# Stalagmometer

A stalagmometer a simple and normally manual instrument for measuring the surface tension (SFT) of liquids and, more rarely, the interfacial tension (IFT) between two liquids. The measurement involves determining the mass or volume of drops of liquid falling from the tip of a vertical capillary after flowing through it. The stalagmometer is an earlier form of the drop volume tensiometer, which measures the dynamic IFT or SFT with the help of an electronically controlled liquid feed and optical drop detection.

## Background

According to Tate's law, the mass m of the falling drops depends on the surface tension (SFT) σ, the inner capillary radius r and the acceleration due to gravity g:

This equation describes the fact that the drop falls at the exact moment that its weight counterbalances the force to be applied to form the new liquid surface at the breakaway limit. The mass or, assuming the density of the liquid is known, the volume of the drops is measured. It is also possible to count the drops which are formed from a given volume. If the internal diameter of the capillary is not known exactly, the relative SFT of the sample can be measured in relation to a liquid with known SFT (usually water).

## Applicability to surfactant solutions

The measured result is not a static but a dynamic SFT, as the measurement is carried out as a new surface forms. In the case of surfactants, due to the diffusion and adsorption dynamics, the result depends on the surface age at the moment of breakaway, as long as an equilibrium value has not yet been reached. With a manual stalagmometer, the flow rate, and therefore the surface age, can only be adjusted to a very limited extent. It also changes during the course of the measurement due to the reducing hydrostatic pressure. This effect therefore cannot be quantified.

## Use of the measuring principle in a drop volume tensiometer

With electronic drop volume tensiometers, it is possible to predetermine the flow speed and to vary it over a large range. These instruments make use of the dependency of the IFT or SFT of a surfactant solution on the surface age in order to investigate the dynamic properties of a surfactant and to quantify their behavior in technical processes with different speeds. Furthermore, with low flow rates, it is often possible to measure the equilibrium value of the IFT/SFT, which corresponds to the result of a static measurement.

## Bibliography

T. Tate, Phil. Mag. 22, 176 (1864)