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In the phase-field description of moving contact line problems, the two-phase system can be described by free energies, and the constitutive relations can be derived based on the assumption of energy dissipation. In this work we propose a novel boundary condition for contact angle hysteresis by exploring wall energy relaxation, which allows the system to be in non-equilibrium at the contact line. Our method captures pinning, advancing and receding automatically without the explicit knowledge of contact line velocity and contact angle. The microscopic dynamic contact angle is computed as part of the solution instead of being imposed. Furthermore, the formulation satisfies a dissipative energy law, where the dissipation terms all have their physical origin. Based on the energy law, we develop an implicit finite element method that is second order in time. The numerical scheme is proven to be unconditionally energy stable for matched density and zero contact angle hysteresis, and is numerically verified to be energy dissipative for a broader range of parameters. We benchmark our method by computing pinned drops and moving interfaces in the plane Poiseuille flow. When the contact line moves, its dynamics agrees with the Cox theory. In the test case of oscillating drops, the contact line transitions smoothly between pinning, advancing and receding. Our method can be directly applied to three-dimensional problems as demonstrated by the test case of sliding drops on an inclined wall.
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Hysteretic Behavior of Capillary Bridges between Flat Plates
We studied the evolution of capillary bridges between nominally flat plates undergoing multiple cycles of compression and stretching in experiments and simulations. We varied the distance between the plates in small increments to study the full evolution of the bridge shape. Experiments show that contact angle hysteresis determines the shape of the bridge. In sliding drops, hysteresis can be modeled using a contact angle-dependent resistive force F̃R applied at the contact line. We developed a model that accurately captures the evolution of the bridge shape by combining F̃R and constrained energy minimization. Unlike previous work, this allows for both complete and partial contact line pinning. We also explored the effect of using nonparallel plates. The asymmetry in the bridge shape causes the movement of the center of mass of the bridge and can be explained by contact angle hysteresis. We find that even a slight misalignment between the flat plates can have a measurable effect.
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- Award ID(s):
- 1743794
- PAR ID:
- 10562620
- Publisher / Repository:
- ACS Langmuir
- Date Published:
- Journal Name:
- Langmuir
- Volume:
- 39
- Issue:
- 37
- ISSN:
- 0743-7463
- Page Range / eLocation ID:
- 13149 to 13157
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1021/acs.langmuir.3c01550
