Mass transfer droplet

If condensation requires gas stream cooling of more than 40—50°C, the rate of heat transfer may appreciably exceed the rate of mass transfer and a condensate fog may form. Fog seldom occurs in direct-contact condensers because of the close proximity of the bulk of the gas to the cold-Hquid droplets. When fog formation is unavoidable, it may be removed with a high efficiency mist collector designed for 0.5—5-p.m droplets. Collectors using Brownian diffusion are usually quite economical. If atmospheric condensation and a visible plume are to be avoided, the condenser must cool the gas sufftciendy to preclude further condensation in the atmosphere. 

Convection heat transfer is dependent largely on the relative velocity between the warm gas and the drying surface. Interest in pulse combustion heat sources anticipates that high frequency reversals of gas flow direction relative to wet material in dispersed-particle dryers can maintain higher gas velocities around the particles for longer periods than possible ia simple cocurrent dryers. This technique is thus expected to enhance heat- and mass-transfer performance. This is apart from the concept that mechanical stresses iaduced ia material by rapid directional reversals of gas flow promote particle deagglomeration, dispersion, and Hquid stream breakup iato fine droplets. Commercial appHcations are needed to confirm the economic value of pulse combustion for drying. 

Flow Reactors Fast reactions and those in the gas phase are generally done in tubular flow reaclors, just as they are often done on the commercial scale. Some heterogeneous reactors are shown in Fig. 23-29 the item in Fig. 23-29g is suited to liquid/liquid as well as gas/liquid. Stirred tanks, bubble and packed towers, and other commercial types are also used. The operadon of such units can sometimes be predicted from independent data of chemical and mass transfer rates, correlations of interfacial areas, droplet sizes, and other data. 

Spray Dryers A spray diyer consists of a large cyhndrical and usu ly vertical chamber into which material to be dried is sprayed in the form of small droplets and into which is fed a large volume of hot gas sufficient to supply the heat necessary to complete evaporation of the liquid. Heat transfer and mass transfer are accomphshed by direct contact of the hot gas with the dispersed droplets. After completion of diying, the cooled gas and solids are separated. This may be accomplished partially at the bottom of the diying chamber by classification and separation of the coarse dried particles. Fine particles are separated from the gas in external cyclones or bag collectors. When only the coarse-particle fraction is desired for fini ed product, fines may be recovered in wet scrubbers the scrubber liquid is concentrated and returned as feed to the diyer. Horizontal spray chambers are manufactured with a longitudinal screw conveyor in the bottom of the diying chamber for continuous removal of settled coarse particles. 

Another type of distributor, not shown in Fig. 14-64, is the spray nozzle. It is usually not recommended for hquid distribution for two reasons. First, except for small columns, it is difficult to obtain a uniform spray pattern for the packing. The fuU-cone nozzle type is usually used, with the need for a bank of nozzles in larger columns. When there is more than one nozzle, the problem of overlap or underlap arises. A second reason for not using spray nozzles is their tendency toward entrainment by the gas, especially the smaller droplets in the spray size distribution. However, some mass transfer in the spray can be expected. 

Commonly, the most important feature of a nozzle is the size of droplet it produces. Since the heat or mass transfer that a given dispersion can produce is often proportional to (1/D ) , fine drops are usually favored. On the other extreme, drops that are too fine will not settle, and a concern is the amount of liquid that will be entrained from a given spray operation. For example, if sprays are used to contact atmospheric air flowing at 1.5 m/s, drops smaller than 350 [Lm [terminal velocity = 1.5 m/s (4.92 ft/s)] will be entrained. Even for the relative coarse spray of the hoUow-cone nozzle shown in Fig. 14-88, 7.5 percent of the total hquid mass will be entrained. 

Prediction methods attempt to quantify the resistances to mass transfer in terms of the raffinate rate R and the extract rate E, per tower cross-sectional area Af, and the mass-transfer coefficient in the raffinate phase and the extract phase times the interfacial (droplet) mass-transfer area per volume of tower a [Eqs. (15-32) and (15-33)]. 

The mass-transfer coefficients depend on complex functions of diffii-sivity, viscosity, density, interfacial tension, and turbulence. Similarly, the mass-transfer area of the droplets depends on complex functions of viscosity, interfacial tension, density difference, extractor geometry, agitation intensity, agitator design, flow rates, and interfacial rag deposits. Only limited success has been achieved in correlating extractor performance with these basic principles. The lumped parameter deals directly with the ultimate design criterion, which is the height of an extraction tower. 

