Effect of surface tension

From a theoretical standpoint surface tension is an important variable. First consider nucleation. The rate of nuclei formation is proportional to 

The semitheoretical approaches which are concerned with bubbles already in existence predict that a is an important variable also. Rohsenow and also Forster and Zuber give h = Ca a i. This agreement is noteworthy. 

Two experimental approaches have been used. The results for different pure liquids have been examined in attempts to detect the effect of a, and surface-active agents have been added to pure liquids artificially to change a. The results by either method are contradictory. Experimentally the effect of a is still unproved. 

If the nucleate-boiling region is represented by an equation such as h = (const.) a, the results of a few workers will serve to show the present state of knowledge. 

One set of observations exists for the effect of surface-active agents on A Tc and The values are somewhat incomplete because the A Tc for pure water could not be obtained with the equipment used. The accompanying table summarizes the results (M9). The results indicate that a decrease in a causes a decrease in the maximum heat flux. Addi- 

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The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

Cavitation and Flashing From the discussion on pressure recoveiy it was seen that the pressure at the vena contracta can be much lower than the downstream pressure. If the pressure on a hquid falls below its vapor pressure (p,J, the liquid will vaporize. Due to the effect of surface tension, this vapor phase will first appear as bubbles. These bubbles are carried downstream with the flow, where they collapse if the pressure recovers to a value above p,. This pressure-driven process of vapor-bubble formation and collapse is known as cavitation. 

The simplified method of calculation outhned includes no allowance for the effect of surface tension. Stroebe, Baker, and Badger (loc. cit.) found that by adding a small amount of surface-... 

Souders-Brown. The Souders-Brown method (References 1, 2) is based on bubble caps, but is handy for modem trays since the effect of surface tension can be evaluated and factors are included to compare various fractionator and absorber services. These same factors may be found to apply for comparing the services when using valve or sieve trays. A copy of the Souders-Brown C factor chart is shown in Reference 2. 

These statements are only true when the liquid is a pure substance, i.e., does not change in composition during evaporation. This constancy of vapour-pressure serves to distinguish pure substances from solutions. The effects of surface tension, appearing when small droplets are used, and of electrification, must also be absent (cf. 100—102). 

Solubility, causes modifying, 319 and chemical potential, 359 curve, 307 equation, 306 of gases in liquids, 275, 371 effect of pressure on, 316 effect of surface tension on, 447 effect of temperature on, 302, 372... 

The log of the reciprocal of the bulk concentration of surfactant (C in mol/ L) necessary to produce a surface or interfacial pressure of 20 raN/m, log( 1 / On= 20 i e > a 20 mN/m reduction in the surface or interfacial tension, is considered a measure of the efficiency of a surfactant. The effectiveness of surface tension reduction is the maximum effect the surfactant can produce irrespective of concentration, (rccmc = [y]0 - y), where [y]0 is the surface tension of the pure solvent and y is the surface tension of the surfactant solution at its cmc. 

In order to take into account the effect of surface tension and micro-channel hydraulic diameter, we have applied the Eotvos number Eo = g(pL — pG)d /(y. Eig-ure 6.40 shows the dependence of the Nu/Eo on the boiling number Bo, where Nu = hd /k] is the Nusselt number, h is the heat transfer coefficient, and k] is the thermal conductivity of fluid. All fluid properties are taken at the saturation temperature. This dependence can be approximated, with a standard deviation of 18%, by the relation ... 

Bellman, R., and R. H. Pennington, 1954, Effects of Surface Tension and Viscosity on Taylor Instability, Quarter. Appl. Math., 12 151. (6)... 

The second effect of surface tension is that it causes the alveolus to become as small as possible. As the water molecules pull toward each other, the alveolus forms a sphere, which is the smallest surface area for a given volume. This generates a pressure directed inward on the alveolus, or a collapsing pressure. The magnitude of this pressure is determined by the Law of LaPlace ... 

Figure 17.2 Effects of surface tension and surfactant on alveolar stability, (a) Effect of surface tension. According to the law of LaPlace (P = 1ST/r), if two alveoli have the same surface tension (ST), the alveolus with the smaller radius (r), and therefore a greater collapsing pressure (P), would tend to empty into the alveolus with the larger radius, (b) Effect of surfactant. Surfactant decreases the surface tension and thus the collapsing pressure in smaller alveoli to a greater extent than it does in larger alveoli. As a result, the collapsing pressures in all alveoli are equal. This prevents alveolar collapse and promotes alveolar stability.

