Dynamic
Surface Tension

The term “dynamic surface tension” should be reserved for a measurement in which the characteristic interfacial age is defined and the method response is understood.

Merely recording γ as a function of laboratory clock time does not automatically define the age of the measured interface.

A pendant drop created at t = 0 provides a comparatively direct age definition if the interface subsequently remains intact.

In maximum bubble pressure measurements, the surface is continuously created during bubble growth, and the relevant lifetime must be separated from deadtime and from the total bubble period.

Adsorption kinetics can be limited by diffusion from the bulk, by convective transport, by an activation barrier near the interface, by molecular reorientation after adsorption, or by combinations of these processes.

At early times, diffusion theory predicts a characteristic square-root-of-time behavior for the accumulation at an initially clean planar interface under idealized conditions.

Curvature, finite volume, concentration-dependent diffusion, micellar relaxation and nonideal adsorption complicate the picture in real experiments.

The experimentally observed γ(t) is not itself the adsorption rate.

Converting tension into Γ(t) requires an equation of state relating the interfacial composition to tension.

A kinetic model therefore contains two conceptually distinct parts: transport determines how Γ evolves, while interfacial thermodynamics determines how a given Γ maps to γ.

Failure to distinguish these steps can cause an empirical fit to be mistaken for a mechanistic adsorption law.

Many practical interfaces do not retain constant area while adsorption occurs.

Drops and bubbles can grow, and a surfactant population already adsorbed at the interface is then diluted by expansion while new molecules continue to arrive from the bulk.

MacLeod and Radke formulated a growing-drop framework in which adsorption kinetics are coupled to the time-dependent radius and surface area.

The problem illustrates why dynamic tensiometry must account for the actual area history rather than assigning all observations to a static planar interface.

Adsorption removes solute from the bulk.

In a macroscopic reservoir this depletion can be negligible; in a small pendant drop it can be substantial.

The available number of surfactant molecules scales with drop volume, whereas the adsorbing interface scales with surface area.

At low concentration and high adsorption, the final bulk concentration can therefore be significantly smaller than the nominal initial concentration. Mass balance must then be included in the interpretation.

The geometry dependence explains an experimentally important asymmetry: depletion can be pronounced for a liquid drop containing the surfactant, whereas for a bubble in a large surrounding liquid reservoir the ratio of available bulk volume to interfacial area can be far greater.

Comparing drop and bubble experiments can therefore reveal finite-volume artefacts rather than an intrinsic difference in adsorption physics.

Bubble pressure tensiometry accesses the shortest practical surface ages, while drop and bubble profile analysis extends observation to seconds, minutes and hours and is particularly versatile for liquid–liquid interfaces.

Intermediate techniques such as drop-volume methods occupy additional time windows.

A scientifically complete kinetic study may therefore combine methods rather than forcing one instrument beyond its physical range.

1. 1.A. I. Rusanov and V. A. Prokhorov, Interfacial Tensiometry, Studies in Interface Science, Vol. 3, Elsevier, Amsterdam, 1996.
2. 2.D. Möbius and R. Miller (Eds.), Drops and Bubbles in Interfacial Research, Studies in Interface Science, Vol. 6, Elsevier, Amsterdam, 1998.
3. 3.V. B. Fainerman, D. Möbius and R. Miller (Eds.), Surfactants: Chemistry, Interfacial Properties, Applications, Studies in Interface Science, Vol. 13, Elsevier, Amsterdam, 2001.
4. 4.C. A. MacLeod and C. J. Radke, A growing drop technique for measuring dynamic interfacial tension, Journal of Colloid and Interface Science 166 (1994) 73–78.