Condensation film thickness

Note that Eq. (9.19) predicts that the actual pressure drop is two orders of magnitude larger than the gas pressure drop. Actually the capillary pressure works on the effective pore radius, which equals (r - f) with t the adsorbed condensate film thickness and which is assumed to be immobile this point is discussed below. A force balance for one end of the capillary with length L and radius r then yields the effective capillary pressure Pc,eif... 

Condensate Waves and Turbulence. As the local condensate film thickness (i.e., the film Reynolds number Rez) increases, the film will become unstable, and waves will begin to grow rapidly. This occurs for Re, > 30. Kapitza [16] has shown that, in this situation, the average film thickness is less than predicted by the Nusselt theory and the heat transfer coefficient increases accordingly. Kutateladze [17] therefore recommends that the following correction be applied to Eq. 14.12 ... 

Effect of Condensate Inundation. In a condenser with quiescent vapor, there is no vapor shear, and condensate flows by gravity onto lower tubes in a bundle. This extra condensate falling on the lower tubes increases the average condensate film thickness around these tubes, and the condensation heat transfer coefficient therefore decreases as one goes further down the bundle. 

Nimmo and Leppert [111] used a Nusselt-type analysis to study laminar film condensation on a finite, upward-facing horizontal plate, assuming that the condensate flow was driven by the hydrostatic pressure gradient due to changes in condensate film thickness from the center of the plate to the edges. They arrived at the following approximate expression for the mean Nusselt number ... 

For an upward flow direction, the shear forces may influence the downward-flow of the condensate, causing an increase of the condensate film thickness. Therefore, the heat transfer coefficient under such conditions shall decrease up to 30 percent compared to the result obtained using the same correlation as the upward-flowing vapor. If the vapor velocity increases substantially, the so-called flooding phenomenon may occur. Under such condition, the shear forces completely prevent the downward condensate flow and flood (block) the tube with the condensate. Prediction of the flooding conditions is discussed by Wallis, as reported by Butterworth [81]. 

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

The Reynolds number of the condensate film (falling film) is 4r/ I, where F is the weight rate of flow (loading rate) of condensate per unit perimeter kg/(s m) [lb/(h ft)]. The thickness of the condensate film for Reynolds number less than 2100 is (SflF/p g). ... 

With tube side condensation, coefficients are generally lower than for comparable shell side condensers. This phenomenon is attributed to (1) lower coolant velocities outside the tubes than are possible with tube side cooling, and (2) increased film thicknesses, namely, film resistance inside the tubes. 

Whereas a film formed in dry air consists essentially of an anhydrous oxide and may reach a thickness of 3 nm, in the presence of water (ranging from condensed films deposited from humid atmospheres to bulk aqueous phases) further thickening occurs as partial hydration increases the electron tunnelling conductivity. Other components in contaminated atmospheres may become incorporated (e.g. HjS, SO2, CO2, Cl ), as described in Sections 2.2 and3.1. 

Since the liquid is produced by condensation, the thickness of the film will be zero at the top and will gradually increase towards the bottom. Under stable conditions the difference in the mass rates of flow at distances x and x + dx from the top of the surface will result from condensation over the small element of the surface of length d r and width w, as shown in Figure 9.47. 

Benzene vapour, at atmospheric pressure, condenses on a plane surface 2 m long and I m wide, maintained at 300 K and inclined at an angle of 45° to the horizontal. Plot the thickness of the condensate film and the point heat transfer coefficient against distance from the top of the surface. 

The most useful type of standard state is one defined in terms of a small number of molecules per unit area of adsorbent surface. In an attempt to have a definition analogous to that for three-dimensional matter—one atmosphere at any temperature—Kemball and Rideal (12) defined a standard state with an area per molecule of 22.53T A.2 where T is the absolute temperature. This corresponds to the same volume per molecule as the three-dimensional state if the thickness of the surface layer is 6A. In terms of surface pressure it corresponds to 0.0608 dynes/cm. for a perfect two-dimensional gas at all temperatures, and as such the definition may be extended to cover condensed films. 

In the following derivation we will assume an almost complete wetting of the substrate by the material, in such a way that a continuous amorphous condensed film is formed at a thickness h smaller than the critical size of nucleation. In order to evaluate dG/dN of the process of incorporation of molecules from the amorphous condensed film to the spherulite, that is the ordered phase, we will hypothesize that the thickness of the amorphous film increases linearly with time, h(t) = Uhf, where the velocity is a constant, and that the spherulite has a cylindrical shape of radius R and height h, as illustrated in Fig. 5.10. 

Excitation Eunctions of O2 and 02-Doped Ar Eilms. Resonances can be best identified by the structures they produce in excitation functions of a particular energy-loss process (i.e., the incident-electron energy dependence of the loss). Fig. 7 is reproduced from a recent study [118] of the electron-induced vibrational and electronic excitation of multilayer films of O2 condensed on the Pt(lll) surface and shows the incident electron energy dependence of major losses at the indicated film thickness and scattering angles. Also shown in this figure is the scattered electron intensity of the inelastic background... 

Equation 1 can be used to determine the pore diameter of an MCM-41 sample which exhibits capillary condensation at a certain relative pressure, or to determine the capillary condensation pressure for an MCM-41 sample of a certain pore diameter. To construct model adsorption isotherms for MCM-41, one also needs a description of the monolayer-multilayer formation on the pore walls. This description can be based on the experimental finding that the statistical film thickness in MCM-41 pores of different sizes (especially above 3 nm) is relatively constant for pressures sufficiently lower from those of the capillaiy condensation and can be adequately approximated by the t-curve for a suitable reference silica [29-31], for instance that reported in Ref. 35. In these studies [29-31], the statistical film thickness in MCM-41 pores, tMcM-4i, was calculated according to the following equation [29] ... 

Figure 1. (a) Experimental relations between the capillary condensation pressure and the pore diameter (hollow circles) and between the capillary evaporation pressure and the pore diameter (filled circles) for nitrogen adsorption at 77 K. The dashed line corresponds to the Kelvin equation with the statistical film thickness correction. The solid line corresponds to Eq. 2 derived using the KJS approach, (b) Relation between pore diameters calculated on the basis of Eq. 1 and the KJS-calibrated BJH algorithm using nitrogen adsorption data at 77 K. 

Since evaporation is done in vacuum the mean free path of the molecules is long and they move practically in straight lines to condense onto the substrate, which is placed at an appropriate position. Typically amorphous or polycrystalline layers of some 10 nm thickness are produced by this technique. To get a crystalline surface the sample is usually annealed during or after evaporation. The film thickness is usually monitored by a quartz crystal microbalance. 

To take a possible condensation of the gas into account we assume that the gas becomes liquid once the pressure exceeds the equilibrium vapor pressure Po- The amount adsorbed is just the thickness of the liquid film multiplied by its density. The film thickness Xf is related to the number of adsorbed moles per unit area by T = Xf/V, where V is the molar volume of the liquid. The energy at which the pressure Po is reached is... 

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