Post-Tanner spreading of nematic droplets

TL;DR

This paper models the accelerated spreading of nematic liquid crystal droplets beyond Tanner law, attributing it to substrate-liquid interactions, and confirms the theory with numerical solutions matching experimental data.

Contribution

It introduces a theoretical framework for post-Tanner spreading in nematic droplets driven by substrate interactions, extending classical spreading laws.

Findings

Numerical solutions align with experimental data for nematic spreading.

Spreading transitions from capillarity-driven to substrate-interaction-driven regime.

The model predicts a faster, diffusive-like spreading stage for nematics.

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 R ~ t^{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 R ~ t^alpha with alpha 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.