Surface tension capillary-rise method

A thin film of water spreads up the inside walls of the capillary because of strong adhesive forces between water and glass (water wets glass). The pressure below the meniscus falls slightly. Atmospheric pressure then pushes a column of water up the tube to eliminate the pressure difference. The smaller the diameter of the capillary, the higherthe liquid rises. Because its magnitude is also directly proportional to surface tension, capillary rise provides a simple experimental method of determining surface tension, described in Exercise 122. 

The following values for the surface tension of a 10 Af solution of sodium oleate at 25°C are reported by various authors (a) by the capillary rise method, y - 43 mN/m (b) by the drop weight method, 7 = 50 mN/m and (c) by the sessile drop method, 7 = 40 mN/m. Explain how these discrepancies might arise. Which value should be the most reliable and why ... 

The capillary-rise method was employed to measure the surface tension of aqueous solutions of disodlum alkyl phosphate at 25 °C. The cmc values of the solutions were obtained from the discontinuity in the surface tension - concentration curves(7). 

Figure 2. Surface tensions of sodium dodecylsulfonate solutions with and without polymer addition as measured by the capillary rise method.

The approximation that limits this analysis of capillary rise originates from neglecting the weight of the liquid in the crown of the curved meniscus. We see in Section 6.8b that the height of capillary rise can be related to surface tension without making this approximation, although the connection is somewhat unwieldy. A more detailed description of the experimental aspects of the capillary rise method can be obtained from advanced textbooks (e.g., Adamson 1990). 

Both the Wilhelmy and capillary rise methods for determining 7 have been based on the concept of surface tension as a force. While this point of view is useful for describing the experimental methods we have discussed, it is only one way of interpreting 7. An energetic interpretation is also possible that makes surface tension amenable to the powerful methods of thermodynamics. 

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 ... 

Surface Tension. The surface tension of various ozone-fluorine mixtures was determined by the capillary rise method in the apparatus used for the viscosity measurements (1) using Equation 4. 

The capillary-rise method is used to study the change in surface tension as a function of concentration for aqueous solutions of />butanol and sodium chloride. The data are interpreted in terms of the surface concentration using the Gibbs isotherm. 

Apparatus for measuring surface tension by the method of capillary rise. 

The surface tension of pure ozone was determined by the capillary rise method in the apparatus used for viscosity measurements. The ratio of the capillary rise of liquid ozone to that of water at 20° C. was measured and zero contact angle was assumed. Results at —183° and —195.5° C. are given in Table III. The parachor for... 

It should be noted that the pressure is always greater on the concave side of the interface irrespective of whether or not this is a condensed phase.) The phenomena due to the presence of curved liquid surfaces are called capillary phenomena, even if no capillaries (tiny cylindrical tubes) are involved. The Young-Laplace equation is the expression that relates the pressure difference, AP, to the curvature of the surface and the surface tension of the liquid. It was derived independently by T. Young and P. S. Laplace around 1805 and relates the surface tension to the curvature of any shape in capillary phenomena. In practice, the pressure drop across curved liquid surfaces should be known from the experimental determination of the surface tension of liquids by the capillary rise method, detailed in Section 6.1. 

When compared with the other methods, the capillary rise method is the ultimate standard method in terms of the degree of theoretical exactitude, and, although it is the oldest method, it still gives the most precise liquid surface tension results if carefully applied, and when the time of measurement is allowed to be sufficiently long. However, with the improvement in computer-controlled electronic equipment, other methods now also have a very high precision. Some of the surface tension results are summarized in Table 6.1, and the interfacial tension between pure liquids in Table 6.2. 

Liquid Surface Tension from the Capillary Rise Method... 

The capillary rise method is a static method, which measures the tension of practically stationary surfaces that have been formed and equilibrated for an appreciable amount of time. The use of a cathetometer and suitable illumination of the menisci is required during the measurement. The capillary tubes must be very clean, be placed as accurately vertical, and be circular in cross section with an accurately known and uniform radius. The... 

While determining the liquid height, it is better to measure with a falling (or receding) meniscus, so that the liquid level is initially raised above its equilibrium value by a slight suction above the capillary tube, and then left to equilibrate. On the other hand, two-armed capillary tubes, connected with a cross tube above the liquid level, are also used to ensure that the pressure in both arms of the glass apparatus is the same. An interesting modification of the capillary rise method is to measure the pressure, AP, that is required to force the meniscus down until it is on the same level as the plane surface of liquid outside the capillary tube. This method is useful to compare the surface tension of water and its dilute solutions. 

The detachment of a ring or a plate (a Wilhelmy plate) from the surface of a liquid or solution is a static surface tension measurement method, which gives the detachment force of a film of the liquid and its extension from the liquid surface. These methods are less accurate than the capillary rise method, but they are normally employed in most surface laboratories because of their ease and rapidity. 

