Surface tension

The ring method

Historically the ring method was the first to be developed; this is why many of the values for interfacial and surface tension given in the literature are the results of the ring method.

In the ring method the liquid is raised until contact with the surface is registered. The sample is then lowered again so that the liquid film produced beneath the ring is stretched.

: Schematic diagram
of the ring method

: Change of force
with ring distance

As the film is stretched a maximum force is experienced; this is recorded in the measurement. At the maximum the force vector is exactly parallel to the direction of motion; at this moment the contact angle θ (see Figure above) is 0°.

The following illustration shows the change in force as the distance of the ring from the surface increases.

: Change of force with ring distance

In practice the distance is first increased until the area of maximum force has been passed through. The sample vessel containing the liquid is then moved back so that the maximum point is passed through a second time. The maximum force is only determined exactly on this return movement and used to calculate the tension.

The calculation is made according to the following equation:

$\sigma = \frac{F_{max} - F_V}{L \cdot cos \theta}$

( $\sigma$ =surface or interfacial tension; $F_{max}$ =maximum force; $F_V$ =weight of volume of liquid lifted; $L$ =wetted length, $\theta$ =contact angle)

The contact angle $\theta$ decreases as the extension increases and has the value 0° at the point of maximum force, this means that the term cos $\theta$ has the value 1.

Ring-tear-off

The film breakage is avoided during the measurement in most cases. Nevertheless, the point of film breakage can also be measured with the “Ring-Tear-off”-Method.

Correction calculations for the ring method

The weight of the volume of liquid lifted beneath the ring, expressed by the term F_V, must be subtracted from the measured maximum force as it also affects the balance.

A solution must also be found for a further problem: the curve of the film is greater at the inside of the ring than at the outside. This means that the maximum force (at which the contact angle θ = 0°is reached at different ring distances for the inside and outside of the ring; as a result the measured maximum force does not agree exactly with the actual value.
The correction methods available apply to different ranges of values. You must select the suitable correction method for your application; with the K11 or K100, the calculation is carried out automatically. The three possible correction methods are:

Harkins & Jordan:
Harkins & Jordan have drawn up tables of correction values by determining different surface tensions with rings of different diameters. This comprehensive program of measurements also provides the basic data for the corrections according to Zuidema & Waters and Huh & Mason.
The Harkins & Jordan correction offers the greatest accuracy, but it is possible to imagine liquid systems which are outside the range of validity for the Harkins & Jordan method. However, in practice such a case is extremely rare.

Zuidema & Waters:
Zuidema & Waters needed correction values for small interfacial tensions. For this reason they carried out interpolation calculation on the data from Harkins & Jordan in order to cover the range of small interfacial tensions more accurately. However, the Zuidema & Waters corrections have the greatest deviation range of all corrections and should only be used for comparative measurements with values given in the literature.

Huh & Mason:
Huh & Mason have used mathematical methods to increase the range of application of the correction calculation; this means that this correction method has the largest range of validity while still possessing sufficient accuracy. This is why we have chosen this correction method as the standard one. If you want to make measurements with the greatest possible accuracy you should change to the Harkins & Jordan correction method but keep its range of validity in mind.