Interfacial areas

The gas-liquid interfacial area per unit volume of gas-liquid mixture, a (L2 L-3 or IT1), calculated by Equation 7.26 from the measured values of the fractional gas holdup and the volume-surface mean bubble diameter dyS, were correlated by the following dimensionless equation  

Values of kL, obtained by dividing kLa by a, were correlated by the following dimensionless equation  

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It is helpful to consider qualitatively the numerical magnitude of the surface tensional stabilization of a particle at a liquid-liquid interface. For simplicity, we will assume 6 = 90°, or that 7sa = 7SB- Also, with respect to the interfacial areas, J sA = SB, since the particle will lie so as to be bisected by the plane of the liquid-liquid interface, and. AB = rcr - The free energy to displace the particle from its stable position will then be just trr 7AB- For a particle of l-mm radius, this would amount to about 1 erg, for Tab = 40 ergs/cm. This corresponds roughly to a restoring force of 10 dyn, since this work must be expended in moving the particle out of the interface, and this amounts to a displacement equal to the radius of the particle. 

It is quite clear, first of all, that since emulsions present a large interfacial area, any reduction in interfacial tension must reduce the driving force toward coalescence and should promote stability. We have here, then, a simple thermodynamic basis for the role of emulsifying agents. Harkins [17] mentions, as an example, the case of the system paraffin oil-water. With pure liquids, the inter-facial tension was 41 dyn/cm, and this was reduced to 31 dyn/cm on making the aqueous phase 0.00 IM in oleic acid, under which conditions a reasonably stable emulsion could be formed. On neutralization by 0.001 M sodium hydroxide, the interfacial tension fell to 7.2 dyn/cm, and if also made O.OOIM in sodium chloride, it became less than 0.01 dyn/cm. With olive oil in place of the paraffin oil, the final interfacial tension was 0.002 dyn/cm. These last systems emulsified spontaneously—that is, on combining the oil and water phases, no agitation was needed for emulsification to occur. 

Lujuid-Pha.se Transfer. It is difficult to measure transfer coefficients separately from the effective interfacial area thus data is usually correlated in a lumped form, eg, as k a or as These parameters are measured for the Hquid film by absorption or desorption of sparingly soluble gases such as O2 or CO2 in water. The Hquid film resistance is completely controlling in such cases, and kjji may be estimated as since x (Fig. 4). This... 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

Aerators designed to faciHtate the transfer of oxygen from air to water increase interfacial area by producing Hquid turbulence and circulation. There are four basic types of aerators summarized in Table 1. 

In the simplest case, the feed solution consists of a solvent A containing a consolute component C, which is brought into contact with a second solvent B. Eor efficient contact there must be a large interfacial area across which component C can transfer until equiHbrium is reached or closely approached. On the laboratory scale this can be achieved in a few minutes simply by hand agitation of the two Hquid phases in a stoppered flask or separatory fuimel. Under continuous flow conditions it is usually necessary to use mechanical agitation to promote coalescence of the phases. After sufficient time and agitation, the system approaches equiHbrium which can be expressed in terms of the extraction factor S for component C ... 

Many industrial processes involve a chemical reaction between two Hquid phases, for example nitration (qv), sulfonation (see Sulfonation and sulfation), alkylation (qv), and saponification. These processes are not always considered to be extractions because the main objective is a new chemical product, rather than separation (30). However these processes have many features in common with extraction, for example the need to maintain a high interfacial area with the aid of agitation and the importance of efficient phase separation after the reaction is completed. 

The rate of mass transfer (qv) depends on the interfacial contact area and on the rate of mass transfer per unit interfacial area, ie, the mass flux. The mass flux very close to the Hquid—Hquid interface is determined by molecular diffusion in accordance with Pick s first law ... 

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... 

Membrane Extraction. An extraction technique which uses a thin Hquid membrane or film has been introduced (80,81). The principal advantages of Hquid-membrane extraction are that the inventory of solvent and extractant is extremely small and the specific interfacial area can be increased without the problems which accompany fine drop dispersions (see Membrane technology). 

The pulsed-plate column is typically fitted with hori2ontal perforated plates or sieve plates which occupy the entire cross section of the column. The total free area of the plate is about 20—25%. The columns ate generally operated at frequencies of 1.5 to 4 H2 with ampHtudes 0.63 to 2.5 cm. The energy dissipated by the pulsations increases both the turbulence and the interfacial areas and greatly improves the mass-transfer efficiency compared to that of an unpulsed column. Pulsed-plate columns in diameters of up to 1.0 m or mote ate widely used in the nuclear industry (139,140). 

Agitation of the Fluid. Agitation of the solvent increases local turbulence and the rate of transfer of material from the surface of the particles to the bulk of the solution. Agitation should prevent settling of the soHds, to enable most effective use of the interfacial area. 

