I read that surface tension acts perpendicular to the line and tangentially to the liquid surface. However I can not able to visualise how both cases can coexist.
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$\begingroup$ What’s the exact source material? “Acts” is ambiguous; the force can act parallel to the surface, and the effect can act to move the surface perpendicularly to reduce its area. $\endgroup$– ChemomechanicsCommented Nov 25 at 12:16
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You can think of surface tension as being like the tension in a drumskin.
For a flat surface, imagine drawing a line or curve on the surface of the fluid. The surface tension is the force per unit length that the fluid surface on one side of the line acts on the fluid on the other the other side of the curve. At each point on the curve this force lies in the plane of the surface and is perpendicular to the curve.
If the surface is not flat than, just as with the tension in a curved piece of string, the force being always along a tangent to the string/surface does not prevent the tangential force at the ends of a piece of string having a different direction to that the tangent at a point between the ends. In this case, as with the string, the surface tension will tend to flatten the surface so at to minimise its area. The surface tension is, after all, defined as the energy per unit area of the surface.
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$\begingroup$ "At each point on the curve this force lies in the plane of the surface and is perpendicular to the curve," just like the force $J \times B$ acting on a current element by the magnetic field; still, instead of teaching that $B$ is an anti-symmetric tensor, a bivector, and is thus a "surface thing", we are taught that "B" is pseudo-vector ... $\endgroup$ Commented Nov 25 at 15:45