Curvature boundary condition for a moving contact line.pdfVIP

Journal of Computational Physics 310 (2016) 329–341 Contents lists available at ScienceDirect Journal of Computational Physics /locate/jcp Curvature boundary condition for a moving contact line J. Luo, X.Y. Hu ?, N.A. Adams Institute of Aerodynamics and Fluid Mechanics, Technische Universit?t München, 85747 Garching, Germany article info Article history: Received 8 December 2014 Received in revised form 19 January 2016 Accepted 21 January 2016 Available online 25 January 2016 Keywords: Moving contact line Dynamic contact angle Surface tension Conservative sharp-interface method Level-set method abstract Effective wall boundary conditions are very important for simulating multi-phase ?ows involving a moving contact line. In this paper we present a curvature boundary condition to circumvent the di?culties of previous approaches on explicitly imposing the contact angle and with respect to mass-loss artifacts near the wall boundary. While employing the asymptotic theory of Cox for imposing an effective curvature directly at the wall surface, the present method avoids a mismatch between the exact and the numerical contact angles. Test simulations on drop spreading and multi-phase ?ow in a channel show that the present method achieves grid-convergent results and ensures mass conservation, and delivers good agreement with theoretical, numerical and experimental data. ? 2016 Elsevier Inc. All rights reserved. 1. Introduction Wetting or dewetting of a solid surface occurs in a number of applications, such as coating, lamination, inkjet printing and spray painting [44,33,35]. A phenomenon common to these applications is the moving contact line, where one ?uid displaces the other. A fundamental di?culty in the numerical treatment of the contact line arises with the conventional no-slip boundary condition, as it leads to inconsistent, grid-dependent results [10,34]. Various approaches have been proposed to alleviate this problem, such as the slip model [39,37], the precursor ?l