Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants
2018
Thiele, Uwe | Snoeijer, Jacco H. | Trinschek, Sarah | John, Karin
The three-phase contact line of a droplet on a smooth surface can be characterized by the Young equation. It relates the interfacial energies to the macroscopic contact angle θₑ. On the mesoscale, wettability is modeled by a film-height-dependent wetting energy f(h). Macro- and mesoscale descriptions are consistent if γ cos θₑ = γ + f(hₐ), where γ and hₐ are the liquid–gas interface energy and the thickness of the equilibrium liquid adsorption layer, respectively. Here, we derive a similar consistency condition for the case of a liquid covered by an insoluble surfactant. At equilibrium, the surfactant is spatially inhomogeneously distributed, implying a nontrivial dependence of θₑ on surfactant concentration. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are consistent only if a particular dependence of the wetting energy on the surfactant concentration is imposed. This is illustrated by a simple example of dilute surfactants, for which we show excellent agreement between theory and time-dependent numerical simulations.
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