Surface tension prediction

The radially dependent surface tension predicted by YBG theory are compared with the results of computer simulation using equations (24) (o) and (25) ( ). The estimated error bars are taken from reference 7. 

The same regression analysis methodology has been appHed for analyzing the model for aggregation of surfactants at the interface. The non-Hnear Eq. 28 has been numerically solved by the bisection method. The surface tension predicted by Eq. 27 has been fitted to the experimental data by min-... 

The physical analyses of the constants k and have not been investigated at this stage. Further, as QSPR models can predict relations between molecular structures and boiling points, it should be possible to extend these models to surface tension prediction based on the above relation. A general and semiempirical correlation between the alkane chain length and surface tension has been described." ... 

There is a theory describing the kinetics of surface wetting due to the action of ca nllary forces in relation to the surface tension predicted by a Laplace equation. One can calculate the rate of liquid flow into a narrow or wedge-like slot, or a round hole. The theory takes into consideration the rheological properties of... 

As a follow-up to Problem 2, the observed nucleation rate for mercury vapor at 400 K is 1000-fold less than predicted by Eq. IX-9. The effect may be attributed to a lowered surface tension of the critical nuclei involved. Calculate this surface tension. 

The critical surface tension concept has provided a useful means of summarizing wetting behavior and allowing predictions of an interpolative nature. A schematic summary of 7 values is given in Fig. X-10 [123]. In addition, actual contact angles for various systems can be estimated since )3 in Eq. X-38 usually has a value of about 0.03-0.04. 

The separation of two surfaces in contact is resisted by adhesive forces. As the nonnal force is decreased, the contact regions pass from conditions of compressive to tensile stress. As revealed by JKR theory, surface tension alone is sufficient to ensure that there is a finite contact area between the two at zero nonnal force. One contribution to adhesion is the work that must be done to increase surface area during separation. If the surfaces have undergone plastic defonnation, the contact area will be even greater at zero nonnal force than predicted by JKR theory. In reality, continued plastic defonnation can occur during separation and also contributes to adhesive work. 

Surface tension is usually predicted using group additivity methods for neat liquids. It is much more difficult to predict the surface tension of a mixture, especially when surfactants are involved. Very large molecular dynamics or Monte Carlo simulations can also be used. Often, it is easier to measure surface tension in the laboratory than to compute it. 

The capillary retention forces in the pores of the filter cake are affected by the size and size range of the particles forming the cake, and by the way the particles have been deposited when the cake was formed. There is no fundamental relation to allow the prediction of cake permeabiUty but, for the sake of the order-of-magnitude estimates, the pore size in the cake may be taken loosely as though it were a cylinder which would just pass between three touching, monosized spheres. If dis the diameter of the spherical particles, the cylinder radius would be 0.0825 d. The capillary pressure of 100 kPa (1 bar) corresponds to d of 17.6 pm, given that the surface tension of water at 20°C is 12.1 b mN /m (= dyn/cm). 

The study of the combustion of sprays of Hquid fuels can be divided into two primary areas for research purposes single-droplet combustion mechanisms and the interaction between different droplets in the spray during combustion with regard to droplet size and distribution in space (91—94). The wide variety of atomization methods used and the interaction of various physical parameters have made it difficult to give general expressions for the prediction of droplet size and distribution in sprays. The main fuel parameters affecting the quaHty of a spray are surface tension, viscosity, and density, with fuel viscosity being by far the most influential parameter (95). 

Eq. (2-163) correctly predicts that the surface tension becomes zero at the critical point. 

Surface tensions for aqueous solutions are more difficult to predict than those for nonaqueous mixtures because of the nonlinear dependence on mole fraction. Small concentrations of the organic material may significantly affect the mixture surface tension value. For many binary organic-water mixtures, the method of Tamura, Kurata, and Odanfi maybe used ... 

Effect of Physical Properties on Drop Size Because of the extreme variety of available geometries, no attempt to encompass this variable is made here. The suggested predictive route starts with air-water droplet size data from the manulac turer at the chosen flow rate. This drop size is then corrected by Eq. (14-195) for different viscosity and surface tension ... 

Bubble sizes at formation generally increase with surface tension and orifice diameter. Prediction of sizes in swarms from multiple orifices is difficult. In aqueous solutions of low surface tension, Bubble diameters of the order of 1 mm are common. Bubbles produced by the more complicated techniques of pressure flotation or vacuum flotation are usually smaller, with diameters of the order of 0.1 mm or less. 

Zisman s plot cos 6 varies linearly with yi,. Zzisman = Predicts critical surface tension linearity does not hold universally y depends on probe liquids. [73-76]... 

Geometric mean approximation Dispersive and polar components of solid surface energy are found by solving yiv(l +COS0) = 2(y,Xf + 2(y Yl S An extension of GGF equation ysa predicted is significantly higher than the critical surface tension. [84]... 

Kister and Haas [184] recommend using 25 dynes/cm in Equation 8-286 when the actual surface tension is a 25 dynes/cm. This correlation is reported [94, 184] to give better effects of physical properties, and predicts most sieve and valve tray entrainment flood data to 15 to 20%, respectively. 

For Yiv > YPv> where y v and Ypv are the surface tensions of liquid and protein, respectively, AFads increases with increasing ysv, predicting decreasing polymer adsorption. An example of this is phosphate buffer saline where y]v = 72.9 mJ/m2 and Ypv is usually between 65 and 70mJ/m2 for most proteins [5]. Therefore, supports for gel-permeation and affinity chromatography should be as hydrophilic as possible in order to minimize undesirable adsorption effects. 

For Yiv < Ypv the opposite behavior pattern is predicted, namely AFads decreases with increasing ysv, thus stronger adsorption occurs. Indeed, adsorption of IgM from the dimethylsulphoxide solutions in water (y,v = 63.2 67.2 69.1) increases with increasing substrate surface tension (ysv)-... 

Sadler [76] analysed the outline of the crystal edges and found that the lateral surface tension compatible with such a curvature would be a 1 — 3 kT/. Although he used a very simplified approach, it seems unlikely that its assumptions could lead to a a 20 kT/<7> as predicted by the LH theory. 

The presence of calcium and magnesium ions increases the adsorption of the surfactants at the water-air interface and leads to a corresponding lowering of the surface tension at the CMC as shown by the data in Table 4. A C16 branched AOS gives a lower surface tension than a linear C16 AOS this too is in agreement with other model studies and theoretical predictions [42, and Sec. 2 on interfacial tension). 

Predict which liquid in each of the following pairs has the greater surface tension (a) c/s-dichloroethene or trans-dichloroethene (see structures 5 and 6) (b) benzene at 20°C or benzene at 60°C. 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

In bubbling, the control of the bubble diameter is a little easier. In these methods bubbles are made at an orifice or a multitude of orifices. If there is only one orifice, of radius r, and if bubble formation is slow and undisturbed, the greatest possible bubble volume is 27rry/gp] y is the surface tension of the liquid, p the difference between the densities of liquid and gas (practically equal to the density of the liquid), and g is acceleration due to gravity. Every type of agitation lowers the real bubble size. On the other hand, if there are many orifices near enough to each other, the actual bubble may be much larger than predicted by the above expression. 

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