Curved liquid films

In this work, microscale evaporation heat transfer and capillary phenomena for ultra thin liquid film area are presented. The interface shapes of curved liquid film in rectangular minichannel and in vicinity of liquid-vapor-solid contact line are determined by a numerical solution of simplified models as derived from Navier-Stokes equations. The local heat transfer is analyzed in term of conduction through liquid layer. The data of numerical calculation of local heat transfer in rectangular channel and for rivulet evaporation are presented. The experimental techniques are described which were used to measure the local heat transfer coefficients in rectangular minichannel and thermal contact angle for rivulet evaporation. A satisfactory agreement between the theory and experiments is obtained. 

In the case of multilayer adsorption it seems reasonable to suppose that condensation to a liquid film occurs (as in curves T or of Fig. XVII-13). If one now assumes that the amount adsorbed can be attributed entirely to such a film, and that the liquid is negligibly compressible, the thickness x of the film is related to n by... 

Figure 14-10 illustrates the gas-film and liquid-film concentration profiles one might find in an extremely fast (gas-phase mass-transfer limited) second-order irreversible reaction system. The solid curve for reagent B represents the case in which there is a large excess of bulk-liquid reagent B. The dashed curve in Fig. 14-10 represents the case in which the bulk concentration B is not sufficiently large to prevent the depletion of B near the liquid interface and for which the equation ( ) = I -t- B /vCj is applicable. 

Fig. 55—Temperature calculation for different liquid films (glycerin and hexadecane) at different locations in the contact region Area A is the central area in the inset photo and area B is the edge area. The filled histogram represents the positive EEF intensity of 518.6 kV/cm, and the empty one of 667.7 V/cm. The solid (glycerin) and dotted (hexadecane) lines are variation curves of the boiling point along the radial direction in the contact region.

Capillary phenomena are due to the curvature of liquid surfaces. To maintain a curved surface, a force is needed. In Eq. (8), this force is related to the second term in the integral. The so-called Laplace pressure due to the force to maintain the curved surface can be expressed as, Pl = 2-yIr, where r is the curvature radius. The combination of the capillary effects and disjoining pressure can make a liquid film climb a wall. 

At very high qualities the liquid film is thin and the rate of entrainment is low. The entrained liquid mass flux curve is almost parallel with the total liquid mass flux in Figure 5.26 i.e., the liquid evaporation rate is supported solely by the liquid deposition rate. If the boiling heat flux q" < q D, where q"D = GDH]g, the boiling crisis can be averted by a deposition liquid mass flux, GD, as shown in Figure 5.26, and therefore is called deposition-controlled CHF. 

As is evident from Figure 13.25a, the area loading of decalin is closely related with the stationary conversion. Because the highest conversion was attained at around the area loading of 70 (L/m2h) (= 4.48 X 102 (mol/m2h)) with the catalyst in the superheated liquid-film state, Equation 13.8 is transformed in to Equation 13.9, giving a reciprocal correlation curve between the one-pass conversion (A) and the reaction area needed to a 50 kW power (S) (Figure 13.25b). 

In Figure 12.11a, the concentration profile through the liquid film of thickness zl is represented by a straight line such that fcz, = Dl/zl In b, component A is removed by chemical reaction, so that the concentration profile is curved. The dotted line gives the concentration profile if, for the same rate of absorption, A were removed only by diffusion. The effective diffusion path is 1/r times the total film thickness zl-... 

Figures 3(a) and 3(b) show the computed fraction profiles of component A and B in the liquid film corresponding to, respectively, run 1 and run 6 from Table 1. Figure 3(a) shows that low fractions of A and B produce straight profiles, whereas high fractions of A and B result in curved profiles [see Fig. 3(b)]. The latter is due to the fact that the mass fluxes consist of a diffusive part as well as a convective (i.e. drift) part. This is also the reason why the fraction of B possesses a gradient, although the flux of component B equals zero.

Thus we would expect water to climb up the walls of a clean (i.e. water-wetting) glass vessel for a few millimetres but not more, and we would expect a sessile water droplet to reach a height of several mm on a hydrophobic surface, before the droplet surface is flattened by gravitational forces. The curved liquid border at the perimeter of a liquid surface or film is called the Plateau border after the French scientist who studied liquid shapes after the onset of blindness, following his personal experiments on the effects of sunlight on the human eye. 

From Figure 4.24, it is clear that in the case of liquid-film control, the curve has a tail in the beginning, while in the case of sohd diffusion control, the tail is at the end. 

In Figure 4.27, some examples of theoretical breakthrough curves calculated from the analytical solutions for the Freundlich isotherm (Fr = 0.5) are presented. As is clear, the curve corresponds to the case of equal and combined solid and liquid-film diffusion resistances ([ = 1) which is between the two extremes, i.e. solid diffusion control (l = 10,000) and liquid-film diffusion control ( = 0.0001). 

Figure 5.6 shows an example of a total interaction energy curve for a thin liquid film stabilized by the presence of ionic surfactant. It can be seen that either the attractive van der Waals forces or the repulsive electric double-layer forces can predominate at different film thicknesses. In the example shown, attractive forces dominate at large film thicknesses. As the thickness decreases the attraction increases but eventually the repulsive forces become significant so that a minimum in the curve may occur, this is called the secondary minimum and may be thought of as a thickness in which a meta-stable state exists, that of the common black film. As the... 

A higher gas flow rate is then required to cause the liquid films to collapse and induce slug formation. Therefore, the curves for the 4mm and 6mm particles intersect due to a balance in the effects of particle size upon the surface tension and liquid holdup. 

Fig. 5.12 depicts the lg Wit dependence for NaDoS foams with thin liquid films, h 16 nm, with CBF, h 8 nm and with NBF, h 4.2 nm. The differences between curve 1, 2 and 3, corresponding to the different foam film types, is clearly expressed and is valid not only for the curve slopes but also for t at which a plateau is reached, that itself corresponds to hydrostatic equilibrium. Fig. 5.12,a and 5.12,b plots the initial linear parts of the experimental Wit dependences where the black circles are for NBF, and the black squares are for CBF. It can be seen that the drainage rate is different for the different types of foam films. 

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