Interface equilibrium relations

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... 

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

In this approach, it is assumed that turbulence dies out at the interface and that a laminar layer exists in each of the two fluids. Outside the laminar layer, turbulent eddies supplement the action caused by the random movement of the molecules, and the resistance to transfer becomes progressively smaller. For equimolecular counterdiffusion the concentration gradient is therefore linear close to the interface, and gradually becomes less at greater distances as shown in Figure 10.5 by the full lines ABC and DEF. The basis of the theory is the assumption that the zones in which the resistance to transfer lies can be replaced by two hypothetical layers, one on each side of the interface, in which the transfer is entirely by molecular diffusion. The concentration gradient is therefore linear in each of these layers and zero outside. The broken lines AGC and DHF indicate the hypothetical concentration distributions, and the thicknesses of the two films arc L and L2. Equilibrium is assumed to exist at the interface and therefore the relative positions of the points C and D are determined by the equilibrium relation between the phases. In Figure 10.5, the scales are not necessarily the same on the two sides of the interface. 

There is equilibrium at the interface, which is another way of assuming that there is no resistance to mass transfer at the interface. The equilibrium relation may... 

It can be assumed for almost all practical cases that equilibrium exists at the interface between the two phases. The concentrations of solute A at the interface, C A G and CAL, are related by the equilibrium relation of Eq. (5) and which, for gases in general and hydrogen in particular, is often described using simplified Henry s law applied at the interface (Eq. (6)). 

It is important to stress that, when measuring the simple concentration ratios of mean abundances in the solid and liquid phases formed at interface equilibrium (as is typically done in comparative studies), the resulting (apparent) partition coefficient is related to partition coefficient K valid at the interface, by... 

The flux rate will be constant with z, unless we are very close to equilibrium or there are sources or sinks of hydroxylbenzene in the container. At the interface, equilibrium is assumed between the air and water phases. This equilibrium may only exist for a thickness of a few molecules, but is assumed to occur quickly compared with the time scale of interest. The concentrations at this air-water interface are related by the following equation ... 

There is an eqnilibrinm constant for the dissolution of hydrogen in each solid phase, Ka and Kb, respectively. Similarly, the activity of hydrogen at the interface, is related to the concentration at the interface and equilibrium constants, Cj = Kaci and c = Kbu, so that Eq. (4.88) becomes... 

Upon introducing the equilibrium relation at the interface, the relation between the various mass-transfer coefficients is... 

In the second part, using the equilibrium relations for the various components present in the water and oil phases and on the interface and coupling them with mass balances, one could calculate the thicknesses of the water and oil layers as functions of the component concentrations. It was shown that the deviation from the ideal dilution law can be accounted for by the partition of the components between phases. A comparison between the calculated and experimental results was made. 

We shall adopt a simple model of the interface itself a surface that offers no resistance to mass transfer and where equilibrium prevails. Thus, the usual equations of phase equilibrium relate the mole fractions y and x j. 

The vapor interface composition is computed directly from the equilibrium relations above as... 

To complete the model of interphase transport, we must say something about the interface. It is usual to assume that equilibrium prevails at the interface, and relate the mole fraction y/ and x/ by... 

Evaluating the equilibrium relations requires us to first compute the vapor pressures and activity coefficients. Note that these thermodynamic properties are computed using the temperature and composition at the interface. Expressions for the activity coefficients are given in Table D.2. Substituting the numerical values of into those equations gives the following results ... 

To evaluate the equilibrium relations requires the computation of the K values. The pure component vapor pressures may be estimated from the Antoine equation. At the interface temperature the vapor pressures are... 

Eliminating the unknown interface quantities using the equilibrium relation and the rates of movement of the two media relative to the interface, the component mass jump condition can be used to calculate the position of the interphase. 

To derive a relation for the overall mass transfer coefficient we consider a gas-liquid interface, as sketched in Fig 5.15. Formulate the expressions for the fluxes at both sides of the interface and relate the two unknown interfacial concentrations to each other by use of an equilibrium relation like Henrys law. The flux relations can then be combined in order to eliminate the interfacial concentrations obtaining an overall driving force. 

The property values on the membrane surface and in the film at the interface are considered at equilibrium, related to each other by equilibrium distribution coefficients, assumed equal on both sides of the membrane ... 

Physical chemists distinguish between adsorption and absorption. Adsorption is a surface phenomenon. Consider a solid or liquid phase (the adsorbent), in contact with another, fluid, phase. Molecules present in the fluid phase may now adsorb onto the interface between the phases, i.e., form a (usually monomolecular) layer of adsorbate. This is discussed in more detail in Section 10.2. The amount adsorbed is governed by the activity of the adsorbate. For any combination of adsorbate, adsorbent, and temperature, an adsorption isotherm can be determined, i.e., a curve that gives the equilibrium relation between the amount adsorbed per unit surface area, and the activity of the adsorbate. Powdered solid materials in contact... 

Fig. 17. PPO4 versus pS for upper 8 cm at FOAM, NWC, and DEEP where pS was detectable. The line drawn is the equilibrium relation between vivianite (Fe3(P04)2 8H2O) and mackinawite (FeS). , FOAM O. NWC A, DEEP. All seasons plotted. The formation of sulfides is generally favored, but regions exist near the sediment-water interface where coexistence of phases or phosphate dominance are possible.

Rose [47,48] points out that when Eq. 14.78 is used in conjunction with an equation relating the heat transfer rate (i.e., condensation rate) to the temperature difference across the condensate film (an appropriate expression for a single tube might be Eq. 14.56), together with the interface equilibrium condition ... 

---