Frigus
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Why direction of surface tension is tangential to the surface and not perpendicular downwards since it is caused by molecules in the bulk?
Charles Link said:To answer your first question, it might be worthwhile to look at an analogous but simpler system=a rope that is wrapped around a cylinder. The tension ## T ## in the rope is along the tangential path, but it exerts a force on the cylinder that is perpendicular to the path, because of the curvature. The normal force on the cylinder per unit length is ## f_l=\frac{T}{r} ##, where ##r ## is the radius of the cylinder.
Charles Link said:The surface tension will create pressure ##P ## inside a spherical droplet. The book "Equilibrium Thermodynamics" by Adkins pp. 39-40 treats this particular case very well. Defining the surface tension ## \gamma=\frac{dW}{dA} ##, we can write ## dW=\gamma \, dA =8 \pi \gamma r \, dr##. We also have ## dW=P \, dV=P \, 4 \pi r^2 \, dr ##. Equating these two expressions for ## dW ## gives ## P=\frac{2 \gamma}{r} ##. ## \\ ## This expression for pressure ## P ## is similar to the expression of the force per unit length in the rope, where, in both cases, the radius ## r ## appears in the denominator.
Sir but how can I understand thatCharles Link said:Pressure is a force per unit area that acts normal to a surface. The ## W ## above is work or energy. Surface tension ## \gamma ## is defined as the work required to increase the area of the surface by one unit, thereby ## \gamma=\frac{dW}{dA} ##.
Sir but from these equations how can I understand that surface tension is tangetial.Charles Link said:Pressure is a force per unit area that acts normal to a surface. The ## W ## above is work or energy. Surface tension ## \gamma ## is defined as the work required to increase the area of the surface by one unit, thereby ## \gamma=\frac{dW}{dA} ##. ## \\ ## Meanwhile, the above area ## A=4 \pi r^2 ##, thereby ## dA=8 \pi r \, dr ##.