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Math Help - Effects of surface tension

  1. #1
    Senior Member TriKri's Avatar
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    Effects of surface tension

    Hello!

    What I have understood about surface tension is that it lays a pressure on the surface in proportion to the bending of it, the angular change per meter surface , which has the unit [rad/m^{-1}]=[m^{-1}]. And pressure has the unit N/m^2. So surface tension would have the unit \left[\frac{N/m^2}{m^{-1}}\right]=[N/m], which it has. Now, is it so that the pressure applied to the surface is given by

    P=S\cdot\frac{\delta^2 y}{\delta x^2}

    Where S is the surface tension, and x and y have the unit [m], so \frac{\delta^2y}{\delta x^2} has the unit [m^{-1}]. \frac{\delta^2 y}{\delta x^2} is the same as \frac{\delta\alpha}{\delta x}, where \alpha is the angle ( \alpha = \frac{\delta y}{\delta x} for small \alpha)
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by TriKri View Post
    Hello!

    What I have understood about surface tension is that it lays a pressure on the surface in proportion to the bending of it, the angular change per meter surface , which has the unit [rad/m^{-1}]=[m^{-1}]. And pressure has the unit N/m^2. So surface tension would have the unit \left[\frac{N/m^2}{m^{-1}}\right]=[N/m], which it has. Now, is it so that the pressure applied to the surface is given by

    P=S\cdot\frac{\delta^2 y}{\delta x^2}

    Where S is the surface tension, and x and y have the unit [m], so \frac{\delta^2y}{\delta x^2} has the unit [m^{-1}]. \frac{\delta^2 y}{\delta x^2} is the same as \frac{\delta\alpha}{\delta x}, where \alpha is the angle ( \alpha = \frac{\delta y}{\delta x} for small \alpha)
    If I am understanding you correct then you are right. There is also another feature of surface tension: the surface formed contains the least possible amount of energy. In this way you can predict the equation for the surface. (There's a partial differential equation for this, but I don't remember it and I'm too lazy right now to look it up. )

    -Dan
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  3. #3
    Senior Member TriKri's Avatar
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    I found a picture on the wikipedia article which made it a bit clearer to me



    I haven't thought of surface tension this way before, like something is pulling sideways in the surface. This clearly motivates the tension part of the name.
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