Surface tension describes the work required to increase the surface area of a liquid. Before an equilibrium of surface-active particles is established on the surface, this is referred to as dynamic surface tension. The maximum bubble pressure method makes it possible to determine the dynamic surface tension as a function of surface age. A bubble pressure tensiometer is required to perform the measurement.

What is surface tension?

Surface tension describes the work that must be done to increase the surface area of a liquid. It is measured in millinewtons per metre (mN/m). Surface tension is therefore an important parameter for assessing the behaviour of a liquid in contact with other phases.

Surface tension can be influenced by surface-active substances known as surfactants. Due to their structure, surfactants prefer to accumulate on surfaces. The speed at which surfactants accumulate on the surface is a characteristic parameter for each surfactant. It is determined by the diffusion and adsorption speed of the surfactant.

Static and dynamic surface tension

As the surfactant diffuses to the surface, the surface tension decreases until, after a certain time, a static surface tension is established. The surface tension values measured before equilibrium is reached are referred to as dynamic surface tension. Dynamic surface tension is specified as a function of surface age. Surface age refers to the time that has elapsed since the surface was formed.

The speed at which surfactants accumulate on a surface is relevant for the investigation of fast processes. In practice, this includes applications such as the rapid wetting of surfaces in spray processes in the field of inkjet printing, spray coating, or plant protection. Surfactants are also used in other industries, for example in the cleaning agent industry for dishwashing or laundry detergents.

Method of maximum bubble pressure for determining dynamic surface tension

The dynamic surface tension can be determined using the maximum bubble pressure method. This involves creating gas bubbles in a liquid or liquid mixture, such as water with added surfactants.

The measurement takes advantage of the fact that surface tension is related to the pressure inside the gas bubble and its radius of its curvature. Specifically, the surface tension acts against the pressure in the bubble and attempts to reduce its surface area. This relationship is defined by the Young-Laplace equation:

Δp = σ * (2/r_B)

Where the following applies:
Δp = pressure difference between the pressure inside the gas bubble and the pressure outside the gas bubble in the liquid
σ = surface tension
r_B = Curvature radius of the gas bubble

Consequently, the surface tension can be calculated from the values for the pressure difference and the radius of curvature of the gas bubble.

Experimental setup for measuring maximum bubble pressure

In practice, a bubble pressure tensiometer such as the MBP 200 from DataPhysics Instruments is used for the determination of the dynamic surface tension. In the experimental setup, the liquid is placed in a vessel under a capillary. The opening of the capillary is then immersed in the liquid. The capillary is connected to a pneumatic system that allows a controlled volume of gas to flow through the capillary. When gas is passed through the capillary into the liquid, gas bubbles form at the opening of the capillary.

The volume of a gas bubble created in this way grows steadily. Initially, the bubble has a large radius of curvature, which then becomes smaller. At the same time, the pressure inside the bubble increases (Fig. 2 [1]→[2]). When the gas bubble forms a hemisphere at the opening of the capillary, the radius of curvature reaches a minimum and the pressure reaches a maximum (see Fig. 2 [3]). The radius of curvature of the hemisphere now corresponds to the radius of the capillary opening. The moment the radii of the capillary opening (r_C) and the gas bubble(r_B) coincide, the maximum bubble pressure is reached. If the volume of the gas bubble continues to grow, the radius of curvature increases again, the pressure drops and the gas bubble breaks away from the capillary (<see Fig. 2 [4]).

The pressure sensor in the bubble pressure tensiometer can be used to determine the pressure inside the gas bubble and thus also its maximum. The pressure outside the gas bubble corresponds to the hydrostatic and atmospheric pressure of the liquid, which results from the immersion depth of the capillary. The capillary radius, which corresponds to the radius of curvature of the hemispherical gas bubble at the point of maximum bubble pressure, is known from a previous calibration measurement. The dynamic surface tension can be calculated from the values for the maximum pressure inside the bubble and the capillary radius. More precisely, the following applies at the point of maximum bubble pressure:

r_B = r_C

This results in the following modification of the Young-Laplace equation:

Δp = σ * (2/r_C)

Since we want to calculate the surface tension at the point of maximum pressure, the following applies:

σ = Δp * r_C / 2

Dynamic surface tension as a function of surface age

The surface age describes the period between the minimum pressure of a bubble – the moment when a new bubble begins to form – and its maximum pressure. The "dead time" of a bubble refers to the period between the maximum pressure and the next minimum pressure, i.e., the time when a bubble breaks away from the capillary and no new bubble has yet formed.

With a constant volume flow, the surface tension value for a specific surface age is obtained. To determine values for different surface ages, the volume flow must be varied. This is done via the valves in the pneumatic system of the bubble pressure tensiometer. This allows the time period after which the maximum pressure is reached to be varied. In this way, dynamic processes such as the speed at which surfactants accumulate on the bubble surface can be investigated.

Dynamic surface tension depends on other external variables. Measurements should therefore be carried out at well-defined temperatures and surfactant concentrations.