A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading

Abstract

The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin two-dimensional droplet on a planar substrate. The models analysed include three disjoining pressure models based on van der Waals interactions, a model introduced for polar fluids, and a liquid-gas diffuse-interface model; Navier-slip and two nonlinear slip models are investigated, with three microscopic contact angle boundary conditions imposed (two of these contact angle conditions having a contact line velocity dependence); and the interface formation model is also considered. In certain parameter regimes it is shown that all of the models predict the same quasistatic droplet spreading behaviour.

Nonequilibrium molecular dynamics simulations of nanoconfined fluids at solid-liquid interfaces

“…The main factors affecting slip are the energy of wall-fluid interactions and the shear rate. 22,23 It should be noted that the exact value of the slip length can have a profound impact even on macroscopic flows, e.g., at the moving contact line (see, e.g., the work of Sibley et al 70 ).…”

The asymptotics of the moving contact line: cracking an old nut

“…To regularise the divergent dissipation predicted by this classical description, a wide range of possible models capturing various physical effects have been considered (see e.g. Bonn et al (2009) ;Snoeijer & Andreotti (2013); Sui et al (2014); Sibley et al (2014)). …”

“…This direct matching procedure has since been used to simplify the asymptotic description when considering other physical effects such as gravity , chemical heterogeneities (Vellingiri et al 2011), and using other models in the thin-film setting (Sibley et al 2012(Sibley et al , 2014.…”

Slip-mediated dewetting of polymer microdroplets

“…In common experience we are surrounded by liquid/vapor interfaces moving along solid surfaces, from water droplets on a wind screen, to the displacement of air by liquid through a capillary or porous medium. This apparent paradox of contact line motion has attracted the attention of many researchers over at least the last four decades (11)(12)(13)(14)(15)(16)(17)(18).…”