Interphase transport in two-phase systems

In general, the interfacial compositions in the two phases are related to each other by equilibrium criteria 

At high mass-transfer rates and with a contaminated interface, interfacial resistance is possible (see Sherwood et at. (1975)). 

The flux of species A in both gtis and liquid phases can be expressed by either 

The strategy is to define the overall mass-transfer coefficient K with respect to a single phase, either gas or liquid, and known huUc concentrations  

Here is a hypothetical gas-phase mole fraction which is in equiUhrium with xaw thus is known. Similarly, x is a 

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The feed and the product phases here are miscible, unlike conventional interphase transport in two-phase systems (liquid-liquid, gas-liquid, etc.), which are immiscible. 

A few distinguishing features of transport of any species through a membrane with respect to interphase transport in two-phase systems are as follows. 

Interphase transport In two-phase systems with phase barrier membranes... 

The effect of physical processes on reactor performance is more complex than for two-phase systems because both gas-liquid and liquid-solid interphase transport effects may be coupled with the intrinsic rate. The most common types of three-phase reactors are the slurry and trickle-bed reactors. These have found wide applications in the petroleum industry. A slurry reactor is a multi-phase flow reactor in which the reactant gas is bubbled through a solution containing solid catalyst particles. The reactor may operate continuously as a steady flow system with respect to both gas and liquid phases. Alternatively, a fixed charge of liquid is initially added to the stirred vessel, and the gas is continuously added such that the reactor is batch with respect to the liquid phase. This method is used in some hydrogenation reactions such as hydrogenation of oils in a slurry of nickel catalyst particles. Figure 4-15 shows a slurry-type reactor used for polymerization of ethylene in a sluiTy of solid catalyst particles in a solvent of cyclohexane. 

Let us consider a two-phase system including a surface of discontinuity (phase interface). Let X and y represent the two phases. For example, y may refer to the gas phase and x to the liquid phase in a two-phase system. Let the number of components in each phase be n. Let I represent the phase interface and the unit normal directed from phase x to y. The system considered is shown pictorially in Figure 1.1. Our immediate task is to develop the balance relations describing the interphase transport processes taking place is this system. 

Consider transport across the phase boundary shown in Figure 11.3. We shall denote the two bulk phases by L and V and the interface by I. Though the analysis below is developed for liquid-vapor interphase transport the formalism is generally valid for all two-phase systems. Therefore, what follows applies equally to distillation, stripping, and absorption operations. With a few modifications (to be described later), the analysis below may be used in the determination of rates of condensation, evaporation, vaporization, and boiling. 

The potential advantages associated with an electrosynthesis include high material utilization and significantly less energy requirement, ease of control of the reaction, less hazardous process, and the ability to perform wide range of oxidation and reduction reactions. Therefore, many electrosynthetic reactions have been reported so far [1]. However, only a few have been employed industrially. The conunercializa-tion of electrosynthetic processes has been restricted by the limited solubility of substrates and products in conventimial electrolytic solutions, the poor interphase mass transport characteristics associated with two phase system in which the reaction occurs at solid (electrode)-liquid (electrolyte) interfaces, the low selectivity for desired reaction products, and the complex processing schemes often used to recover products. 

The following is a partial list of two-phase systems encountered in separation processes involving interphase transport gas-liquid (alternatively vapor-liquid), liquid-liquid, solid-liquid, Uquid-ion exchange resin, solid-supercritical fluid, liquid-supercritical fluid, etc. The first four systems are used much more frequently. Note that the two phases in each system are immiscible. 

Here, is a hypothetical concentration of i in the phase k which would be in equilibrium with the concentration of species i in the other phase of the interphase transport system (see equation (3.4.6)) a is the interfacial area of transport per unit control/system volume. In a two-phase system, where fc = 1,2, the equation for C,i will have a sign for this term which will he opposite to that in the equation for C,2 since species 1 comes into one phase while it goes out of the other phase. 

Interphase mass transport also represents a possible input to or output from the system. In Fig. 1.13., transfer of a soluble component takes place across the interface which separates the two phases. Shown here is the transfer from phase G to phase L, where the separate phases may be gas, liquid or solid. 

Multiphase system — An inhomogeneous system consists of two or more phases of one or more substances. In electrochemistry, where all processes occur at the interface thus all measurement systems must contain at least two - phases. In common understanding so-called multi-phase systems contain more than two phases. Good examples of such systems are -> electrode contacting a solid phase (immobilized at the electrode electroactive material or heterogeneous -> amalgams) and electrolyte solution, and an electrode that remains in contact with two immiscible liquids [i]. All phenomena appearing in such multi-phase systems are usually more complicated and additional effects as - interphase formation and -> mass transport often combined with - ion transfer must be taken into account [ii]. 

In the K-L model, reaction occurs within the bed s phases, and material is continuously transferred between the phases. Two limiting situations thus arise. In one, the interphase transport is relatively fast and transport equilibrium is maintained, causing the system performance to be controlled by the rate of reaction. In the other, the reaction rate is relatively fast and the performance is controlled by interphase transport. It will be shown that the ammonia oxidation example used above is essentially a reaction-limited system. 

It should be pointed out that there are many one-phase open systems in which the composition is changing due to irreversible chemical reactions. Two or more-phase open systems are also present if the irreversible interphase transport of matter takes place in the closed system. In chemistry, the independent variables of T and P are mostly used. Consequently, the chemical potential is generally expressed as the partial molar... 

This discussion has brought attention to the potential presence of two classes of interphase transport conditions in solid state systems. Let us examine these for a moment from the perspective of forming solid phases under model conditions. 

A membrane can be defined as an interphase between two adjacent phases acting as a selective barrier, regulating the transport of substances between the two compartments ([1], p. 2217). Monhrane technologies are widely recognized as advanced separation/concentration processes, which are ideally placed to aid process inten-siflcation [2], thanks to the possibility of exploiting the synergy between different manbrane operations in an integrated system [3]. Membrane processes are now... 

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