# CSC Scientific Blog

The definition of Liquid Surface Tension is simple.

It's the force that keeps a liquid from flying off into space.

However, the measurement of surface tension can take many forms, which can be confusing. In an attempt to get some clarity, we have articulated two principle measurement concepts in this article: drop-based measurement and force-based measurement.

## Drop-Based Concepts of Surface Tension Measurement

One of the concepts is based on the analysis of a drop. This analysis can be:

1. A complex optical analysis of the drop shape,
2. Related to the pressure needed to make a bubble burst, or,
3. Associated with the time it takes a series of drops to traverse a tube of small diameter.

These methods either require advanced mathematical analysis, or are hard to perform.

## Force-Based Concepts of Surface Tension Measurement

The other concept is based on the force exerted on a foreign body by the surface of a liquid. The underlying task is the measurement of the this force.

One of these techniques, known as the DuNouy Ring method, starts with the insertion of a ring below the liquid surface. The ring is moved upward through the interface between the liquid and the air (or between the liquid and a lighter or less dense liquid). The force required to get the ring free of the surface or interface is measured.

The other major force method uses a thin rectangle. The rectangle and the test process are referred to as Wilhelmy Plate. When the plate is lowered to touch the liquid, the surface tension grabs the plate and pulls down. The level of this force is used to calculate the surface tension of the liquid.

## Bubble and Drop Techniques for Surface Tension Determination

The test routines we classified as drop-based include Spinning Drop, Pendant Drop, Bubble Pressure, and investigation of capillary rise and drop volume.

Spinning Drop is useful for very low surface tension liquids. Pendant drop analysis has the benefit of characterizing network properties. Bubble pressure instruments are particularly useful for in-line measurement and for time-phased changes.

The other techniques that include capillary rise and drop volume are used for special applications and education.

## Surface Tensiometers — DuNouy Ring and Wilhelmy Plate

Our target is techniques of force measurement. Some of the earliest measurements were with the DuNouy Ring. This measurement starts when a ring is fully below the liquid surface.

At that juncture there is no force on the ring, except gravity. A force measuring mechanism is used to pull the ring up through the liquid surface. A retarding force begins as the ring approaches the surface, and reaches a maximum when the ring releases from the liquid above the surface. This maximum force is the basis for calculating surface tension.

Some of the early surface tension instruments used a torsion balance mechanism to determine this force. This mechanism is still used today. When calibrated, these torsion balances provide a sensitive, solid, geo-mechanical structure to ensure precision and  repeatability. Newer designs use electronic balances to measure the forces.

The plate technique (Wilhelmy Plate) uses a thin rectangle, often made of platinum. As the plate is inserted into a liquid, the surface tension force pulls the plate downward. This force is used to calculate the final result. The forces on the Wilhelmy Plate are usually measured with an electronic balance.

The calculation of surface tension is usually in terms of Dynes/cm as follows:

• For the DuNouy ring method, the formula uses the inner and outer radius of the ring and the force required to pull the ring through the surface.
• For the Wilhelmy Plate, the formula uses the downward force of the liquid against the plate and the perimeter of the plate.
One of the new developments based on Wilhelmy concepts is the use of platinum rods instead of plates. These use the same factors of force and circumference to calculate the surface tension.

## Apparent and Actual Surface Tension

The DuNouy Ring method measures apparent surface tension.  A conversion formula is needed to obtain actual surface tension. The correction factor ranges from 0.8 times the apparent surface tension at low levels to more than 1.3 times the apparent surface tension for liquids with high surface tension. In many industrial applications, standards are based on apparent readings.

Wilhelmy Plate results are actual surface tension and do not need correction.

## Applications for DuNouy Ring and Wilhelmy Plate Instruments

Force-based surface tension instruments have a wide application range. Here is a sample of applications:

• Testing transformer oils
• Checking surfactant content
• Quality assurance and optimization of emulsifiers
• Determining effectiveness of wetting media
• Checking electroplating baths

## Take Away

In summary, we defined two categories of surface tension instruments.

Drop-based instruments, which include Spinning and Pendant Drop instruments, use complex optical drop shape analysis. Bubble Tube instruments are suited to in-line and portable use. There are a number of instruments based on capillary action used for special measurement and education.

Force-measuring surface tensiometers, which include DuNouy Ring and Wilhelmy Plate instruments, have a long history and a wide scope of applications. The available instruments range from manual classics to multi-task automated devices. Prices for the manual classic instrument start at a few thousand dollars. Costs for automated multi-task surface tensiometers can exceed \$50,000.

If you find this article useful, please share it with associates who deal with liquid surface tension.

I start on these subjects that seem to be clear-cut and easy to describe, but they end up with snags that mystify me.

Hope this treatise is useful,

Art