Maximum bubble pressure method

Theory: Dynamic Surface Tension

Though the static surface tension is obtained with conventional surface tension measuring methods based on static equilibrium state, such as the Wilhelmy plate method, many fluids which contain surfactant molecules or other impurities require a much longer time than water and other liquids to achieve a completely formed surface which is in dynamic equilibrium. This is because of the molecular construction of the surfactants: they consist of a hydrophilic water-attracting head group and a hydrophobic water-repelling tail group. As a result of this molecular structure the surfactant molecules migrate to and occupy the space called “interface” between the gas and fluid, where the tail projects from the surface and causes a reduction in the surface tension. Such a process is shown in the following illustration (σ_t1 > σ_t2 > σ_equilibrium).

Surfactants greatly reduce the surface tension of solvents, water and water-based solutions, inks, fountain solutions, adhesives and other coating formulations. To reduce the surface tension, however, the surfactant molecules have to migrate to the interface, and this takes some finite amount of time. Given enough time, the formulation will eventually reach equilibrium surface tension. This takes several seconds or even several minutes depending on the type of surfactant and the concentration. The molecular mobility of the surfactants used assumes a considerable influencing factor on the formation of the surface tension. In addition to the chemical structure, the concentration also has a decisive influence on the surface tension. The equilibrium value of the surface tension decreases as the number of surfactant molecules accumulating at the surface increases. It achieves its final value when the surface is completely occupied and offers no place for further molecules. If the concentration is further increased from this point then the surfactant molecules will accumulate within the solution and form aggregates, the so-called “micelles”. The concentration at which this effect occurs is known as the “critical micelle formation concentration” (CMC) which is an important characteristic for surfactants. This means that methods for measuring the dynamic surface tensions should only be used above the CMC. In such a case the concentration only influences the chronological function of the surface tension and no longer has any influence on its static value. The following illustration shows the measuring ranges of static and dynamic methods (e.g. the bubble pressure method).

Bubble Pressure Method

One of the useful methods to determine the dynamic surface tension is measuring the maximum bubble pressure. In a bubble pressure tensiometer gas bubbles (ex. Air) are produced in the sample liquid at an exactly defined bubble generation rate. The gas bubbles enter the liquid through a capillary whose radius is known. Through the attraction between the molecules of a liquid, air bubbles within a liquid are also subject to these forces i.e. a bubble formed within a liquid is being compressed by the surface tension. The resulting pressure rises with the decreasing bubble radius. This increased pressure, in comparison to the outside of the bubble, is used to measure surface tension. Air is pumped through a capillary into a liquid. The created bubble surface bulges and hence continuously decreases the bubble radius. During this process the pressure rises to a maximum pressure. Here the bubble has its smallest radius. This radius equals the radius of the capillary and forms a half sphere. After passing this point the bubble bursts and breaks away from the capillary. Now a new bubble can form at the capillary. During this process the pressure passes through a maximum whose value is recorded by the instrument. Following scheme shows each step of bubble forming and pressure change.

A, B: A bubble is formed and the pressure is below the maximum pressure; the radius of curvature of the air bubble is larger than the radius of the capillary.
C: The pressure curve passes through a maximum. At this point the air bubble radius is the same as that of the capillary; the air bubble forms an exact hemisphere. The following relationship exists between the maximum pressure ρmax, the hydro-static pressure in the capillary ρ_o, the inner radius r of the capillary and the surface tension:

$\sigma ={\frac {(\rho _{max}-\rho _{o})*r}{2}}$

D: After the maximum the “dead time” of the measurement starts. The pressure decreases again, the radius of the air bubble becomes larger. The bubble finally escapes from the capillary and rises. The cycle begins again with the formation of the next bubble. Currently developed tensiometers monitors the pressure needed to form a bubble, the pressure difference between inside and outside the bubble, the radius of the bubble, and the surface tension of the sample are calculated. A data acquisition is carried out via PC control.