- #1

sunquick

- 18

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## Homework Statement

A loop of cotton floats on the surface of some water. A little detergent is dropped onto the water surface inside the loop, and the loop opens out and becomes circular. Explain why this happens. Draw a diagram showing the forces acting on a short length of the circumference of the loop has been added. Explain how the short length is in mechanical equilibrium

## Homework Equations

To calculate the force on the string

[itex]\textbf{F} = \gamma L [/itex]

[itex] \gamma [/itex] is the surface tension in the water-soap boundary

[itex]L[/itex] is the length of string we're considering.

[itex]dW = \gamma dA [/itex]

## The Attempt at a Solution

From a mechanics point of view, because the detergent lowers the surface tension inside the loop, the water outside the loop pulls the string with a larger force. From an energy point of view, I think that the water surface is minimized by maximizing the area of detergent, and that is achieved by turning the loop into a circle.

I don't know how to put this description into a mathematical statement, since I don't understand fluid mechanics very well. That's why I'm also struggling with the part where I'm asked to explain the mechanical equilibrium. Considering that the water outside has a larger pull than the detergent inside, and they are acting on the same length of string, I don't see how mechanical equilibrium can be achieved.

As a side question,are there any good books dealing with surface tension effects and how they can be explained mathematically? The ntroductory fluid mechanics books I looked into mention surface tension only in the first chapters and don't go into great detail about it.