The chemical composition, physical stmcture, and key physical properties of a foam, namely its stabiHty and theology, are all closely interrelated. Since there is a large interfacial area of contact between Hquid and vapor inside a foam, the physical chemistry of Hquid—vapor interfaces and their modification by surface-active molecules plays a primary role underlying these interrelationships. Thus the behavior of individual surface-active molecules in solution and near a vapor interface and their influence on interfacial forces is considered here first. 

Direct photography of drops in done with the use of fiber optic probes using either direct or reflected light. StiU or video pictures can be obtained for detailed analysis. The light transmittance method uses three components a light source to provide a uniform collimated beam, a sensitive light detector, and an electronic circuit to measure the amplified output of the detector. The ratio of incident light intensity to transmitted intensity is related to interfacial area per unit volume. 

R is rate of reaction per unit area, a is interfacial area per unit volume, S is solubiHty of solute in continuous phase, D is diffusivity of solute, k is rate constant, kj is mass-transfer coefficient, is concentration of reactive species, and Z is stoichiometric coefficient. When Dk is considerably greater (10 times) than Ra = aS Dk. 

The integral values of effective interfacial area can thus be obtained by measuring the reaction (extraction) rate and using physico-chemical properties of the reactants. A reaction satisfying the above conditions consists of hydrolysis of hexyl formate (11) ... 

At a given gas sparging rate, interfacial area a is constant at low mixer speeds. When mixer speed is increased above a critical speed a starts increasing and varies linearly with Ai For Rushton turbines this critical speed, as deterrnined in an sodium sulfate system, is given by the following ... 

The interfacial area in the region with agitation effect N > and Hquid height, F/, is given by... 

Static mixing of gas—Hquid systems can provide good interphase contacting for mass transfer and heat transfer. Specific interfacial area for the SMV (Koch/Sulzer) mixer is related to gas velocity and gas holdup ( ) by the following ... 

Most ionic nitrations are performed at 0—120°C. For nitrations of most aromatics, there are two Hquid phases an organic and an acid phase. Sufficient pressure, usually slightly above atmospheric, is provided to maintain the Hquid phases. A large interfacial area between the two phases is needed to expedite transfer of the reactants to the interface and of the products from the interface. The site of the main reactions is often at or close to the interface (2). To provide large interfacial areas, a mechanical agitator is frequently used. 

Rates of nitration determined over a range of temperatures in two-phase dispersions have been used to calculate energies of activation from 59—75 kj/mol (14—18 kcal/mol). Such energies of activation must be considered as only apparent, since the tme kinetic rate constants, NO2 concentrations, and interfacial area all change as temperature is increased. 

Increased agitation of a given acid—hydrocarbon dispersion results in an increase in interfacial areas owing to a decrease in the average diameter of the dispersed droplets. In addition, the diameters of the droplets also decrease to relatively low and nearly constant values as the volume % acid in the dispersions approaches either 0 or 100%. As the droplets decrease in si2e, the ease of separation of the two phases, following completion of nitration, also decreases. 

Reactions 8 and 9 are important steps for the Hquid-phase nitration of paraffins. The nitric oxide which is produced is oxidized with nitric acid to reform nitrogen dioxide, which continues the reaction. The process is compHcated by the presence of two Hquid phases consequentiy, the nitrogen oxides must transfer from one phase to another. A large interfacial area is needed between the two phases. 

Because the highest possible interfacial area is desired for the heterogeneous reaction mixture, advances have also been made in the techniques used for mixing the two reaction phases. Several jet impingement reactors have been developed that are especially suited for nitration reactions (14). The process boosts reaction rates and yields. It also reduces the formation of by-products such as mono-, di-, and trinitrophenol by 50%. First Chemical (Pascagoula, Mississippi) uses this process at its plant. Another technique is to atomize the reactant layers by pressure injection through an orifice nozzle into a reaction chamber (15). The technique uses pressures of typically 0.21—0.93 MPa (30—135 psi) and consistendy produces droplets less than 1 p.m in size. The process is economical to build and operate, is safe, and leads to a substantially pure product. 

Manufacture and Processing. Mononitrotoluenes are produced by the nitration of toluene in a manner similar to that described for nitrobenzene. The presence of the methyl group on the aromatic ring faciUtates the nitration of toluene, as compared to that of benzene, and increases the ease of oxidation which results in undesirable by-products. Thus the nitration of toluene generally is carried out at lower temperatures than the nitration of benzene to minimize oxidative side reactions. Because toluene nitrates at a faster rate than benzene, the milder conditions also reduce the formation of dinitrotoluenes. Toluene is less soluble than benzene in the acid phase, thus vigorous agitation of the reaction mixture is necessary to maximize the interfacial area of the two phases and the mass transfer of the reactants. The rate of a typical industrial nitration can be modeled in terms of a fast reaction taking place in a zone in the aqueous phase adjacent to the interface where the reaction is diffusion controlled. 

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