Abstract
The experimental results of Xia and Steen for the contact line dynamics of a drop placed on a vertically oscillating surface are analyzed by numerical phase field simulations. The concept of contact line mobility or friction is discussed, and an angle-dependent model is formulated. The results of numerical simulations based on this model are compared to the detailed experimental results of Xia and Steen with good general agreement. The total energy input in terms of work done by the oscillating support, and the dissipation at the contact line, are calculated from the simulated results. It is found that the contact line dissipation is almost entirely responsible for the dissipation that sets the amplitude of the response. It is argued that angle-dependent line friction may be a fruitful interpretation of the relations between contact line speed and dynamic contact angle that are often used in practical computational fluid dynamics.
Highlights
A liquid spreading over a dry surface is a phenomenon that is crucial to many natural processes and important in technology
We evaluate the detailed experimental results of Xia and Steen[9], using phase field simulations, with the aim of (3) determining precisely what is required in the mathematical model, in order to faithfully reproduce the experiments
The order unity value of the angular velocity shows that the equilibrium at the contact line (CL), an explicit relation between CL speed UCL and dynamic contact angle θ can be derived from Eq (11), see oscillations are reasonably matched with the inertial timescale, as is expected since the experiment aims at being near resonance
Summary
A liquid spreading over a dry surface is a phenomenon that is crucial to many natural processes and important in technology. The simulations are performed in a cylindrical coordinate with hydrogen bonds with the water molecules, the first layer of system that follows the oscillating substrate, giving rise to the water molecules are effectively bound to the surface, a no-slip acceleration term on the right-hand side of the momentum condition is appropriate, and the contact angle deviates from the equilibrium value[21,22]. The order unity value of the angular velocity shows that the equilibrium at the CL, an explicit relation between CL speed UCL and dynamic contact angle θ can be derived from Eq (11), see oscillations are reasonably matched with the inertial timescale, as is expected since the experiment aims at being near resonance. Reporting summary Further information on research design is available in the Nature where the nondimensional μÃf ðθÞ is Research Reporting Summary linked to this article
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