# I What do surface tension vectors mean in this quote?

Tags:
1. Nov 21, 2018

### APUGYael

I was reading Fundamentals of Inket Printing and it said the following:

"The surface tension in a liquid causes a force to act in the plane of the free surface
perpendicularly to a free edge in that surface."

Can someone explain to me what this means? What's the direction of the force? I have no idea what a free edge is. Google made me none the wiser.

2. Nov 21, 2018

### phinds

I've never heard this before (this is in now way an area of expertise for me) but it seems clear to me that it means that if you have a liquid bubble that is captive in all but one area, then surface tension causes a force to be exerted normal to the surface in that area so that the bubble doesn't just dissipate. That interpretation comports with my own observation on how liquids behave. It means that a bubble can be partly forced out of a small opening in a print head and it won't just run all over the surface out of which it is protruding but rather will just sit there (and then can be pressed into paper as a dot).

3. Nov 22, 2018

### lightarrow

I have understood that phrase this way.
Consider for example the ring used to make soap bubbles: when the ring is filled in, you have a disc made of soap water; surface tensions on this disc acts as concentrical forces on the ring, directed towards the centre. If the ring weren't rigid but could be easily deformed, you would see it contract as soon as it were filled by water.

--
lightarrow

4. Nov 22, 2018

### Staff: Mentor

Surface tension is like the 2D version of stress. Are you familiar with the stress tensor?

If not, imagine the free surface of a liquid. The surface may be flat or it may be curved (out-of-plane). The surface tension acts like a membrane that is stretched over the free surface. Imagine a small window shaped section of the membrane. Along each edge of the window, the portion of the membrane outside the window exerts a tension on the portion of the membrane inside the window (and vice versa). The tension exerted by the portion of the membrane outside the window on the portion inside the window is equal to the surface tension times the length of the edge. This force acts within the plane of the membrane, perpendicular to the edge of the window, and is directed outward. So surface tension is the force per unit length within a membrane, and it is always directed perpendicular to any imaginary line within the plane of the membrane.