Pendent drop method

Basically one measures the force required to detach a ring or loop of wire from the liquid/liquid interface [6], As a first approximation, the detachment force is taken to be equal to the interfadal tension y muMphed by the perimeter of the ring, i.e., 

Values of the correction factor / were tabulated by Harkins and Jordan [7]. A theoretical account of f was given by Freud and Freud [8]. 

When using the du Nouy method to obtain y the ring must be kept horizontal during the measurement. Moreover, the ring should be free from contaminant, which is usually achieved by using a platinum ring that is flamed before use. 

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A recently developed modification of the pendent drop method gives definite area changes of the drop surface, which can be used to initiate transient relaxation processes (Miller et al. 1993a, b). A metering system consisting of two syringes (cf Fig. 6.7) is used to form a drop... 

Fig. 6.7 Video enhanced pendent drop method modified for relaxation experiments according to Miller et al. (1993a)...

It should be possible to describe the exchange of matter by a diffusion model for surfactant mixtures, as shown by Miller et al (1993b). They also developed another new relaxation technique, based on the pendent drop method (cf. Section 6.3.4), and studied the relaxation behaviour of SDS at the water/air interface. It could be shown that surface active impurities can alter the relaxation behaviour of the adsorption layer tremendously. The same method was also applied to detect impurities in organic solvents (cf Section 5.1.2., Fig. 5.7.). 

Surface tension relaxation to a surface area square pulse of an aqueous 0.1 mg/ml HA solutions with the modified pendent drop method at the water/air interface symbols - experimental data,... 

The advantages of the pendent drop method is numerous only small amounts of the liquid are required, suitable for both liquid-vapour and liquid-liquid interfaces, applicable to materials ranging from organic liquids to molten metals and from pure solvents to concentrated solutions, no limitation to the magnitude of surface or interfacial tension, accessible in a broad range of temperatures and pressures. The time interval available is of the order of part of a second up to hours and even days so that extremely slow processes can be easily followed. 

Let us consider the results obtained for C QEOg for the water/hexane interface using the pendent-drop method (73). Figure 2 shows the experimental and theoretical interface-tension isotherms. 

Interfacial tension measurement techniques can be divided into two categories equilibrium and transient methods [41]. The pendent-drop method is the most commonly applied method to measure interfadal tension under pressure and involves the measurement of density differences between two fluids and the equilibrium drop profile shape. In the following section, examples of interfacial tension reduction are presented for binary polymer/C02 systems and for polymer blends. 

Li et al. [43] appHed the pendent-drop method to study the interfacial tension of a PS/CO2 system. A Hnear decrease in interfadal tension was observed in the temperature range 190-240 °C. Interfadal tension reduced from 24 to 12 dyn cm up to a pressure of 70 atm, but at higher pressure the rate of reduction was suppressed. These observations were explained by two competing effects interfacial tension reduction with temperature increase combined with a reduc-... 

The importance of interfacial tension reduction in polymer blends by CO2 has been addressed by Xue et al. [44] The pendent-drop method was utilized to investigate the interfacial tension between PS/LDPE saturated with SCCO2 and compared to the same system in the absence of CO2. At 200 °C the interfacial tension decreased from 6.62 mN m at 0.1 MPa to 4.69 mN m at CO2 pressure of 9.2 MPa, corresponding to a 30% absolute reduction. This decreased interfacial tension was explained by the presence of dissolved CO2 at the interface of the polymers reducing unfavorable interactions between the two phases and thereby enhancing the miscibility. 

The accuracy of the diameter determination depends only on the accuracy of the liquid surface tension yi, which can be measured with high precision using the pendent drop method [34,35]. 

Roe R-J, Bacchetta VL, Wong PMG (1967) Refincanent of pendent drop method for the measurement of surface tension of viscous liquid. J Phys Chem 71 4190-4193... 

Qtc is zero because Qx 0. Thus, for zero flow rate, the equation reduces to the well-known Tate s law, which is used for finding the surface tension of liquids by the pendent drop or the forming bubble method. 

Sitting or pendent drop. Both methods involve the determination of the shape of the drop in mechanical equilibrium. The shape is determined by the balance between gravitation and surface tensional forces. If gravitation is negligible the shape is always spherical irrespective of the surface tension. 

