Post-Tanner spreading of nematic droplets

Abstract

The quasistationary spreading of a circular liquid drop on a solid substratetypically obeys the so-called Tanner law, with the instantaneous base radiusR(t) growingwith time as R∼t1/10—an effect of the dominant role of capillary forces for a small-sized droplet. However, fordroplets of nematic liquid crystals, a faster spreading law sets in at long times, so thatR∼tα withα significantly larger than the Tanner exponent1/10. 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 strongsubstrate–liquid interaction specific to nematics (antagonistic anchoring at theinterfaces). The numerical solution of the thin film equation agrees well withthe available experimental data for nematics, even though the non-Newtonianrheology has yet to be taken into account. Thus we complement the theory ofspreading with a post-Tanner stage, noting that the spreading process can beexpected to cross over from the usual capillarity-dominated stage to a regimewhere the whole reservoir becomes a diffusive film in the sense of Derjaguin.