Film condensation transition

Carpenter and Colburn (C3, C12), 1951 Review of research on film condensation shows importance of gas stream effects, waves, transition to turbulence, etc. 

Takeyama, T. and Shimizu, S., On the Transition of Dropwise-Film Condensation, Proc. 5th. Int. Heat Trans. Conf., Tokyo, Vol. HI, 274, 1974. 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

The adsorption and desorption isotherms have been calculated for the Nj sorption at 77K in cylindrical pores of MCM-41 materials in the range 1-12 nm. The points of spinodal and equilibrium transitions are plotted in Fig. 2. There are several features worth noticing. As the pore size increases, the line of spinodal desorption saturates at the value corresponding to the spinodal decomposition of the bulk liquid. The line of equilibrium capillary condensation asymptotically approaches the Kelvin equation for the spherical meniscus and the line of spontaneous capillary condensation asymptotically approaches the Kelvin equation for the cylindrical meniscus. This asymptotic behavior is in agreement with the classical scenario of capillary hysteresis [12] capillary condensation occurs spontaneously after the formation of the cylindrical adsorption film on the pore walls while evaporation occurs after the formation of the equilibrium meniscus at the pore end. Most interestingly, the NLDFT predictions of equilibrium and spontaneous capillary condensation transitions for pores wider than 6 nm are approximated by the semi-empirical equations of the Deijaguin-Broekhoff-de Boer theory [13]. 

In the calculation of heat transfer in the transition region between laminar and turbulent film condensation, empirical interpolation formulae are well established. One of these types of formulae is... 

Transition region between laminar and turbulent film condensation. 

Rohsenow et al. [21] extended the analysis into the turbulent film regime using the heat transfer-momentum analogy. The results for a downward flowing vapor are shown in Fig. 14.7 for Prf = 1.0 and 10.0. At high vapor velocities, as the dimensionless shear stress x increases, the transition to turbulence occurs at smaller values of the film Reynolds number (Eq. 14.31) as represented by the dashed lines. The influence of x on both laminar and turbulent film condensation is evident. 

This interfacial layer is characterized by a gradual change of the lattice and the composition within the film-substrate transition area. At least partial solubility is required for diffusion between the film and the substrate material to take place. The necessary energy of 1 to 5 eV must be supplied from elsewhere, e.g. when copper is evaporated onto an unheated gold substrate the heat of condensation is sufficient for diffusion to take place. Diffusion layers may have advantageous characteristics as transitional layer between very different materials, e.g. for reducing mechanical stress resulting from different thermal expansions. 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

It is evident that boundary lubrication is considerably dependent on the state of the monolayer. Frewing [48] found that, on heating, the value of fi rose sharply near the melting point sometimes accompanied by a change from smooth to stick-slip sliding. Very likely these points of change correspond to the transition between an expanded film and a condensed film in analogy with... 

In Fig. 15 we show similar results, but for = 10. Part (a) displays some examples of the adsorption isotherms at three temperatures. The highest temperature, T = 1.27, is the critical temperature for this system. At any T > 0.7 the layering transition is not observed, always the condensation in the pore is via an instantaneous filling of the entire pore. Part (b) shows the density profiles at T = 1. The transition from gas to hquid occurs at p/, = 0.004 15. Before the capillary condensation point, only a thin film adjacent to a pore wall is formed. The capillary condensation is now competing with wetting. 

Figure 10-67B. Correlation of McAdams representing the condensing film coefficient on the outside of vertical tubes, integrated for the entire tube length. This represents the streamline transition and turbulent flow conditions for Prandtl numbers 1 and 5. Do not extrapolate Prandtl numbers, Pr beyond 5. (Used by permission Engineering Data Book II 1984, Wolverine Tube, Inc.)...

A,A -di(/>-dimethylamino-benzyl) derivatives of di(imidazolidinylidene)gold(i) salts were polymerized into polyimides by condensation with arene-tetracarboxylic anhydrides. The products are tough, but flexible, and have high glass transition temperatures and high thermal stability. Yellow films of the materials are transparent above 365 nm.279... 

Taken together, the equilibrium spreading pressures of films spread from the bulk surfactant, the dynamic properties of the films spread from solution, the shape of the Ylj A isotherms, the monolayer stability limits, and the dependence of all these properties on temperature indicate that the primary mechanism for enantiomeric discrimination in monolayers of SSME is the onset of a highly condensed phase during compression of the films. This condensed phase transition occurs at lower surface pressures for the R( —)- or S( + )-films than for their racemic mixture. 

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