  When a flexible filament is confined to a fluid interface, the balance
between capillary attraction, bending resistance, and tension from an external
source can lead to a self-buckling instability. We perform an analysis of this
instability and provide analytical formulae that compare favorably with the
results of detailed numerical computations. The stability and long-time
dynamics of the filament are governed by a single dimensionless elastocapillary
number quantifying the ratio between capillary to bending stresses. Complex,
folded filament configurations such as loops, needles, and racquet shapes may
be reached at longer times, and long filaments can undergo a cascade of
self-folding events.
