Stalagmometric method

The stalagmometric method is one of the most common methods for measuring surface tension. The principle is to measure the weight of the drops of the fluid falling from the capillary glass tube, and then calculate the surface tension of the specific fluid which we are interested in. We know the weight of each drop of the liquid by counting the number of the drops falling out. From this we can determine the surface tension ^{[1] [2]}

Stalagmometer

A stalagmometer, straight form.

A stalagmometer is a device for investigating surface tension using the stalagmometric method. It is also called a stactometer or stalogometer. The device is based on a capillary glass tube whose middle section is widened. In terms of the volume of the drop, it could be calibrated to the same size based on the design of the stalagmometer. The part of the bottom of the device is narrowed down to let the fluid fall out from the tube in a shape of drop.^[2][3] In the experiments, the drops of the specific fluid are flowing slowly from the tube in a vertical direction. The drops hanging on the bottom of the tube start to fall when the volume of the drop reaches the maximum value which is dependent on the characteristic of the solution. In this moment, the weight of the drops is in an equilibrium state with the surface tension. Based on the Tate’s law:^[4]

The drop is falling when the weight (mg) is equal to the circumference (2πr) multiplied by the surface tension (σ). The surface tension can be calculated provided the radius of the tube (r) and mass of the fluid droplet (m) are known. Alternatively, since the surface tension is proportional to the weight of the drop, the fluid of interest may be compared to a reference fluid of known surface tension (typically water):

In the equation, m₁ and σ₁ can be the mass and surface tension of the reference fluid, and m₂ and σ₂ can be the mass and surface tension of the fluid we want to investigate. If we take water as a reference fluid, then:

If the surface tension of water is known, we can calculate the surface tension of the specific fluid from the equation. The weight of more drops we measure, the more precise we calculate the surface tension from the equation.^[2] One thing we need to notice is that keeping the stalagmometer clean is really important so as to get meaningful reading. There are commercial tubes for stalagmometric method in three kinds of size: 2.5, 3.5, and 5.0 (ml). The size of 2,5 (ml) is suitable for small volume and low viscosity, of 3.5 (ml) for relatively high viscous fluid, of 5.0 (ml) for large volume and low viscosity, 2,5 (ml) for small volume and high viscosity and are flexible for different size of most of the fluids.^[5] "Survismeter" produces ultra accurate results of surface tension along with viscosity, interfacial tension, wetting coefficient and density data. The survismeter is most accurate and safer for volatile, inflammable and carcinogenic liquids.

Modified method

During the experiment, we may sizes of the drops each time, thus reduce the precision of value of the surface tension. The stalagmometric method was currently improved by S. V. Chichkanov and his colleagues^[1] that they modify the experiment to measure the weight of the drops in a fixed number rather than directly measure the number of the drops. The modified method to determine the surface tension based on the weight of the drops in a fixed number can be more precise than the original method based on the number of drops, especially for the fluid which surface is highly active. The advantage of the modified method is that it actually get more precise value of the surface tension and reduce the duration of experiments.^[1]

References