Two-film

The efficiency of gas turbines is limited by the maximum allowable turbine inlet temperature (TIT). The TIT may be increased by cooling of the blades and vanes of the high pressure turbine. Cooling channels can be casted into the components or may be drilled afterwards. Non-conventional processes like EDM, ECD or Laser are used for drilling. Radiographic examination of the drilled components is part of the inspection procedure. Traditional X-Ray film technique has been used. The consumable costs, the waste disposal and the limited capacity of the two film units lead to the decision to investigate the alternative of Real-Time X-Ray. 

Twin-fluid atomizer Twisted pair cable Twitchell splitting Twitchell s reagents Two-film theory... 

Fig. 3. The two-film concept and x are the concentrations in the bulk of the phases jy and x are the actual interfacial concentrations at equiHbrium ...

Fig. 2. Schematic representation for the two-film theory of gas transfer = partial pressure of gas Pj = partial pressure of the gas at the interface Cj = concentration of gas at time t, Cj = initial concentration of gas at the interface Cg = initial concentration of gas at t = 0 and S = gas saturation.

On tbe basis of tbe two-film model for mass transfer, and relating all efficiencies to gas-pbase concentrations (for convenience only a similar development can be made on tbe basis of bquid concentrations), point efficiency can be expressed in terms of transfer units ... 

For example, XRF was used successfully ro analyze two triple-layer films of Cr, Cu, and FeNi deposired on Si substrates. The two films, Tl and T2, have... 

A typical structure capable of being analyzed is shown in Figure 3, consisting of a substrate, two films (thicknesses q and t ), two roughness regions (one is an interfacial region of thickness and the other is a surfiice region of thickness One of... 

The dry adhesive films on the two substrates to be joined must be placed in contact to develop adequate autoadhesion, i.e. diffusion of polymer rubber chains must be achieved across the interface between the two films to produce intimate adhesion at molecular level. The application of pressure and/or temperature for a given time allows the desired level of intimate contact (coalescence) between the two adhesive film surfaces. Obviously, the rheological and mechanical properties of the rubber adhesives will determine the degree of intimacy at the interface. These properties can be optimized by selecting the adequate rubber grade, the nature and amount of tackifier and the amount of filler, among other factors. 

Overall coefficients cannot be predicted directly from the physical properties and flow rates of a system but must be derived from the individual film coefficients. It is important therefore to be able to relate overall and film coefficients. This can be done if it is realized that the coefficients are in effect conductances. The diffusional resistance of the two films are equal to the reciprocals of the film coefficients, and... 

F = Function of the molecular volume of the solute. Correlations for this parameter are given in Figure 7 as a function of the parameter (j), which is an empirical constant that depends on the solvent characteristics. As points of reference for water, (j) = 1.0 for methanol, (j) = 0.82 and for benzene, (j) = 0.70. The two-film theory is convenient for describing gas-liquid mass transfer where the pollutant solute is considered to be continuously diffusing through the gas and liquid films. 

Because of the difficulties in determining x, the thickness of the film between the two vapor pressures, an overall transfer coefficient is introduced. Based on the two film theory, the overall transfer coefficient is used. In the case of water evaporation, the gas film is the controlling mechanism and the resulting equation is... 

Let us consider a surface film (say a soap film, which however is composed of two films) of area o> and having a surface tension a (T) at the temperature T. 

The two-film theory of WHITMAN119 was the first serious attempt to represent conditions occurring when material is transferred from one fluid stream to another. Although it does not closely reproduce the conditions in most practical equipment, the theory gives expressions which can be applied to the experimental data which are generally available, and for that reason it is still extensively used. 

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. 

From equation 10.22 the rate of transfer per unit area in terms of the two-film theory for equimolecular counterdiffusion is given for the first phase as ... 

If it is assumed that each element resides for the same time interval te in the surface, equation 10.115 gives the overall mean rate of transfer. It may be noted that the rate is a linear- function of the driving force expressed as a concentration difference, as in the two-film theory, but that it is proportional to the diffusivity raised to the power of 0.5 instead of unity. 

When the film theory is applicable to each phase (the two-film theory), the process is steady state throughout and the interface composition does not then vary with time. For this case the two film coefficients can readily be combined. Because material does not accumulate at the interface, the mass transfer rate on each side of the phase boundary will be the same and for two phases it follows that ... 

These relations between the various coefficients are valid provided that the transfer rate is linearly related to the driving force and that the equilibrium relationship is a straight line. They are therefore applicable for the two-film theory, and for any instant of time for the penetration and film-penetration theories. In general, application to time-averaged coefficients obtained from the penetration and film-penetration theories is not permissible because the condition at the interface will be time-dependent unless all of the resistance lies in one of the phases. 

As noted previously, for equimolecular counterdiffusion, the film transfer coefficients, and hence the corresponding HTUs, may be expressed in terms of the physical properties of the system and the assumed film thickness or exposure time, using the two-film, the penetration, or the film-penetration theories. For conditions where bulk flow is important, however, the transfer rate of constituent A is increased by the factor Cr/Cgm and the diffusion equations can be solved only on the basis of the two-film theory. In the design of equipment it is usual to work in terms of transfer coefficients or HTUs and not to endeavour to evaluate them in terms of properties of the system. 

What are the general principles underlying the two-film, penetration and film-penetration theories for mass transfer across a phase boundary Give the basic differential equations which have to be solved for these theories with the appropriate boundary conditions. 

According to the Whitman Two-Film theory, the actual concentration profiles, as shown in Fig. 1.28 are approximated for the steady state with no chemical reaction, by that of Fig. 1.29. 

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