Susanna Laurén Sep 1, ’20 <6 min

# Pendant drop method for surface tension measurements

## Surface Science Blog

Surface tension measurements are important in many industrial applications. There are several ways to measure surface tension such asDu Noüy ring, Wilhelmy plate, and pendant drop. The first two are force-based methods whereas the pendant drop is done with the optical tensiometer.

## Pendant drop is an optical method

Surface and interfacial tension measurements can be performed optically using pendant drop shape analysis. The shape of the drop hanging from a needle is determined from the balance of forces which include the surface tension of the liquid being investigated.The surface or interfacial tension can be related to the drop shape by the equation;

γ = ΔρgR0

where γ is the surface tension, Δρ is the density difference between fluids, g is the gravitational constant, R0is the drop radius of curvature at the apex and β is the shape factor. β can be defined through the Young-Laplace equation expressed as 3 dimensionless first-order equations as shown in the image.

Modern computational methods using iterative approximations allow for solutions of the Young-Laplace equation to be found. Thus, the surface or interfacial tension between any two immiscible fluids with known densities can be determined. For optical tensiometry the size of the droplet is important, and it should have a tear or pendant shape. Care must be taken to ensure that the needle tip is not influencing the drop shape. When measuring surface tension, the density difference between liquid and gas (usually air) is large enough that volumes between 5 μl to 20 μl are generally sufficient to provide pendant or tear shapes. When measuring interfacial tensions, both density difference and interfacial tension affect the required volume to achieve a pendant or tear shape drop. As a guideline, the smaller the density difference, the larger the volume required.

## Benefits of pendant drop compared to force-based methods

The force-based methods are somewhat more established, andseveral standards描述的表面张力的测量Du Noüy ring method. The pendant drop method is however gaining popularity due to various benefits the method can offer.

1. Small sample volumes

The pendant drop method is especially suited when the sample volumes available are small. With the force-based method, the minimum sample volume is few milliliters at best but with the pendant drop, about 100 μl or even less is sufficient to conduct the measurement. This is important for example when measuring biological samples that are typically limited in volume. Small sample volumes are also beneficial when hazardous samples are measured.

2. Easy liquid handling

The pendant drop method can be done by using the disposable pipette tip. Sample can be easily drawn to the pipette. After the measurements, the pipette tip can be changed. This reduces the risk of having contaminants in the sample. It also makes the measurement of sticky samples (such as paints and glues) easier and faster, as there is no need to clean the measurements cup and probes after the measurement is completed.

3. Probe quality doesn’t affect the results

The force-based methods utilize the measurement probe i.e. the Du Noüy ring or the Wilhelmy plate to conduct the measurements. The dimensions of the probe are critical for successful surface and interfacial tension measurements. The probes are somewhat fragile and need to be handled with care to ensure the correct shape and size of the probe. With the pendant drop method, this is not an issue as the method is based on the free-hanging drop shape.

4. Check the purity of liquids before contact angle measurements

Pendant drop measurement can also be combined with the contact angle measurements easily. It is thus possible to check the purity of the liquid used before contact angle measurements. In the OneAttension software, it is possible to determine the acceptable surface tension range for the liquid used. When the contact angle measurement is conducted the software will automatically check the purity of the liquid before droplet deposition.

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