Table 1.2. Surface tensions of water in mN m , obtained by various investigations using different techniques. Temperatures in degrees Celsius. Abbreviations for methods CR = capillary rise, WP = Wilhelmy plate, DNR = Du Nouy ring, DM = other detachment method or object in the surface. HD = hanging (pendent) drop, SD = sessile drop, MBP = maximum bubble pressure DW = drop weight.

Table 1.5 reviews the capabilities of the most common (quasi-)static methods (we excluded the very fast oscillating jet and pulsating bubble), obtaining dynamic information. Some of these are intrinsically dynamic in that the measurement requires the extension of an interface (drop weight, maximum bubble pressure), so that y(t) data can in principle be obtained when the rate of extension can be varied in a controlled fashion. Others are basically static (shapes of sessile or pendent drops and bubbles), but can be rendered dynamic by disequilibratlon. 

Perhaps the most striking property of a microemulsion in equilibrium with an excess phase is the very low interfacial tension between the macroscopic phases. In the case where the microemulsion coexists simultaneously with a water-rich and an oil-rich excess phase, the interfacial tension between the latter two phases becomes ultra-low [70,71 ]. This striking phenomenon is related to the formation and properties of the amphiphilic film within the microemulsion. Within this internal amphiphilic film the surfactant molecules optimise the area occupied until lateral interaction and screening of the direct water-oil contact is minimised [2, 42, 72]. Needless to say that low interfacial tensions play a major role in the use of micro emulsions in technical applications [73] as, e.g. in enhanced oil recovery (see Section 10.2 in Chapter 10) and washing processes (see Section 10.3 in Chapter 10). Suitable methods to measure interfacial tensions as low as 10 3 mN m 1 are the sessile or pendent drop technique [74]. Ultra-low interfacial tensions (as low as 10 r> mN m-1) can be determined with the surface light scattering [75] and the spinning drop technique [76]. 

Eq. (2.18) is the exact definition of the experimental relationship for the determination of surface tension by measuring the corresponding pressure differences and radii of curvature. This relationship is the basis of many experimental surface and interfacial tension methods measuring for example the volume of detaching drops (Section 5.2), the pressure inside bubbles (Section 5.3) or drops (Section 5.5), and the shape of sessile or pendent drops (Section 5.4). 

Harmonic and transient relaxation experiments for dodecyl dimethyl phosphine oxide solutions were performed with the elastic ring method by Loglio [240]. This methods allows oscillation experiments in the frequency range from about 0.5 to 0.001 Hz and is suitable for comparatively slow relaxing systems. Slow oscillation experiments can be performed much easier now with the pendent drop apparatus [186]. Both techniques are also able to perform transient relaxation experiments. The two types of experiments have a characteristic frequency defined in the same way by Eq. (4.110). 

As mentioned above the oscillating drop or bubble method, based on profile analysis tensiometry, is the most recently developed method to investigate the surface relaxation of soluble adsorption layers. By increasing/decreasing the volume of a pendent drop or bubble, a variety of area changes can be performed, such as step, square pulse, ramp type, trapezoidal, and of course harmonic area changes at low frequencies. 

Pendent drop Surface and interfacial tension are measured by this method. 

A wide range of experimental techniques has been proposed through the years to measure the interfacial tension. Most popular has been the pendent drop technique but there has been increasing interest in techniques based upon breaking molten polymer threads. Methods of measurement of interfacial tension are summarized in Table 6.1 and values of the interfacial tension for different polymer-melt pairs are summarized in Table 6.2. The larger the polarity difference is, the larger the interfacial tension. Thus the greatest interfacial tension in Table 6,2 is for polyethylene and polyamide 6,... 

The above discussion explains the possible separation at the interface that leads to adhesive failure. The most satisfactory criterion for selecting an adhesive is its surface tension y, which should be less than the critical surface tension of wetting y. Measurement of the surface tension of an adhesive can be carried out using the pendent or sessile drop method (due to the high viscosity of most adhesives). 

The pendent drop or sessile drop method based on Axisymmetric Drop Shape Analysis (ADSA) [18], which is commonly used for surface tension measurement, has been used for measuring the density of pure polymer melts under ambient pressure. The major drawbacks of this method is the inaccuracy associated with determining the boundary of the polymer melt the required accuracy in the density of polymer melts is of three to four decimal points. 

Jennings, W.J. Pallas, N.R. An efficient (calculation) method for the determination of interfacial tensions from drop profiles (for pendent or sessile drops oriented up or down). 195th ACS National Meeting, 3rd Chemical Congress of North... 

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