Coalescence The coalescence of droplets can occur whenever two or more droplets collide and remain in contact long enough for the continuous-phase film to become so thin that a hole develops and allows the liquid to become one body. A clean system with a high interfacial tension will generally coalesce quite rapidly. Particulates and polymeric films tend to accumulate at droplet surfaces and reduce the rate of coalescence. This can lead to the ouildup of a rag layer at the liquid-hquid interface in an extractor. Rapid drop breakup and rapid coalescence can significantly enhance the rate of mass transfer between phases. 

An impeller with a high fluid head is one with high peripheral velocity and discharge velocity. Such impellers are useful for (I) rapid reduction of concentration differences in the impeller discharge stream (rapid mixing), (2) production of large interfacial area and small droplets in gas-hquid and immiscible-liquid systems, (3) sohds deagglomeration, and (4) promotion of mass transfer between phases. 

The latter have obseivations during mass transfer. Coalescence Rates The droplets coalesce and redisperse at rates... 

Product diameter is small and bulk density is low in most cases, except prilling. Feed hquids must be pumpable and capable of atomization or dispersion. Attrition is usually high, requiring fines recycle or recoveiy. Given the importance of the droplet-size distribution, nozzle design and an understanding of the fluid mechanics of drop formation are critical. In addition, heat and mass-transfer rates during... 

When a liquid is dispersed into droplets the surface area is increased, which enhances the rates of heat and mass transfer. For a particular liquid dispersed at constant concentration in air the MIE varies with approximately the cube of surface average droplet diameter, hence the MIE decreases by a factor of about 8 when the surface average diameter D is halved (A-5-1.4.4). Ease of ignition is greatly enhanced for finely divided mists with D less than about 20 /rm, whose MIE approaches that of the vapor. Below 10 /rm a high flash point liquid mist (tetrahydronaphthalene) was found to behave like vapor while above about 40/rm the droplets tended to burn individually [ 142]. Since liquid mists must partially evaporate and mix with air before they ignite, the ease with which a liquid evaporates also affects MIE (Eigure 5-1.4.4). 

Semidry Scrubbers The advantage of semidry scrubbers is in that they remove contaminants by way of a solid waste that is easier to dispose of (less expensive). Initially, the scrubbing medium is wet (such as a lime or soda ash slurry). Then a spray dryer is used to atomize the slurry into the gas which evaporates the water in the droplets. As this takes place, the acid in the gas neutralizes the alkali material and forms a fine white solid. Most of the white solids are removed at the bottom of the scrubber while some are carried into the gas stream and have to be removed by a filter or electrostatic precipitator (discussed later). Although semidry systems cost 5-15% more than wet systems, when combined with a fabric filter, they can achieve 90-95% efficiencies. Dry scrubbers are sometimes used in a very similar fashion, but without the help of gas-liquid-solid mass transfer, these systems use much higher amounts of the solid alkali materials. 

Water-cooling in towers operates on the evaporative principles, which are a combination of several heat/mass transfer processes. The most important of these is the transfer of liquid into a vapor/air mixture, as, for example, the surface area of a droplet of water. Convective transfer occurs as a result of the difference in temperature between the water and the surrounding air. Both these processes take place at the interface of the water surface and the air. Thus it is considered to behave as a film of saturated air at the same temperature as the bulk of the water droplet. 

Experimental observations (S3) indicate that a stagnant cap is formed over the rear of the droplet as surface-active agents are added, and that this cap tends to enlarge with increasing concentrations until the entire droplet is enveloped. Thus, circulation may occur only in the front portion of the bubble. In contrast to this mechanism, Thorsen and Terjesen (T3) and Gamer (Gil) concluded that most of the mass transfer takes place at the rear of the bubble. 

Thus either the penetration theory or the film theory (equation 10.144 or 10.145) respectively can be used to describe the mass transfer process. The error will not exceed some 9 per cent provided that the appropriate equation is used, equation 10.144 for L2 jDt > n and equation 10.145 for L2/Dt < n. Equation 10.145 will frequently apply quite closely in a wetted-wall column or in a packed tower with large packings. Equation 10.144 will apply when one of the phases is dispersed in the form of droplets, as in a spray tower, or in a packed tower with small packing elements. 

