Study on the Navier boundary condition for flows with a moving contact line by means of molecular dynamics simulation

• Published in: Nihon Kikai Gakkai ronbunshu
• Main Authors: Yuka HIZUMI, Takeshi OMORI, Yasutaka YAMAGUCHI, Takeo KAJISHIMA
• Format: Article
• Language: Japanese
• Published: The Japan Society of Mechanical Engineers 2015-10-01
• Subjects: dynamic wetting; moving contact line; contact line dynamics; slip velocity; molecular dynamics; navier boundary condition
• Online Access: https://www.jstage.jst.go.jp/article/transjsme/81/831/81_15-00409/_pdf/-char/en

While the Navier boundary condition, which claims the proportionality between fluid slip velocity and wall shear stress (Qian et al., 2003, Bocquet and Barrat, 2007), was established by Thompson and Troian (1997) for a single-phase Newtonian fluid flowing along an atomically defect-less solid wall under a wide range of shear rate conditions, its validity for flows with a contact line has not been proved yet even for the simplest pairing of a monoatomic fluid and a solid with a face-centered cubic structure. In the studies of Qian et al. (2003, 2006) the static wall shear stress was subtracted in the formulation of their Navier boundary condition, but as we show, it is not physically justified. Ren and E (2007) formulated a Navier boundary condition in terms of the fluid slip velocity and wall shear stress integrated through the region containing the contact line in a similar fashion to the present work, providing no physical grounds regarding their particular choice of the integration region and the interfacial region. We performed molecular dynamics simulations of Couette flows where two immiscible liquids with an identical molecular mass and identical interaction potentials were driven by two parallel solid walls so that steady flows with moving contact lines were formed. Based on the detailed analysis of stress tensor and slip velocity distributions both for static and dynamic cases, we show that the Navier boundary condition should be formulated in terms of the quantities integrated through the fluid-fluid interaction region in the first adsorption layer formed on the solid wall. In order to investigate the relevance of the Navier boundary condition as a boundary condition of the Navier-Stokes equation, the validity of Newton's law of viscosity between the first and second adsorption layers is also examined.