The static methods are based on studies of stable equilibrium spontaneously reached by the system. These techniques yield truly equilibrium values of the surface tension, essential for the investigation of properties of solutions. Examples of the static methods include the capillary rise method, the pendant and sessile drop (or bubble) methods, the spinning (rotating) drop method, and the Wilhelmy plate method. 

The precision of surface tension measurements using the capillary rise method can be further increased if the deviation of the meniscus shape from the spherical is taken into account. This correction is especially important when capillaries of large radii are used. Corrections for non-spherical meniscus curvature are based on tabulated numerical solutions of the differential Laplace equation [6]. The capillary rise method yields a values with a precision of up to hundredths of mN/m. 

Crystals, mild characteristic odor, bitter taste, mp 112-113°. Freely sol in water ([00 g/ 100 ml), much less sol at low temps. Sol in ethanol, acetone, ethyl acetate, chloroform very slightly sol in benzene, Aq solns are clear, colorless, and foam profusely on shaking- pH of 10% soln 6.42 of 1% commercial product at 25 5,5 of 0,1% 6,8, Surface tension values at 25 (by the capillary rise method) range from 26,75 dynes/cm (]0% soln) to 22.08 dynes/em (0.1% soln). Incompatible with soap. therap cat Topical anti-infective. 

From Eq. (10.2.4) it is evident that for small capillaries Hg can become relatively large. For example, for water with o- = 73mNmin a 0.1-mm-radius clean glass capillary the liquid will rise to an equilibrium height of about 0.15 m. The capillary rise method is one of the most accurate means for the measurement of surface tension. 

In the capillary rise method, the surface tension, 7, of a liquid can be determined from the height, h, of the liquid column in a capillary tube of radius r. If the liquid completely wets the tube (zero contact angle). 

Figure 2.4. Measurement of surface tension by the differential capillary rise method...

Equation 14 therefore represents an equilibrium dominant balance between the gravitational and surface tension forces. Thus, given that p and cos 0 are known for a given fluid, the capillary rise can be determined. It is also evident from Eq. 14 that the capillary rise is dependent on the capillary radius. For small capillaries, H can therefore become relatively large. This capillary rise method is therefore very useful and accurate for measuring the surface tension of liquids. 

Classically, the approach used to calculate capillary flow has been to determine the curvature of liquid interfaces in the system and calculate Pcap from Equation (6.1). Those values could then be used to calculate the direction and magnitude of the driving forces. In systems of simple geometry such as liquids which form spherical interfaces and smooth cylindrical solid surfaces, the technique works out very well. Perhaps the best known example of such a system is the capillary rise method for determining the surface tension of a hquid, illustrated in Figure 6.10. In this system, capillary forces cause the hquid to rise in the tube due to differences in curvature of the liquid-air interface within the tube (a small radius of curvature) and that in the reservoir... 

FIGURE 6.10. In the capillary rise method of surface tension measurement, surface tension effects canse the wetting hquid to rise in the small capillary to a height that just balances the hydrodynamic force dne to gravity (a). For non-wetting liquids such as mercury, a depressing effect is observed (Z>). 

Equation 6.9 is the classic equation for determining the surface tension of a liquid by the capillary rise method. When 9 = 0°, the equation simplifies to... 

The capillary rise method was used to measure the surface tension of a liquid that wetted glass. A glass capillary tube of 0.0200 cm diameter was used and a capillary rise of 10.47 cm was measured. The liquid density was 1.000 g cm". What is the surface tension of the liquid What influence do corrections for the weight and nonsphericity of the meniscus have on the surface tension ... 

Jones G, Ray J (1939) A theoretical and experimental analysis of the capillary rise method for measuring the surface tension of solutions of electrolytes. J Am Chem Soc 59 187... 

Surface tension of liquids can be measured by either of the two methods static and dynamic. The static methods are based on the assumption that the liquid has attained surface equilibrium. For pure liquids and solutions of crystalloids the process of attainment of equilibrium is very fast and the static methods are best suitable. But for colloidal solutions a considerable time is required to reach the equilibrium state and therefore the dynamic methods of measuring surfacf tension are preferred. The dynanJc methods measure the tension of a liquid before the surface film has had time to form. TTiere are other methods too which fall between the static and the dynamic methods. Among the static methods, the most commonly used ones are (0 the capillary rise method, (ip the du Nouy ring method, (Up the Wilhelmy balance method, and (iv) the drop-weight method.,... 

Capillary Rise Method In this approach a capillary tube is immersed into the liquid. The surface tension is calculated by measuring the liquid height in the capillary tube via Eq. (9). The capillary rise is also a measure of the vertical component of surface tension. 

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