Determination surface tension

While Eq. 11-14 is exact, its use to determine surface tension from capillary rise experiments is not convenient. More commonly, one measures the height, h, to the bottom of the meniscus. 

Using these two relationships, it is possible to determine surface tension as a... 

The atoms and molecules at the interface between a Hquid (or soHd) and a vacuum are attracted more strongly toward the interior than toward the vacuum. The material parameter used to characterize this imbalance is the interfacial energy density y, usually called surface tension. It is highest for metals (<1 J/m ) (1 J/m = N/m), moderate for metal oxides (<0.1 J/m ), and lowest for hydrocarbons and fluorocarbons (0.02 J /m minimum) (4). The International Standards Organization describes weU-estabHshed methods for determining surface tension, eg, ISO 304 for Hquids containing surfactants and ISO 6889 for two-Hquid systems containing surfactants. 

Recently, the size and shape of a liquid droplet at the molten tip of an arc electrode have been studied,12151 and an iterative method for the shape of static drops has been proposed. 216 Shapes, stabilities and oscillations of pendant droplets in an electric field have also been addressed in some investigations. 217 218 The pendant drop process has found applications in determining surface tensions of molten substances. 152 However, the liquid dripping process is not an effective means for those practical applications that necessitate high liquid flow rates and fine droplets (typically 1-300 pm). For such fine droplets, gravitational forces become negligible in the droplet formation mechanism. 

Neumann, A.W. and Good, R.J., Hope, C.J. and Sejpal, M. (1974). An equation od state approach to determine surface tension of low energy solids from contact angles. J. Colloid. Interface Sci. 49, 291-303. 

Methods of determining surface tension by measuring the force required to detach a body from a liquid are therefore similar to the stalagmometer method described earlier. 

EXAMPLE 6.2 Use of the Kelvin Equation for Determining Surface Tension. Figure 6.5 shows a plot of experimental data that demonstrates the validity of the Kelvin effect. Necks of liquid cyclohexane were formed between mica surfaces at 20°C, and the radius of curvature was measured by interferometry. Vapor pressures were measured for surfaces with different curvature. Use these data to evaluate 7 for cyclohexane. Comment on the significance of the fact that the linearity of Figure 6.5 extends all the way to a p/p0 value of 0.77. 

Laplace equation A thermodynamic derivation Determining surface tension from the Kelvin equation Heat of immersion from surface tension and contact angle Surface tension and the height of a meniscus at a wall Interfacial tensions from the Girifalco-Good-Fowkes equation... 

This is, when properly performed, the most accurate method available for determining surface tensions. Since the measurements do not involve a disturbance of the surface, slow time effects can be followed. 

The capillary rise method is a classical method for determining surface tension that has important applications. For capillary rise in a narrow capillary (Figure 3.7) a force balance yields ... 

Equipment. A Brookfield synchro-lectric viscometer, serial no. 758, is used to measure viscosity in the range of 0-100,000 cP. Sugden s double capillary modification of the maximum bubble pressure method is used to determine surface tensions. The apparatus is calibrated with benzene and is checked by determining the surface tension of chloroform at 25°C, which is found to be 23.5 dyn cm"1 (26.5 dyn cm 1) (35). 

Although the capillary tube method has recently fallen into disfavour, which is unfortunate, it can with careful work give very accurate results, and some of the best values of g have been found by this method. The tube (which may be freshly drawn) must be free from grease Volkmann washed the tube with potash solution and then distilled water (the chromic-sulphuric acid mixture should always be avoided). Schultzei said the walls of the tube should first be wetted, to fill the capillary pores of the glass surface. The rate of rise of a liquid in a capillary was studied by Le Grand and Reuse. Muller 12 determined surface tension and viscosity simultaneously from the rate of flow back to the equilibrium position in a capillary. 

In order to calculate the effective adsorption time teff which is necessary to compare the determined surface tension dependence with data from other methods an exact determination of the so-called deadtime is required. From some easy assumption the Poiseuille approximation results which yields [178]... 

FACTORS DETERMINING SURFACE TENSION. ABRAMZONAA KOLLOIDZH... 

In 2008, Qian et al. synthesized two series of four-arm and eleven-arm star polystyrene with six different molar masses for each case. They determined surface tension of single component polymer film using a Wilhelmy plate technique... 

Here the deviation of the bubble from sphericity and any dynamic corrections are disregarded. For capillaries of small radii (ca. 0.1 mm) the bubbles are essentially spherical and the error in the calculation of y from Eq. (48) is less than 0.5% and calibration with a know liquid almost eliminates this error. For wider capillaries, the error in the determined surface tension of water can be quite large and for surfactants solutions, this error increases and is roughly proportional to the... 

The drop weight, or Tate s, method is yet another technique for determining surface tension. This approach relies on dripping of a liquid in a gas from a capillary and measuring the combined volumes of the primary and satellite drops that are formed. In this case one can write Tate s law for the weight of the drop... 

Surface tension measurements via the volume drop method determined surface tensions of the cation-anion pairs [RMIM][Anion], where R stands for alkyl chains on the cation ranging from C4 to Cjj, combined with various anions. Surface... 

We see from these data that the values of surface tension calculated from known forces of adhesion (which are equal to the capillary forces) are low in comparison with the actual values. The point is that these investigators failed to account for the disjoining pressure of the thin layer of liquid (see Fig. IV.6.c), which weakens the capillary interaction. This is why their method for determining surface tension by measurement of adhesive force did not give accurate results. 

Figure 10. Experimentally determined surface tension between three different gases and liquid water at two temperatures in dependence of pressure to 3000 bar [80].

Drops of liquids have held researchers interest for many years. As mathematical curiosities for famous early fluid dynamicists, the pendant drop from a capillary provided an interesting and practical challenge. Young (1805) and Laplace (1806) independently developed the theory of surface tension and drop formation while the first analytical solutions to their theory were completed by Gauss in 1830. Much of the early woik on pendant drops involved numerous methods involving the determination of drop volume or shape with experimental techniques and using the available theory to determine surface tension of the liquid-gas interface. These methods are well detailed in the works by Adamson, Padday, and Reed Hah. ITie studies of the early researches developed into the rich and diversified field of interfacial fluid dynamics. The advancement of theory and numerical techniques has steadily increased the ability of researchers to better understand and control interfacial behaviors. 

Finally, measuring the forces involved is another way to determine surface tensions. The procedure here consists of bringing into contact a liquid and an object with a well-defined geometry (often a plate or a fiber Figure 2.24). The objective is to measure the capillary force exerted on the object (Wilhelmy s method). As we have seen in equation (2.35), this force can be written as... 

In the following, we start by describing the equilibrium relations that determine surface tension as a function of surfactant concentration. Then the mechanisms for dynamic variation are incorporated. Finally, the dynamic variations are related to the presence of Marangoni surface stresses and therefore Marangoni convection. 

The contact angle of mercury on glass is about 120° (cosd = —0.5). What is the significance of the -0.5 for the cos 9 in terms of the capillary method of determining surface tension. 

McFarlane and Tabor [81] recommend using (111.37) and (111,38) to determine the surface tension of water (or any other liquid) provided that the values of Fj and r are known. Experimental results obtained by these authors on determining surface tension by reference to the adhesion of glass spheres in the presence of a liquid held by capillary forces on glass surfaces are given below ... 

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