Math. Model. Nat. Phenom.
Volume 10, Number 4, 2015Micro-nanophenomena
|Page(s)||111 - 125|
|Published online||15 July 2015|
Nanoscale Fluid Structure of Liquid-solid-vapour Contact Lines for a Wide Range of Contact Angles
1 Department of Chemical Engineering,
2 The School of Mathematics and Maxwell Institute for Mathematical Sciences The University of Edinburgh, Edinburgh EH9 3JZ, UK
Corresponding author. E-mail: firstname.lastname@example.org
We study the nanoscale behaviour of the density of a simple fluid in the vicinity of an equilibrium contact line for a wide range of Young contact angles θY ∈ [ 40°,135° ]. Cuts of the density profile at various positions along the contact line are presented, unravelling the apparent step-wise increase of the film height profile observed in contour plots of the density. The density profile is employed to compute the normal pressure acting on the substrate along the contact line. We observe that for the full range of contact angles, the maximal normal pressure cannot solely be predicted by the curvature of the adsorption film height, but is instead softened – likely by the width of the liquid-vapour interface. Somewhat surprisingly however, the adsorption film height profile can be predicted to a very good accuracy by the Derjaguin-Frumkin disjoining pressure obtained from planar computations, as was first shown in [Nold et al., Phys. Fluids, 26, 072001, 2014] for contact angles θY< 90°, a result which here we show to be valid for the full range of contact angles. This suggests that while two-dimensional effects cannot be neglected for the computation of the normal pressure distribution along the substrate, one-dimensional planar computations of the Derjaguin-Frumkin disjoining pressure are sufficient to accurately predict the adsorption height profile.
Mathematics Subject Classification: 76T10 / 82B05
Key words: adsorption / contact line / simple fluid / disjoining pressure / Derjaguin-Frumkin / Hamiltonian
© EDP Sciences, 2015
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