ABSTRACT
The spreading of a circular liquid drop on a solid substrate can be described in terms of the time evolution of its base radius R(t). In complete wetting, the quasistationary regime (far away from initial and final transients) typically obeys the so-called Tanner law, with Râ¼t(α(T)), α(T) = 1/10. Late-time spreading may differ significantly from the Tanner law: in some cases the drop does not thin down to a molecular film and instead reaches an equilibrium pancake-like shape; in other situations, as revealed by recent experiments with spontaneously spreading nematic crystals, the growth of the base radius accelerates after the Tanner stage. Here we demonstrate that these two seemingly conflicting trends can be reconciled within a suitably revisited energy balance approach, by taking into account the line tension contribution to the driving force of spreading: a positive line tension is responsible for the formation of pancake-like structures, whereas a negative line tension tends to lengthen the contact line and induces an accelerated spreading (a transition to a faster power law for R(t) than in the Tanner stage).
ABSTRACT
The quasistationary spreading of a circular liquid drop on a solid substrate typically obeys the so-called Tanner law, with the instantaneous base radius R(t) growing with time as Râ¼t(1/10)-an effect of the dominant role of capillary forces for a small-sized droplet. However, for droplets of nematic liquid crystals, a faster spreading law sets in at long times, so that Râ¼t(α) with α significantly larger than the Tanner exponent 1/10. In the framework of the thin film model (or lubrication approximation), we describe this 'acceleration' as a transition to a qualitatively different spreading regime driven by a strong substrate-liquid interaction specific to nematics (antagonistic anchoring at the interfaces). The numerical solution of the thin film equation agrees well with the available experimental data for nematics, even though the non-Newtonian rheology has yet to be taken into account. Thus we complement the theory of spreading with a post-Tanner stage, noting that the spreading process can be expected to cross over from the usual capillarity-dominated stage to a regime where the whole reservoir becomes a diffusive film in the sense of Derjaguin.
ABSTRACT
We analyze the stability of sessile filaments (ridges) of nonvolatile liquids versus pearling in the case of externally driven flow along a chemical stripe within the framework of the thin-film approximation. The ridges can be stable with respect to pearling even if the contact line is not completely pinned. A generalized stability criterion for moving contact lines is provided. For large wavelengths and no driving force, within perturbation theory, an analytical expression of the growth rate of pearling instabilities is derived. A numerical analysis shows that a body force along the ridge further stabilizes the ridge by reducing the growth rate of unstable perturbations, even though there is no complete stabilization. Hence the stability criteria established in the absence of driven flow ensure overall stability.
