Surface tension - normal or tangential ?
 

Hi,

The surface tension forces at the contact line, as per the young's equation for contact angle, is tangential to the interfaces. (see Pic1.)

But I also came across another form of equation for surface tension as shown in Pic2 from FLUENT (which is also commonly used elsewhere). Here, the surface tension forces are normal to the interface (because of the gradient of Volume fraction, alpha).

The above mentioned models quite clearly contradict each other !

How are the surface tension forces acting at the contact line ? Tangential or normal ? Are both these models equivalent ? Did I miss anything ?


Thanks.

parallel to the surface ... the normal direction is referred to as force for unit line, eg. see

http://en.wikipedia.org/wiki/Surface_tension

I'm not sure how this works at the contact line as its quite hard to visualise. But if you imagine a section of fluid-fluid interface with the surface tension acting tangential to it, at the ends of this interface. I've included a simplistic diagram for clarity here.

If it is flat, the forces cancel out there is no net force on the section. However, if it is curved there is a net force that acts normal to the interface.

I think that the misleading could be due to the fact that a component of the stress tensor is associated to 2 directions...

I haven't used fluent before but by the looks of it sigma_ij is the surface tension coefficient between the fluids i and j.

Yes, sigma_ij is the surface tension coefficient. So, at the contact line, as you said, although its quite tough to visualize, atleast the values of surface tension based on these two models should match. Moreover, the fluent based model is a volumetric force whereas the young's equation based model is Force/length.

Still couldn't get a good picture of how these two models are equivalent !