Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics

Area of Science:

• Fluid dynamics
• Surface science
• Materials science

Background:

• Liquid spreading on solid surfaces is governed by energy minimization.
• Classic thin-film models neglect non-hydrodynamic liquid-solid interactions, failing to predict the cessation of spreading in partial-wetting regimes.
• These neglected interactions near the contact line have significant macroscopic consequences.

Purpose of the Study:

• To develop a mesoscopic thin-film model that accurately describes liquid spreading in the partial-wetting regime.
• To incorporate non-hydrodynamic liquid-solid interactions into a free energy framework.
• To investigate the statics and dynamics of liquid spreading influenced by these interactions.

Main Methods:

• Developed a free energy formulation within a Cahn-Hilliard framework, incorporating height-dependent interfacial tension.
• Derived a mesoscopic thin-film model based on this free energy.
• Analyzed the model to understand the emergence of contact-line dynamics and spreading states.

Main Results:

• The model predicts compactly supported spreading states, explaining why liquid puddles stop spreading.
• Height-dependent interfacial tension introduces localized apparent slip near the contact line.
• Contact-line dynamics emerge naturally and are nonlocally coupled to the bulk flow.

Conclusions:

• The enhanced thin-film model successfully describes liquid spreading in partial-wetting regimes by including intermolecular forces.
• The model provides a unified framework for understanding both the statics and dynamics of spreading.
• The study confirms that the dynamic contact angle follows the Cox-Voinov law even in gravity-dominated scenarios.