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Surface piercing elastic beams: buckling by capillary forces
joint work with José Bico and Benoît Roman
Due to the small value of the surface tension, capillary effects normally happen at small (microscopic) scales. Nevertheless, can a macroscopic elastic beam be deflected by surface tension ?
To answer the question, we anchor an elastic beam at the bottom of a small tank full of silicon oil. At first the beam is completely immersed. We then gradually lower the bath height to a value less than the length of the beam. If the beam is rigid enough (or short enough) it will pierce the surface and stay straight:
However if you do the same experiment with a longer beam, surface tension is strong enough to deflect the beam:
Once the beam is deflected, if we further lower the bath, we see several different bent states arising, e.g.:
There are even states where the beam pierces the surface twice:
We use the following experimental rig:
to list all the existing stable states as the bath height H and the length of beam L are varied. Numerical computations are also performed and a nice agreement is found with experimental data (see below).The results are summarized in the following phase diagram. In each region of the plane (H,L) the different stable equilibrium states of a beam in interaction with a liquid interface are drawn:
Symbols: experiments / Continuous lines: numerics.
Our article: here.
Some slides in html or PDF format.