Stability of liquid channels or filaments in the presence of line tension

Abstract

The local stability of a cylindrical liquid channel or filament deposited on a planarhomogeneous substrate is studied in the framework of an effective interface model includingthe line tension of the three phase contact line. We discuss the stability with respect totransversally symmetric and antisymmetric deformation modes and compute a stabilitydiagram in terms of the contact angle and the longitudinal wavelength of these modes fordifferent values of line tension. An increase in the line tension always leads to anincrease in the local stability of liquid channels or filaments. For large positive linetension, the behaviour with pinned contact lines is recovered. As one decreasesthe line tension to negative values, deformation modes of arbitrary wavelengthdestabilize the channel or filament for sufficiently small contact angles. In addition, anegative line tension leads to a band of unstable short wavelength modes within thecontinuum theory considered here. It is argued that the presence or absence of theselatter modes depends on the ratio of the contact line width to the molecular size.