# Equilibrium of a free surface under surface tensio

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 August 7, 2001, 10:09 Equilibrium of a free surface under surface tensio #1 Ryan Guest   Posts: n/a Hi All! In a paper I found a equation which describes the equilibrium of the normal and the tangential force of a free surface under surface tension. The equation is face integral of (£GP dS) = line integral of(£n|dx|) where £n=£m* nx * (dx/|dx|) and S, dx, nx are vector. dx means the lines along the boundary of the surface. I'm not really sure about the meaning of other symbol, "maybe" they are.... £GP = pressure difference £m = surface tension coefficient nx = x component of the face normal vector n so the final equation is face integral of (£GP dS) = line integral of(£m*nx*dx) And the question is : 1.How to explain this equation? I mean why the normal force acting on the surface should be equal to the summation of all the tangential force? 2. This equation is derived form.....(how to obtain this equation?)

 August 7, 2001, 16:14 Re: Equilibrium of a free surface under surface te #2 Dr Strangelove Guest   Posts: n/a 1.How to explain this equation? I mean why the normal force acting on the surface should be equal to the summation of all the tangential force?
Because the surface has curvature. You can easily imagine the same effects if you were required to hold a blanket or parachute on its edges only (providing only tangential forces) while a fan or blower pushed the central portion outward.
2. This equation is derived form.....(how to obtain this equation?)
The equation symbols were garbled in your message. However, this balance of forces can be derived using thermodynamic arguments based on the free energy associated with the surface. Also, look for ealier references going back to Young and Laplace.