Interfaces interfacial area

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. 

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 ... 

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. 

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. 

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. 

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. 

Under equiUbrium or near-equiUbrium conditions, the distribution of volatile species between gas and water phases can be described in terms of Henry s law. The rate of transfer of a compound across the water-gas phase boundary can be characterized by a mass-transfer coefficient and the activity gradient at the air—water interface. In addition, these substance-specific coefficients depend on the turbulence, interfacial area, and other conditions of the aquatic systems. They may be related to the exchange constant of oxygen as a reference substance for a system-independent parameter reaeration coefficients are often known for individual rivers and lakes. 

Pi =f Ci) or Pi = HCi, equilibrium relation at the interface a = interfacial area/iinit volume Zg, Z-L = film thicknesses The steady rates of solute transfer are... 

The total area of b.c.c.-f.c.c. interface is obviously related to the number of b.c.c. nuclei. As Fig. 8.2 shows, fewer nuclei mean a smaller interfacial area and a smaller volume transforming per second. Indeed, if there are no nuclei at all, then the rate of transformation is obviously zero. The overall rate of transformation is thus given approximately by... 

Horizontal vessels as cylinders are generally more suitable for diameters up to about 8 feet than other shapes, or vertical, due in part to the increased interfacial area for interface formation. For a horizontal drum (See Figure 4-12) ... 

Consequently, interpenetrating phase-separated D/A network composites, i.e. bulk heterojunction , would appear to be ideal photovoltaic materials [5]. By controlling the morphology of the phase separation into an interpenetrating network, one can achieve a high interfacial area within a bulk material. Since any point in the composite is within a few nanometers of a D/A interface, such a composite is a bulk D/A heterojunction material. If the network in a device is bicontinuous, as shown in Figure 15-26, the collection efficiency can be equally efficient. 

CAL Oxygen concentration in equilibrium with liquid phase at the interface, kmol/m3 CAL Oxygen concentration in the bulk of liquid, kmol/m3 a Interfacial area in surface area of bubbles per unit volume of broth, m2/m3 PQ, Oxygen partial pressure at the interface, atm H Henry s law constant, atm... 

It is seen from these examples that, in appropriate systems, it is possible to introduce product into the reactant in such a manner that an effective reaction interface is established before the reactant has been heated to the decomposition temperature. Accordingly, the induction period is removed and the acceleratory process may be less pronounced or eliminated altogether. Artificial nucleation results in changes in reaction geometry with consequent variation in the a—time curve shape and the maximum value of da/dt but does not enhance the rate of interface advance. We have found no studies in which increases in reaction rates were quantitatively correlated with the increased interfacial area and/or density of nucleation which resulted from the reactant pretreatment. 

The interfacial area AtV usually excludes the contact area between the vapor space and the liquid at the top of the reactor. The justification for this is that most gas-liquid reactors have gas bubbles as a dispersed phase. This gives a much larger interfacial area than the nominal contact area at the top of the reactor. There are exceptions—e.g., polyester reactors where by-product water is removed only through the nominal interface at the top of the reactor— but these are old and inefficient designs. This nominal area scales as while the contact area with a dispersed phase can scale as S. 

Mass Transfer Rates. Mass transfer occurs across the interface. The rate of mass transfer is proportional to the interfacial area and the concentration driving force. Suppose component A is being transferred from the gas to the liquid. The concentration of A in the gas phase is Ug and the concentration of A in the liquid phase is u . Both concentrations have units of moles per cubic meter however they are not directly comparable because they are in different phases. This fact makes mass transfer more difficult than heat transfer since the temperature is the temperature regardless of what phase it is measured in, and the driving force for heat transfer across an interface is just the temperature difference Tg—Ti. For mass transfer, the driving force is not Ug—ai. Instead, one of the concentrations must be converted to its equivalent value in the other phase. 

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