Interface area per unit volume

The product of weight specific surface and concentration of the mineral phase characterizes interface area per unit volume of ground water ... 

Systems seek to minimize their total free energy G. Since surfaces and interfaces carry excess free energy, systems will seek to minimize the amount of surface/interface area per unit volume. 

For a semi-batch operation for the first stages, optimal variations of pressure and temperature can be calculated based on the above relationships plus the assumption of phase equilibrium, or on a simple relationship for the mass transfer of each volatile component Y (Eq. (55), with the mass transfer rates per unit volume Ji of component Y , mass transfer coefficient of component i kfi, interface area per unit volume a , and equilibrium concentration [Yj at the interface). 

Fig. 4.29. Changes of the crystallinity c, the interface area per unit volume Oac and the mean thickness of the amorphous layers da during cooling of samples of linear PE left column) and branched PE right column) as derived from SAXS experiments and complementary density measurements [32], [46]...

Equation (A.160), known as Torod s law , is generally valid for arbitrary two-phase systems. Indeed, an asymptotic law S q) 1/q is the characteristic signature of two-phase systems with sharp boundaries. According to Eq. (A.160), the asymptotic behavior depends only on the interface area per unit volume, multiplied by the square of the density difference. 

Tcpo initial interface area per unit volume of composite... 

Aj = interfacial area per unit volume (m2-m 3) Chi = concentration of Component i at the interface (kmol m-3)... 

The surface area per unit volume can be also measured in scattering experiments. For the fully developed system containing the domains of size L and the interface of the intrinsic width c (c -C L), the Porod law [1] predicts the following asymptotic for the structure factor S(k)... 

The high surface-to-volume ratio can also significantly improve both thermal and mass transfer conditions within micro-channels in two ways firstly, the convective heat and mass transfers, which take place at the multi-phase interface, are improved via a significant increase in heat and mass transfer area per unit volume. Secondly, heat and mass transfers within a small volume of fluid take a relatively short time to occur, enabling a thermally and diffusively homogeneous state to be reached quickly. The improvement in heat and mass transfer can certainly influence overall reaction rates and, in some cases, product selectivity. Perhaps one of the more profound effects of the efficient heat and mass transfer property of micro-reactors is the ability to carry potentially explosive or highly exothermic reactions in a safe way, due to the relatively small thermal mass and rapid dissipation of heat. 

Two immiscible fluids, in contact with each other, share a common surface, called the interface. Operations involving transfer of matter or of heat across an interface are very common in chemical industry. In such operations a large interfacial area per unit volume is necessary if the desired transfer is to be obtained rapidly in equipment of finite size. Three common methods of providing a high ratio of interfacial area to volume are now discussed. 

Figure 12.18 illustrates the conditions that occur during the steady operation of a countercurrent gas-liquid absorption tower. It is convenient to express the concentration of the streams in terms of moles of solute gas per mole of inert gas in the gas phase, and as moles of solute gas per mole of solute free liquid in the liquid phase. The actual area of interface between the two phases is not known, and the term a is introduced as the interfacial area per unit volume of the column. On this basis the general equation, 12.13,... 

Inlerfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell are often operated with a flat liquid-liquid interface the area of which can easily he measured. In the single-drop apparatus, a regular sequence of drops uf known diameter is released through the continuous phase. 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 inlerfacial area. u. defined as the inlerfacial conlael area per unit volume of two-phase dispersion. Thus the mass-lransler rale obtainable per unit volume... 

To obtain the boundary condition for A we note that, except for the amount of A which reacts in the film, A is transferred across this boundary and reacts in the bulk of the liquid. For unit area of interface, the volume of this bulk liquid may be written as [(eja) - <5], where eL is the volume of liquid per unit volume of reactor space (i.e. the liquid hold-up), a is the gas-liquid interfacial area per unit volume... 

A reaction occurring in a bulk phase will show an increase in the rate with the area as shown in Fig. 5.3 for a reaction occurring in the film or at the interface, the rate will be linearly dependent on the interfacial area. The interfacial area in a dispersed two-phase liquid-liquid system can be estimated by measuring the rate of a suitable test reaction in a reactor with the known interfacial area (a flat interface, Section 5.3.2.1), and comparing it with the reaction rate in a dispersed system [6, 15]. A convenient reactive system for this purpose is a formate ester and 1-2 M aqueous NaOH. Formate esters are very reactive to hydroxide ion (fo typically around 25 M 1 s 1), so the reaction is complete inside the diffusion film, and the reaction rate is proportional to the interfacial area. A plot of the interfacial area per unit volume against the agitator speed obtained in this way in the author s laboratory for the equipment shown in Fig. 5.12 is shown in Fig. 5.14 [8]. 

The mass transfer resistance at a liquid-vapor interface results from two resistances, the liquid boundary layer and the gas boundary layer. In conditions involving water and sparingly soluble gases, such as occurs here, the liquid-phase resistance is almost always predominant [71]. For this reason, equation (16) involves only k, the mass transfer coefficient across the liquid boundary, and a, which is the gas bubble surface area per unit volume of liquid. Often, as here, those factors cannot be estimated individually, so k is treated as a single parameter. 

Here, II,L is the hydrogen solubility, which is assumed to remain essentially constant along the entire length of the reactor. The quantity r.V is the open volume of the reactor, A is the transverse cross-sectional area for the hydrogen transfer (as shown in Fig. 7-32), k, is the liquid-film mass-transfer coefficient at the gas -liquid interface, and a is the gas-liquid interfacial area per unit volume of the open space in the reactor. In a physical sense, Eq. (7-39) equates the mass transfer from the gas into the liquid phase with the mass transfer at the surface of the catalyst tube. The constant C, in Eq. (7-39) is obtained, by using the condition (7-40), as... 

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