  The sticky fluids found in pitcher plant leaf vessels can leave fractal-like
filaments behind when dewetting from a substrate. To understand the origin of
these filaments, we investigate the dynamics of a retreating thin-film of
aqueous polyethylene oxide (PEO) solutions which partially wet polydimethyl
siloxane (PDMS) substrates. Under certain conditions the retreating film
generates regularly-spaced liquid filaments. The early-stage thin-film dynamics
of dewetting are investigated to identify a theoretical criterion for liquid
filament formation. Starting with a linear stability analysis of a Newtonian or
simple non-Newtonian (power-law) thin-film, a critical film thickness is
identified which depends on the Hamaker constant for the fluid-substrate pair
and the surface tension of the fluid. When the measured film thickness is
smaller than this value, the film is unstable and forms filaments as a result
of van der Waals forces dominating its behaviour. This critical film-height is
compared with experimental measurements of film thickness obtained for receding
films of Newtonian (glycerol-water mixtures) and non-Newtonian (PEO) solutions
generated on substrates inclined at angles 0 $^{\circ}$, 30 $^{\circ}$, and 60
$^{\circ}$ to the vertical. The observations of filament and its absence show
good agreement with the theory. The evolution of the thin-film shape is
modelled numerically to show that the formation of filaments arises because the
thin-film equation features a singular solution after a finite-time, hence
termed a "finite-time singularity".
