Form my opinion influences of surfactants (particles or molecules) are very similar whereby some differences due to the size are likely (even more non-ideal situation). --> just a value obtained

For example start with the ideal case of two liquid phases A, B. If A is not soluble in B and vice versa this results in in an interphase with a “sharp” transition of the molar fractions which can be assumed by a Gibb’s dividing surface resulting in the interfacial tension for AB system. Note that even in this case the position of the zero surface excess for compound A and B will most likely not be the same. Hence the energy and forces (I guess a tensiometric method is used to measure the values) are also dependent from the chemical potential (of the compounds within the phases).

If we add a non-soluble surfactant C this results in a significant variation of the interphase. In ideal case we will have three phases ACB (as correclty stated in your question) with a surface between AC and a surface between CB. It is more likely (due to the dimensions) that a molecule can result in the ideal case (no AB surfaces). We cannot assume the interphase as one surface (strictly speaking) if we have a surface excess of C compound (resulting in something like a own phase) and we cannot call this the variation in the interfacial tension of the AB system. From my opinion this is a completely different situation. We might call it surface tension of this system (ABC, T, p) even if for me presenting the influence on the measured signal (use this as name) is more reasonable than calling the measured value by some names or even calulating some other values.

The question is closely related to the discussion whether Wenzel and Cassie models for wetting angle of rough and heterogeneous surfaces are conceptually correct - I recommend the work of Marmur and Bittoun which gives a straightforward answer:

http://pubs.acs.org/doi/abs/10.1021/la802667b.

My short answer - I disagree. Unique interfacial tension of a heterogeneous surface can be defined theoretically and measured, provided that the length scale of the heterogeneity is much smaller than the length scale of the capillary shape one looks at (e.g. particle size much smaller than capillary length). The general definition of surface tension as stress tensor excess is not limited by the complexity of the surface. Of course, time scale to reach equilibrium may be long for a complex surface.

I agree this is a dark area of knowlege with ill-defined quantities. The length-scale (mentioned above) is a clever approach, I think. We have methods of measuremenet of surface tension (such as bubble pressure, etc...). Now, the question is if the particles are much smaller than the length taken into account by this measurement, then some "modified surface tension" is obtained as a result. First, it can be considered "just as a number". But it provokes a theoretical task: connect the real surface tension (without particles) + maybe wettability of the particles + maybe their surface coverage (etc...) with this new measured value. I am interested to see further ideas, or even be part of a paper to be developed ([email protected]). Let me send my recent papers on Gibbs - Langmuir - Butler. with my best, George (the attached file: G. Kaptay: On the partial surface tension of components of a solution. Langmuir, 2015, vol.31, No.21, pp. 5796-5804.)

My argument is simply from what one should consider an interface. When we define particles, automatically they have an interface with surrounding media. When they are located at the interface and we neglect their interface to the other phases we would conclude that they influence interfacial tension. But why should we do this. Problem of interfacial tension towards a heterogeneous surface (on a molecular level) is different. As soon as we have 3 phases, e.g. 2 fluid and a solid we have fluid-fluid and fluid-solid interfaces, respectively the related interfacial tensions.

Dear Titus, you are absolutely right. But in engineering / practice, people can apply surface tension measurmenet techniques to interfaces with particles, and get a number. Although it is ill defined to call it "surface tension", it is a measurable and reproducible quantity, so it is a scientific quantity. Maybe we have to find another name for it. And certainly we need to understandd the connection between real surface tension and this "whatever surface tension". George