Mesoscopic analysis of Gibbs' criterion for sessile nanodroplets on trapezoidal substrates

TL;DR

This study uses a mesoscopic approach to analyze nanodroplet behavior on trapezoidal substrates, showing the absence of contact line pinning and continuous variation of contact angles within Gibbs' criterion, contrasting macroscopic predictions.

Contribution

It demonstrates that mesoscopic modeling reveals smooth contact line movement and continuous contact angle changes, challenging macroscopic pinning phenomena on trapezoidal substrates.

Findings

No contact line pinning observed at mesoscopic level.

Contact angle varies continuously within Gibbs' range.

Contact line moves smoothly across substrate edges.

Abstract

By taking into account precursor films accompanying nanodroplets on trapezoidal substrates we show that on a mesoscopic level of description one does not observe the phenomenon of liquid-gas-substrate contact line pinning at substrate edges. This phenomenon is present in a macroscopic description and leads to non-unique contact angles which can take values within a range determined by the so-called Gibbs' criterion. Upon increasing the volume of the nanodroplet the apparent contact angle evaluated within the mesoscopic approach changes continuously between two limiting values fulfilling Gibbs' criterion while the contact line moves smoothly across the edge of the trapezoidal substrate. The spatial extent of the range of positions of the contact line, corresponding to the variations of the contact angle between the values given by Gibbs' criterion, is of the order of ten fluid particle diameters.