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As the surface of a liquid will have imbalanced cohesive forces leading to the phenomenon of surface tension,we just consider the forces among the surface molecules which act tangentially and dont consider the component of cohesive force towards the center of the droplet while formulating excess pressure inside a droplet due to surface tension.Is there any valid reason for this or is it just a convention for the sake of simplicity?

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The surface tension is due precisely to the cohesive forces that you say are ignored. Surface tension is defined to be the surface free-energy $F=E-TS$ per unit area of the surface, and so takes into account the unsatisfied bonds that are present because the inside and outside environments of a surface molecule are different- i.e because the bulk is pulling the surface molecules inwards. The tangential bonds differ very little from the ones in the bulk. As long as there is an energy that depends on the surface area it acts like a tangential force because increasing the area costs energy -- just as stretching a rubber band costs energy. This is very clear when you use the virtual work method of computing the excess pressure by saying that $$ \sigma \delta {\rm Area}= P_{\rm excess} \delta {\rm Volume} $$

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  • $\begingroup$ The tangential component of imbalanced cohesive forces,surface tension,acting along the surface of the droplet will cause compression to some extent and the radial component of the imbalanced cohesive forces,not named,acting towards the center of the droplet will also try to compress.What are your comments on this statement?If you agree with this,why don't we consider the compression due to that radial component while formulating the excess pressure in the droplet? $\endgroup$ Mar 17, 2020 at 16:39

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