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Why the force exerted by a thin soap film is on a movable wire of length L is $2TL$ where $T$ is the surface Tension of the liquid? Why is there a factor of $2$? I can't understand it because there are many many layers between the two outermost layers and they should also exert a pulling force on the wire. ki

The movable wire is in blue. the outer surface layers are

The outer surface layers are GF and DE

The molecules b and f should also exert pulling force on the wire. Where am i wrong?

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1 Answer 1

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Inner layers do exert a pulling force (it's the wetting force) but that isn't a surface term. A wetting-force (if considered to be a spring-like element) for the liquid will be in series with millimeter after millimeter of OTHER wetting-force springs, and springs in series are weak.

Surface energy, on the other hand, as a function of area-of-surface, linearly increases with that area, so the energy= work = force x distance implies a constant force-per-millimeter (that we call the surface tension) on each millimeter of the length of wire. And, a factor of two because a liquid film has both a back and front surface.

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  • $\begingroup$ Sorry, Can u explain a bit more? Also why does the outer surface different from the inner in any way?why are the inner layer associated with wetting forces? $\endgroup$
    – shahrOZe
    Commented May 16, 2020 at 8:39
  • $\begingroup$ The surface, with (air?) on one side, is a different material from the bulk liquid; every weak bond that would hold a molecule has... no liquid on that outside. The 'extra' bonds create extra tension, but only on the surface. $\endgroup$
    – Whit3rd
    Commented May 16, 2020 at 8:44
  • $\begingroup$ So the outer surfaces are pulled in by the inner liquid layers causing extra tension? Do we neglect the force by the inner layers just because they are negligibly smaller than the force exerted by the outer layers? $\endgroup$
    – shahrOZe
    Commented May 16, 2020 at 8:51
  • $\begingroup$ @shahrozeshahab We don't 'neglect' the force by inner layers, it's how we make glue. Glue, in a thin film, uses that wetting force to hold surfaces together, but it is different from a liquid's surface tension because the surface bonds do NOT stay empty, in air. Rather bonds get filled by a stamp on one side, an envelope on the other. $\endgroup$
    – Whit3rd
    Commented May 16, 2020 at 9:05
  • $\begingroup$ So what will happen if only a single layer of liquid molecules were there? Will the force by half? $\endgroup$
    – shahrOZe
    Commented May 16, 2020 at 9:16

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