Interfacial tension or surface tension is purely a phenomenon related to the surface chemistry and chemical properties of the fluid in contact with it. Therefore, the geometry of the pore should not affect the interfacial tension. However, in the nano-scale the surface forces may interact differently. The capillary forces will definitely be affected by the size and shape of the pores which I presume is not what your question is about.

Dear Reza Asin,

you may try to find the answer in the works of Edward Bormashenko on wetting of rough surfaces (for example, https://www.researchgate.net/publication/260232837_Progress_in_Understanding_Wetting_Transitions_on_Rough_Surfaces?ev=prf_pub )

Best regards

Article Progress in Understanding Wetting Transitions on Rough Surfaces

Interfacial tension or surface tension is purely a phenomenon related to the surface chemistry and chemical properties of the fluid in contact with it. Therefore, the geometry of the pore should not affect the interfacial tension. However, in the nano-scale the surface forces may interact differently. The capillary forces will definitely be affected by the size and shape of the pores which I presume is not what your question is about.

Fluid / fluid (e.g. surface tension), fluid rock (e.g. contact angle) and rock properties (e.g. pore diameter) together control fluid flow in porous media but are distinct concepts with no relationship with one another. Imperial College has put together some useful resources on the matter at http://www3.imperial.ac.uk/earthscienceandengineering/research/perm/porescalemodelling

Regards.

each of advisers (Vlad, Ramanathan and Pierre) have a very good points. I would add more simple answer to address your question: think about pore system on the surface in terms of "excluded volume" or "excluded surface". Than the surface tension will be just proportional to this value in percolation model. Note that this approach should work either for hydrophobic or hydrophilic surfaces.

The contact angle is the ONLY factor that determines whether a fluid is classified as a wetting or non-wetting fluid in contact with a particular surface.

Your question is explained with an analogy of bubble formation over a heated surface. Certain locations on a heated surface are favorable for the incipience of a vapor bubble. For a bubble to form, the vapor pressure inside the bubble should be higher than the surrounding liquid pressure, The bubble will not detach from the surface as long as the pressure difference is balanced by the surface tension of the liquid film at the interface as it holds it down. The condition for stability (the continuation of the bubble attached to the heated surface) can be ensured from a force balance. The excess pressure (pv-pl) = 2 sigma/Radius, where sigma is the surface tension and radius is that of the bubble at the mouth of the cavity.. The concept is analogous to the situation in a porous medium. In the case of a porous medium , the liquid pressure should be higher for it to flow through the pores. It depends on the geometry of the pore (diameter) and the surface tension of the liquid. This is how the property of the liquid is important.

Sadykh-Zade, E. S., Mamedov, J. G. and Rafibejli,N. M.: “Determination of the Dynamic Pressure of the Beginning of Condensation in the Presence of a porous Medium,’’ Net’i Gaz. (1963) VO1. 12, 268-270.

Sigmund, P. M., P. M. Dranchuk, N. R. Morrow, and R. A. Purvis (1973), Retrograde Condensation in Porous Media, Society of Petroleum Engineers Journal, 13(2), 93-104.

Singh, S. K., A. Sinha, G. Deo, and J. K. Singh (2009), Vapor−Liquid Phase Coexistence, Critical Properties, and Surface Tension of Confined Alkanes, The Journal of Physical Chemistry C, 113(17), 7170-7180.

Luchao, J., Yixin, M., Jamili, A., 2013. Investigating the Effect of Pore Proximity on Phase Behavior and Fluid Properties in Shale Formations. SPE Annual Technical Conference and Exhibition, 30 September-2 October, New Orleans, Louisiana, USA, 1/7, 1422-1438.