THE BUCKLING AND STRETCHING OF A VISCIDA II. EFFECTS OF SURFACE TENSION

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Abstract
We consider the deformation of a two-dimensional viscida due to the slow motion of its ends and the influence of surface tension. The governing equations which describe how both the thickness and the centre-line slope change with time are deduced by formally expanding the solution of the Stokes equations in powers of a small parameter ε which is a measure of the thickness of the viscida. These equations show that if the ends of a deformed viscida are pushed towards each other at constant speed, the qualitative response depends on the magnitude of the surface tension. When the surface tension is small enough, the viscida buckles and the mean displacement of the centre-line increases. On the other hand when the surface tension is large enough, the mean displacement decreases and after a finite time the viscida is straight. At intermediate values of surface tension it is possible for the displacement to decrease initially, but subsequently increase. During an increase in displacement the lowest-order modes of the initial disturbance grow most rapidly. These modes decay most rapidly if the displacement decreases.

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