The basic idea is to examine operating parameters to find the optimum combination of them for optimum performance. A short list of the most important might include the following Fj, Cjo, Cj, v, V, T, Tq, u, P, and, of course. For catalytic processes additional variables include D, d, Sg, e, shape, and catalyst chemical properties such as chemical composition, activity, and selectivity. Most catalytic reactors operate with significant mass transfer limitations because one usually wants to raise the temperature until mass transfer becomes noticeable in order to attain the highest rate possible. In all cases one determines the effects of these variables on reactor performance. 

Thus, a low diffusion coefficient for the analyte in the mobile phase increases efficiency with regard to the A term but decreases efficiency with respect to the C , term. On balance, a higher diffusion coefficient is more favourable. Higher column temperatures reduce mass transfer effects because the rate of diffusion of a molecule in the mobile phase increases. 

With the addition of bentonite to a crushed basalt backfill, aqueous diffusion would be the most effective mass transfer process (31). Aagaard and Helgeson (32) state that at temperatures <200°C, aqueous diffusion rates are orders of magnitude greater than rates of silicate hydrolysis even in acid solutions. Therefore, the dissolution rate of backfill phases and the overall mass transfer process could be controlled by reactions at the mineral-fluid interface. As stated earlier, dissolution of basalt phases in the sampling autoclave experiments may also be controlled by interface reactions. 

Ranz and Marshall (13) carefully studied the evaporation of water droplets in still and moving air. They found that the steady-state temperature at the surface of a small evaporating drop was the wet bulb temperature of the surrounding air. Marshall considered the dependence of the effective mass transfer coefficient on air velocity to be determined largely by the boundary layer of less mobile air at the droplet surface, and he reported correlations which show that varied linearly with v1/2. Ranz and Marshall s data clearly show this relation, which we may write as Equation 5. 

The main effects through which work is lost are pressure drops due to fluid flows, heat transfer between fluids with different temperatures, and mass transfer between streams that are not in equilibrium ... 

The effect of product temperature and mass transfer resistance on sublimation rate may be mathematically illustrated by expressing the sublimation rate per vial, dm/dt, in terms of the driving force for transport of water vapor from the ice-vapor interface to the chamber, Pq - Po,... 

In the case of polyester synthesis from divinyl esters, hydrolysis of the vinyl end group partly took place, resulting in the limitation of the polymer growth.201 A mathematical model showing the kinetics of the polymerization predicts the product composition. On the basis of these data, a batch-stirred reactor was designed to minimize temperature and mass-transfer effects.202 The efficient enzymatic production of polyesters was achieved using this reactor poly(l,4-butylene adipate) with Mn 2 x 104 was synthesized in 1 h at 60 °C. 

FIGURE 19,4-5 Effect of temperature on mass transfer rate in uranium extraction from wet process phosphoric acid. Redrawn from dela in Hayworth et al.33 and Hunt et al.38... 

P.P. Lewicki, H. Kowalska, and A. Lenart, Effect of temperature on mass transfer during osmotic dehydration of plant tissue. In Industrial Application of Osmotic Dehydration/ Treatments of Food (M. Dalla Rosa and W.E.L. Spiess, eds.). Forum, Udine, 2000, p. 31. 

The time-dependence of void formation in Inconel, as observed both in thermal-convection and forced-circulation systems, indicates that the attack is initially quite rapid but that, it then decreases until a straight-line relationship exists between depth of void formation and time. This effect can 1)0 explained in terms of the corrosion reactions discussed above. The initial rapid attack found for both types of loops stems from the reaction of cliromium with impurities in the molt [reactions (13-1) and (13-2)] and with the FF4 constituent of the salt [reaction (13-3)] to establish a quasi-etiuilibrium amount of CrF2 in the salt. At this point attack proceeds linearly with time and occurs by a mass-transfer mechanism which, although it arises from a different cause, is similar to the phenomenon of temperature-gradient mass transfer observed in liquid metal corrosion. 

Mass transfer effects may also be minimized by operating the system at lower temperatures since mass transfer involves gaseous diffusion through a boundary layer, which is not an activated process, while the chemical reaction between the gas and the solid generally has a substantial activation energy, operation at progressively lower temperatures will eventually lead to control by chemical kinetics, as shown in Fig. 6.11. 

The effect can be important in mass-transfer problems (see Ref. 57 and citations therein). The Marangoni instability is often associated with a temperature gradient characterized by the Marangoni number Ma ... 

Humidification. For wiater operation, or for special process requirements, humidification maybe required (see Simultaneous HEAT and mass transfer). Humidification can be effected by an air washer which employs direct water sprays (see Evaporation). Regulation is maintained by cycling the water sprays or by temperature control of the air or water. Where a large humidification capacity is required, an ejector which direcdy mixes air and water in a no22le may be employed. Steam may be used to power the no22le. Live low pressure steam can also be released directly into the air stream. Capillary-type humidifiers employ wetted porous media to provide extended air and water contact. Pan-type humidifiers are employed where the required capacity is small. A water filled pan is located on one side of the air duct. The water is heated electrically or by steam. The use of steam, however, necessitates additional boiler feed water treatment and may add odors to the air stream. Direct use of steam for humidification also requires careful attention to indoor air quahty. 

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). 

---