So far in this chapter, consideration has been given to transfer taking place in a single direction of a rectangular coordinate system. In many applications of mass transfer, one of the fluids is injected as approximately spherical droplets into a second immiscible fluid, and transfer of the solute occurs as the droplet passes through the continuous medium. 

In a liquid-liquid extraction unit, spherical drops of solvent of uniform size are continuously fed to a continuous phase of lower density which is flowing vertically upwards, and hence countercurrently with respect to the droplets. The resistance to mass transfer may be regarded as lying wholly within the drops and the penetration theory may be applied. The upward velocity of the liquid, which may be taken as uniform over the cross-section of the vessel, is one-half of the terminal falling velocity of the droplets in the still liquid. 

Occasionally, two droplets coalesce on formation giving rise to a single drop of twice the volume. What is the ratio of the mass transfer rate (kmol/s) to a coalesced drop to that of a single droplet when each has fallen the same distance, that is to the bottom of the equipment ... 

In a drop extractor, liquid droplets of approximate uniform size and spherical shape are formed at a series of nozzles and rise eountercurrently through the continuous phase which is flowing downwards at a velocity equal to one half of the terminal rising velocity of the droplets. The flowrates of both phases are then increased by 25 per cent. Because of the greater shear rate at the nozzles, the mean diameter of the droplets is however only 90 per cent of the original value. By what factor will the overall mass transfer rate change ... 

It may be assumed that the penetration model may be used to represent the mass transfer process. The depth of penetration is small compared with the radius of the droplets and the effects of surface curvature may he neglected. From the penetration theory, the concentration C, at a depth y below the surface at time r is given by ... 

Spherical droplet in a liquid, mass transfer 617 Spiral heat exchangers 550 Spray dryers 393... 

The parameter p (= 7(5 ) in gas-liquid sy.stems plays the same role as V/Aex in catalytic reactions. This parameter amounts to 10-40 for a gas and liquid in film contact, and increases to lO -lO" for gas bubbles dispersed in a liquid. If the Hatta number (see section 5.4.3) is low (below I) this indicates a slow reaction, and high values of p (e.g. bubble columns) should be chosen. For instantaneous reactions Ha > 100, enhancement factor E = 10-50) a low p should be selected with a high degree of gas-phase turbulence. The sulphonation of aromatics with gaseous SO3 is an instantaneous reaction and is controlled by gas-phase mass transfer. In commercial thin-film sulphonators, the liquid reactant flows down as a thin film (low p) in contact with a highly turbulent gas stream (high ka). A thin-film reactor was chosen instead of a liquid droplet system due to the desire to remove heat generated in the liquid phase as a result of the exothermic reaction. Similar considerations are valid for liquid-liquid systems. Sometimes, practical considerations prevail over the decisions dictated from a transport-reaction analysis. Corrosive liquids should always be in the dispersed phase to reduce contact with the reactor walls. Hazardous liquids are usually dispensed to reduce their hold-up, i.e. their inventory inside the reactor. 

The archetypal, stagewise extraction device is the mixer-settler. This consists essentially of a well-mixed agitated vessel, in which the two liquid phases are mixed and brought into intimate contact to form a two phase dispersion, which then flows into the settler for the mechanical separation of the two liquid phases by continuous decantation. The settler, in its most basic form, consists of a large empty tank, provided with weirs to allow the separated phases to discharge. The dispersion entering the settler from the mixer forms an emulsion band, from which the dispersed phase droplets coalesce into the two separate liquid phases. The mixer must adequately disperse the two phases, and the hydrodynamic conditions within the mixer are usually such that a close approach to equilibrium is obtained within the mixer. The settler therefore contributes little mass transfer function to the overall extraction device. 

Stirred suspensions of droplets have proven to be a popular approach for studying the kinetics of liquid-liquid reactions [54-57]. The basic principle is that one liquid phase takes the form of droplets in the other phase when two immiscible liquids are dispersed. The droplet size can be controlled by changing the agitator speed. For droplets with a diameter < 0.15 cm the inside of the drop is essentially stagnant [54], so that mass transfer to the inside surface of the droplet occurs only by diffusion. In many cases, this technique can lack the necessary control over both the interfacial area and the transport step for determination of fundamental interfacial processes [3], but is still of some value as it reproduces conditions in industrial reactors. 

Mass transfer to an expanding droplet has been considered previously for the DME arrangement [33,74,75] and other growing liquid drop techniques [53,76]. At a simple level,... 

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