Primal-dual splitting methods for phase-field surfactant model with moving contact lines

Fuente: arXiv
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Autores principales: Wu, Wei, Zhang, Zhen, Wei, Chaozhen
Formato: Preprint
Publicado: 2025
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author Wu, Wei
Zhang, Zhen
Wei, Chaozhen
author_facet Wu, Wei
Zhang, Zhen
Wei, Chaozhen
contents Surfactants have important effects on the dynamics of droplets on solid surfaces, which has inspired many industrial applications. Phase-field surfactant model with moving contact lines (PFS-MCL) has been employed to investigate the complex droplet dynamics with surfactants, while its numerical simulation remains challenging due to the coupling of gradient flows with respect to transport distances involving nonlinear and degenerate mobilities. We propose a novel structure-preserving variational scheme for PFS-MCL model with the dynamic boundary condition based on the minimizing movement scheme and optimal transport theory for Wasserstein gradient flows. The proposed scheme consists of a series of convex minimization problems and can be efficiently solved by our proposed primal-dual splitting method and its accelerated versions. By respecting the underlying PDE's variational structure with respect to the transport distance, the proposed scheme is proved to inherits the desirable properties including original energy dissipation, bound-preserving, and mass conservation. Through a suite of numerical simulations, we validate the performance of the proposed scheme and investigate the effects of surfactants on the droplet dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2505_09469
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Primal-dual splitting methods for phase-field surfactant model with moving contact lines
Wu, Wei
Zhang, Zhen
Wei, Chaozhen
Numerical Analysis
Optimization and Control
Computational Physics
35A15, 35Q35, 35Q70, 47J25, 47J35, 65K10, 76M30
Surfactants have important effects on the dynamics of droplets on solid surfaces, which has inspired many industrial applications. Phase-field surfactant model with moving contact lines (PFS-MCL) has been employed to investigate the complex droplet dynamics with surfactants, while its numerical simulation remains challenging due to the coupling of gradient flows with respect to transport distances involving nonlinear and degenerate mobilities. We propose a novel structure-preserving variational scheme for PFS-MCL model with the dynamic boundary condition based on the minimizing movement scheme and optimal transport theory for Wasserstein gradient flows. The proposed scheme consists of a series of convex minimization problems and can be efficiently solved by our proposed primal-dual splitting method and its accelerated versions. By respecting the underlying PDE's variational structure with respect to the transport distance, the proposed scheme is proved to inherits the desirable properties including original energy dissipation, bound-preserving, and mass conservation. Through a suite of numerical simulations, we validate the performance of the proposed scheme and investigate the effects of surfactants on the droplet dynamics.
title Primal-dual splitting methods for phase-field surfactant model with moving contact lines
topic Numerical Analysis
Optimization and Control
Computational Physics
35A15, 35Q35, 35Q70, 47J25, 47J35, 65K10, 76M30
url https://arxiv.org/abs/2505.09469