Oscillations Modes of a Triple Line

A triple line can vibrate somewhat in the manner of a guitar string. Unlike the case of a string, however, two effects must be included here  

On a solid substrate, and particularly for small angles 6e viscous friction 

The fringe elasticity has been discussed in chapter 3 (where we chose = 7t/2). Here, when the angle is small, and for a mode of wavevector q and amplitude Uq the energy retains the same functional dependence on q but with a different prefactor  

A viscous force can balance this force out, which we write as 

This gives an exponential relaxation, with a relaxation frequency  

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