The Drop Weight Method

This is a fairly accurate and convenient method for measuring the surface tension of a liquid-vapor or liquid-liquid interface. The procedure, in its simpli-est form, is to form drops of the liquid at the end of a tube, allowing them to fall into a container until enough have been collected to accurately determine the weight per drop. Recently developed computer-controlled devices track individual drop volumes to = 0.1 p [32]. 

The method is a very old one, remarks on it having been made by Tate in 1864 (33), and a simple expression for the weight W of a drop is given by what 

Here again, the older concept of surface tension appears since Eq. 11-22 is best understood in terms of the argument that the maximum force available to support the weight of the drop is given by the surface tension force per centimeter times the circumference of the tip. 

In actual practice, a weight W is obtained, which is less than the ideal value W. The reason for this becomes evident when the process of drop formation is observed closely. What actually happens is illustrated in Fig. 11-10. The small drops arise from the mechanical instability of the thin cylindrical neck that develops (see Section II-3) in any event, it is clear that only a portion of the drop that has reached the point of instability actually falls—as much as 40% of the liquid may remain attached to the tip. 

The usual procedure is to apply a correction factor/ to Eq. 11-22, so that W is given by 

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Harkins and Jordan [43] found, however, that Eq. 11-26 was generally in serious error and worked out an empirical correction factor in much the same way as was done for the drop weight method. Here, however, there is one additional variable so that the correction factor/ now depends on two dimensionless ratios. Thus... 

The surface tension of a liquid is determined by the drop weight method. Using a tip whose outside diameter is 5 x 10 m and whose inside diameter is 2.5 x 10 m, it is found that the weight of 20 drops is 7 x 10 kg. The density of the liquid is 982.4 kg/m, and it wets the tip. Using r/V /, determine the appropriate correction factor and calculate the surface tension of this liquid. 

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 same system has been studied previously by Boguslavsky et al. [29], who also used the drop weight method. While qualitatively the same behavior was observed over the broad concentration range up to the solubility limit, the data were fitted to a Frumkin isotherm, i.e., the ions were supposed to be specifically adsorbed as the interfacial ion pair [29]. The equation of the Frumkin-type isotherm was derived by Krylov et al. [31], on assuming that the electrolyte concentration in each phase is high, so that the potential difference across the diffuse double layer can be neglected. 

The slow formation of a drop at a submerged circular orifice or nozzle will result in a drop size, predicted by equations for determining interfacial tension by the drop-weight method. At the instant a slowly forming drop breaks away from a nozzle, the force balance may be written... 

Many modifications of the drop weight method have been utilised in practice. 

As we shall have occasion to note in dealing with solutions, the composition of the surface phase is very different from that of the bulk liquid. When a liquid interface is newly formed the system is unstable until the surface phase has acquired its correct excess or deficit of solute by diffusion from or into the bulk of the solution. This process of diffusion is by no means instantaneous and, as has been observed in discussing the drop weight method, several minutes may elapse before equilibrium is established. In the ripple method the surfece is not renewed instantaneously but may be regarded as undergoing a series of expansions and contractions, thus we should anticipate that the value of the surface tension of a solution determined by this method would lie between those determined by the static and an ideal dynamic method respectively. 

Goard has determined the surface tensions of a few salt solutions hy the drop weight method employing the method of Iredale for calculating the surface tension, the following values were obtained. 

The surface tension of mercury in the presence of the vapour at various partial pressures was measured by the drop weight method. The following values were obtained for the surface tensions of mercury in the presence of vapours of methyl acetate, water and benzene at various partial pressures at 26 —27° C. 

OP) J. McCormack et al, "A New Procedure for the Estimation of the Impact Sensitiveness of Explosives , Explosivstoffe 17(10), 225—28(1969). Abstracted in Expls Pyrots 3(8), 1970 (Measurement of the Figure of In sensitiveness for relatively insensitive expls by the drop weight method is improved by detecting gas evolved in "no-fires" with starch-iodide impregnated filter paper. Quantities of gas less than 1 cc are readily detected)... 

Impact Sensitivity. Values determined by the drop weight method have the usual dependence... 

Several additional points might be noted about the use of the Bashforth-Adams tables to evaluate 7. If interpolation is necessary to arrive at the proper (3 value, then interpolation will also be necessary to determine (x/bl. . This results in some loss of accuracy. With pendant drops or sessile bubbles (i.e., negative /3 values), it is difficult to measure the maximum radius since the curvature is least along the equator of such drops (see Figure 6.15b). The Bashforth-Adams tables have been rearranged to facilitate their use for pendant drops. The interested reader will find tables adapted for pendant drops in the material by Padday (1969). The pendant drop method utilizes an equilibrium drop attached to a support and should not be confused with the drop weight method, which involves drop detachment. 

Harkins and his colleagues1 have extended these measurements of the work of adhesion to water, and also to mercury.2 The measurements of surface tension were made by the drop-weight method, using the corrections necessary for accurate results as three separate measurements of surface tension are required, considerable accuracy is desirable for trustworthy results in the work of adhesion. 

There are static and dynamic methods. The static methods measure the tension of practically stationary surfaces which have been formed for an appreciable time, and depend on one of two principles. The most accurate depend on the pressure difference set up on the two sides of a curved surface possessing surface tension (Chap. I, 10), and are often only devices for the determination of hydrostatic pressure at a prescribed curvature of the liquid these include the capillary height method, with its numerous variants, the maximum bubble pressure method, the drop-weight method, and the method of sessile drops. The second principle, less accurate, but very often convenient because of its rapidity, is the formation of a film of the liquid and its extension by means of a support caused to adhere to the liquid temporarily methods in this class include the detachment of a ring or plate from the surface of any liquid, and the measurement of the tension of soap solutions by extending a film. 

For rapid work, requiring an accuracy of about three-tenths per cent., Sugden s modification of the maximum bubble-pressure method is probably the most convenient very little apparatus is required, and a complete measurement can easily be made in 15 minutes. Two or three cubic centimetres of the liquid are all that is necessary. The drop-weight method (using Harkins s indispensable corrections) is also simple and equally accurate. 

Only the two first methods allow measurement of the temperature coefficient of the surface energy. The maximum bubble pressure technique is well-adapted for metals with low and intermediate melting points and specially for oxidizable metals, while the sessile drop technique has been applied with success to measure ctlv values up to 1500°C. The drop weight method is particularly useful for very high melting-point metals because it avoids liquid contact with container materials. This is also true for the recently developed levitation drop technique that analyses the oscillation spectrum of a magnetically levitated droplet. 

The capillary tube method can be used to determine the interfacial tension Gi2 between two immiscible, or partially miscible liquids (Fig. 12.VIII G.) The drop weight method ( 14.VIIIG) has also been used. Bartell, Case, and Brown measured the interfacial tensions between mercury and organic liquids by the capillary tube and the drop weight methods and found that the two methods gave the same results. Some values for water are also given. Values in dynes/cm. are ... 

The question of the existence of an adsorbed gas film on liquids has some bearing on the drop-weight method. A micro-method in which drops are delivered from a micrometer syringe has been used. ... 

The drop-weight method was used by Morgan and co-workers, and Harkins and co-workers, 1 who used the formula ... 

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