# Is there surface tension between a solid and a liquid?

The molecules of a solid are so tightly bound together that they are fixed in position unlike in a liquid or gas where they may move freely. In that case it seems like the surface tension between the liquid and solid would be zero as the solid is so rigid there are no forces acting within it that will lead to the shape of its surface deforming.

So the surface tension in this case is zero? Is that correct?

• Are you asking if a solid has surface tension? and then asking if you put it at the interface with a liquid, then that surface tension of the solid is zero? – John M Aug 14 '15 at 23:51
• Well I was under the impression that surface tension is due to a material and its interface with another medium. In this case surface tension due to solid and its interface with a liquid. – sonicboom Aug 15 '15 at 0:52
• If you drop a small marble into a cup of water will there be surface tension at the surface of the marble? – sonicboom Aug 15 '15 at 0:56
• This may help: answers.com/Q/Does_a_solid_have_surface_tension. – Ernie Aug 15 '15 at 1:14
• Not so sure I agree with that answers.com post. Atoms at a surf. have less bonds and will relax differently than atoms within the bulk leading to different elastic prop. This leads to a surf. free energy dens. $f_s = C^s_{ijkl} \epsilon^s_{ij} \epsilon_{kl}^s$ where $s$ denotes the projection of the tensor onto the surf. plane regardless of the medium the solid is in. Also $C^s_{ijkl}$ is related to an instrinsic surf. stress. In fact, some works show from the framework of DFT that there is a surf. tension that arises in some materials. See JAP 111, 124305 (2012) and PRL 109, 156104 (2012) – John M Aug 15 '15 at 2:15

Surface tension is equivalent to an interfacial energy. They are equivalent because if you increase the area of the interface you increase the energy of the interface, so you have to do work. The work done is the surface tension of the interface times the increase in area.

So we can associate a surface tension to gas-solid or liquid-solid interfaces even though the solid can't flow. These surface tensions are not some hypothetical quantity but have real physical significance, for example in the calculation of contact angles.

• In a liquid-liquid or liquid-gas flow, at the interphase between the phases, the normal forces from each phase are balanced with the force surface tension. $\sum_{k = 1,2} M_k = M_m$ where $M_k$ are the normal forces and $M_m$ is a force due to the surface tension. But in a liquid-solid flow is it the case that $M_m = 0$ and hence the normal forces from each phase are balanced, ie. $M_1 = M_2$? – sonicboom Aug 15 '15 at 11:08
• No that isn't the case in general. See this paper: utd.edu/~son051000/my_publications/… – John M Aug 15 '15 at 14:31
• Looks like it's time for an "assumption" so! :D – sonicboom Aug 15 '15 at 17:15

Work done by surface tension always comes from reducing the surface area. There is no surface tension on a dry solid because a solid does not deform spontaneously and thus cannot reduce its surface area.

However, the question here was on surface tension between a solid and a liquid. This situation can be viewed from the liquid's side as well! Hence, the answer is: yes.

• One can view surface reconstructions as a deformation of the surface, and they are driven by free energy considerations (and happen spontaneously). So, your first paragraph is incorrect. – Jon Custer Mar 7 '17 at 16:03
• The argument was on reducing the surface area. Surface reconstruction does not specifically reduce the total surface area, and even if it did, this would happen within milliseconds after creating the surface. Note also that surface tension is defined in a way that is unrelated to reconstruction. – RTELAM Mar 25 '17 at 11:51