The Wilhelmy plate method is a force-based measuring method for determining the interfacial and surface tension of a liquid. A tensiometer with a high-precision balance is required to carry out this measurement. The so-called Wilhelmy-equation is then used for the calculation.

The interfacial tension of a liquid describes the tension force that counteracts an enlargement of the interface. It allows conclusions to be drawn about how well the liquid spreads on a solid or mixes with another liquid.

A common method for determining surface and interfacial tensions is the Wilhelmy plate method. This force-based method can be carried out with tensiometers, for example those of the DCAT series from DataPhysics Instruments.

The measurement setup of the Wilhelmy plate method

The most important component of a tensiometer is a high-precision balance, often in the upper part of the device. The sample body, in this case the Wilhelmy plate, is suspended from this balance. A Wilhelmy plate is a thin, usually rectangular plate, coated with a platinum-iridium alloy, a few centimeters in length and height. The material is chosen so that it wets easily on contact with a liquid.

A container with the liquid to be examined is placed on a height-adjustable table under the Wilhelmy plate (see Figure 2). The table is then slowly moved upwards until the surface of the liquid touches the Wilhelmy plate. A lamella then springs against the plate, the shape of which is determined by the surface tension of the liquid.

In practice, complete wetting is favored by the plate material platinum-iridium and is also ensured by the measurement procedure: The Wilhelmy plate is first immersed in the liquid and then withdrawn to the touch position. The prior wetting of the surface ensures that the lamella accurately reflects the surface tension.

Determining the surface tension with the Wilhelmy plate method

The volume and therefore the weight of the lamella depends on the wetted length of the Wilhelmy plate (see Figure 3). The line where the upper edge of the lamella, the plate, and the ambient air meet is called the three-phase contact line. A tension force F_tens acts here (see Figure 3). F_tens can be divided into a force parallel F_∥ and a force perpendicular F_⊥ to the liquid surface:

Only the tension force component F_⊥, i.e., the component that is perpendicular to the surface of the liquid, acts on the scale. It corresponds to the weight F_G of the formed lamella, which can be determined using the balance. It should be noted that the weight of the Wilhelmy plate does not play a role here, as the balance of the tensiometer is calibrated at the start of the experiment with the Wilhelmy plate attached. Together with the definition equation for surface tension, this gives the so-called Wilhelmy equation:

The following symbols have been used:

• F_tens: tension force acting on the Wilhelmy plate
• F_∥: force parallel to the liquid surface
• F_⊥: force perpendicular to the liquid surface
• F_G: weight force of the formed lamella
• Θ_C: static contact angle
• σ: surface tension
• L: wetted length of the Wilhelmy plate

When the Wilhelmy plate is completely wetted, i.e., at a contact angle of 0°, the equation is simplified and thus enables the surface tension to be determined directly from the plate dimensions and the measured weight force.

Measuring and determining the interfacial tension using the Wilhelmy plate method

Just as the surface tension, the interfacial tension between two liquids can also be determined using the Wilhelmy plate method. This involves determining the weight of the lamella that forms when the Wilhelmy plate is situated at the interface between the two liquids. To do so, the plate is placed in the upper, i.e., less dense or "lighter" phase, where it experiences a certain buoyancy force.

The measurement is carried out as follows: First immerse the Wilhelmy plate completely in the liquid of the "lighter" phase and tare the balance in this state. The vessel with the lighter liquid is then removed from the sample table and replaced with a vessel containing the "heavier" liquid. To form the interfacial lamella, the Wilhelmy plate is completely immersed in the "heavier" liquid. The "lighter" liquid is then carefully poured onto the existing "heavier" liquid and the Wilhelmy plate is pulled back up to the interface. The weight now measured corresponds to the weight of the interfacial lamella, so that the interfacial tension can be determined using the Wilhelmy equation.