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# Bubble pressure tensiometer

A bubble pressure tensiometer is an instrument for determining the dynamic surface tension. The maximum internal pressure of a gas bubble which is formed in a liquid by means of a capillary is measured.

###### Background

According to the Young-Laplace equation, the internal pressure p of a spherical gas bubble (Laplace pressure) depends on the radius of curvature r and the surface tension σ.

When a gas bubble is produced in a liquid at the tip of a capillary, the curvature initially increases and then decreases, resulting in the occurrence of a pressure maximum. The greatest curvature and therefore the greatest pressure occurs when the radius of curvature is equal to the radius of the capillary.

The radius of the capillary is determined with a reference measurement carried out with a liquid with known surface tension, usually water. Once the radius is known, the surface tension can be calculated from the pressure maximum Pmax. The hydrostatic pressure P0 due to the immersion of the capillary must be subtracted from the measured pressure (which is done automatically with state-of-the-art instruments). This results in the following formula for the bubble pressure measurement:

###### Analyzing the dynamic behavior of surfactants

The measured value corresponds to the surface tension at a certain surface age, the time from the start of the bubble formation to the occurrence of the pressure maximum. The dependence of surface tension on surface age can be measured by varying the speed at which bubbles are produced.

This dependency plays an important part in the use of surfactants, as in many processes the equilibrium value of the interfacial tension is never reached due to the sometimes low surfactant diffusion and adsorption rates.

Bubble pressure measurements enable surfactant rate parameters such as the diffusion coefficient and the adsorption coefficient to be calculated.

###### Determining the surfactant content in cleaning and coating baths

Measurements of the dynamic surface tension are also used for an indirect determination of the concentration of cleaning or wetting agents in industrial baths. The concentration in such liquids usually lies above the critical micelle concentration (CMC), i.e. in a range where the static SFT does not change with increasing concentration. However, this does not apply to the dynamic SFT, which shows a strong dependency on the concentration at short surface ages. When recording measuring curves in a wide dynamic range from short to long surface ages for different surfactant concentrations (see figure above), the optimal surface age and a calibration curve can be obtained and then used for quality control of cleaning or coating baths by carrying out single-point measurements.