Effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions

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• 作者：Jianwei Guo^a ; Sté ; phanie Veran-Tissoires^a ; ^b ; ^{stephanie.veran@u-bordeaux.fr" class="auth_mail" title="E-mail the corresponding author} ; Michel Quintard^a ; ^c
• 关键词：Heterogeneous surface ; Multi-domain decomposition ; Closure problems ; Effective surface ; Effective boundary conditions
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：305
• 期：Complete
• 页码：942-963
• 全文大小：3361 K

文摘

To deal with multi-scale problems involving transport from a heterogeneous and rough surface characterized by a mixed boundary condition, an effective surface theory is developed, which replaces the original surface by a homogeneous and smooth surface with specific boundary conditions. A typical example corresponds to a laminar flow over a soluble salt medium which contains insoluble material. To develop the concept of effective surface, a multi-domain decomposition approach is applied. In this framework, velocity and concentration at micro-scale are estimated with an asymptotic expansion of deviation terms with respect to macro-scale velocity and concentration fields. Closure problems for the deviations are obtained and used to define the effective surface position and the related boundary conditions. The evolution of some effective properties and the impact of surface geometry, Péclet, Schmidt and Damköhler numbers are investigated. Finally, comparisons are made between the numerical results obtained with the effective models and those from direct numerical simulations with the original rough surface, for two kinds of configurations.