The correlation derived by Dombrowski and Johns covers a large range of liquid viscosity and agrees favorably with experimental results. Crapper et al.[236] further applied second order and large amplitude theories to achieve better predictions. In addition, the effects of surface tension, and viscosity of a liquid sheet as well as the radial spreading and the resultant changes in the sheet thickness on the stability have been examined by Weihs.[257]... 

Droplet Formation in Water Atomization. In water atomization of melts, liquid metal stream may be shattered by impact of water droplets, rather than by shear mechanism. When water droplets at high velocities strike the liquid metal stream, some liquid metal fragments are knocked out by the exploding steam packets originated from the water droplets and subsequently contract into spheroidal droplets under the effect of surface tension if spheroidization time is less than solidification time. It is assumed that each water droplet may be able to knock out one or more metal droplet. However, the actual number of metal droplets produced by each water droplet may vary, depending on operation conditions, material properties, and atomizer designs. 

One of the earliest analytical models for the calculation of flattening ratio of a droplet impinging on a solid surface was developed by Jones.1508] In this model, the effects of surface tension and solidification were ignored. Thus, the flattening ratio is only a function of the Reynolds number. Discrepancies between experimental results and the predictions by this model have been reported and discussed by Bennett and PoulikakosJ380]... 

A combination of adhesion and surface tension gives rise (pardon the pun) to capillary action. By its adhesion to the solid surface of the soil particles, the water wants to cover as much solid surface as possible. However, by the effect of surface tension, the water molecules adhering to the solid surface are connected with a surface him in which the stresses cannot exceed the surface tension. As water is attracted to the soil particles by adhesion, it will rise upward until attractive forces balance the pull of gravity (Figure 3.28). Smaller-diameter tubes force the air-water surface into a smaller radius, with a lower solid-surface-to-volume ratio, which results in a greater capillary force. Typical heights of capillary rise for several soil types are presented in Table 3.9. The practical relationship between normal subsurface water and capillary rise is presented in the following equation. 

F. Effect of Surface Tension of the Liquid and the Wetting Properties of the... 

At constant pressure conditions, Quigley, Johnson, and Harris (Ql) find that for higher flow rates, the effect of surface tension on bubble volume is negligible. These authors may not have adequately accounted for the large difference in the densities of the two liquids—water and carbon tetrachloride —used by them. Davidson and Schuler find that under constant pressure conditions, surface tension does appreciably affect the bubble volume. 

The work currently being conducted by Satyanarayan, Kumar, and Kuloor (S3) indicates that the effect of surface tension is more involved than hitherto appreciated. Some of their data are presented in Figs. 6. and 7. They find that at very small orifice diameters or at very large flow rates, the surface tension variation has negligible influence on the bubble volume. For higher orifice diameters, the influence is more pronounced at small flow rates, as is evident from Fig. 7. 

Fig. 5. Effect of surface tension on bubble volume under constant flow conditions.

Investigators Viscosity Reported effect of Surface tension Density... 

To recapitulate the discrepancies in literature, Datta et al. (D4) varied the viscosity of water from 0.012 to 1.108 poise and found that with an increase in the viscosity, the bubble volume decreased for all the nozzles used. This is in apparent contradiction to the observations of most of the other investigators. An effort can now be made to explain this discrepancy on the basis of the present model. Note is to be made of the extremely small volumetric flow rates employed by Datta et al. (D4). In fact, they are in the range where effects due to viscosity are negligible when compared to the effects of surface tension. Thus, though there is a hundredfold increase in the viscosity, it is accompanied by a large variation in the surface tension, which decreases from 72.8 to 65.7 dyn per centimeter. At the very small flow rates employed, the decrease in the bubble volume observed by Datta et al. (D4) seems more likely to be due to this decrease in the surface tension rather than to the hundredfold increase in the viscosity. Thus, the influence of surface tension has been mistakenly attributed to the effect of viscosity. The actual values of the bubble volumes obtained by these authors for a typical nozzle are given in Table VI along with those obtained by the application of the present model. 

The range of variables investigated by Davidson and Schuler (D8) is once again such that the influence of viscosity is predominant. This has already been discussed in the section dealing with the effect of surface tension. 

The arguments used, however, referred to an empty cavity and neglected the effects of surface tension (a). 

Values of the critical micelle concentration (cmc), minimum area per molecules " cnic effectiveness of surface tension reduc-... 

The foaming ability of a liquid mixture depends on the magnitude of the variation of surface-tension with concentration, but not on its sign 95). In practice, however, the effect of surface tension on plate efficiency... 

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