Curvature boundary condition for a moving contact line

Effective wall boundary conditions are very important for simulating multi-phase flows involving a moving contact line. In this paper we present a curvature boundary condition to circumvent the difficulties 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 flow 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.

[1]  I. Hutchings,et al.  Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface , 2009 .

[2]  M. Sussman,et al.  A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows , 2000 .

[3]  Yi Sui,et al.  An efficient computational model for macroscale simulations of moving contact lines , 2013, J. Comput. Phys..

[4]  Nikolaus A. Adams,et al.  A physically consistent weakly compressible high-resolution approach to underresolved simulations of incompressible flows , 2013 .

[5]  R. G. Cox.  The dynamics of the spreading of liquids on a solid surface. Part 2. Surfactants , 1986, Journal of Fluid Mechanics.

[6]  Oleg Weinstein,et al.  Scale Dependence of Contact Line Computations , 2006 .

[7]  R. G. Cox.  The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow , 1986, Journal of Fluid Mechanics.

[8]  Ping Sheng,et al.  Molecular scale contact line hydrodynamics of immiscible flows. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[10]  James J. Feng,et al.  Can diffuse-interface models quantitatively describe moving contact lines? , 2011 .

[11]  Yasufumi Yamamoto,et al.  Modeling of the dynamic wetting behavior in a capillary tube considering the macroscopic–microscopic contact angle relation and generalized Navier boundary condition , 2014 .

[12]  Nikolaus A. Adams,et al.  A conservative interface method for compressible flows , 2006, J. Comput. Phys..

[13]  M. Wörner.  Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications , 2012 .

[14]  Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact angle , 2002, Journal of Fluid Mechanics.

[15]  Enrique Rame,et al.  On an approximate model for the shape of a liquid–air interface receding in a capillary tube , 1997, Journal of Fluid Mechanics.

[16]  G. Blanquart,et al.  A Level Set Based Method to Simulate Contact Line Motion and Dynamic Contact Angles for Multiphase Flow , 2012 .

[17]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[18]  Suchuan Dong,et al.  On imposing dynamic contact-angle boundary conditions for wall-bounded liquid–gas flows , 2012 .

[19]  Nikolaus A. Adams,et al.  Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure , 2014, J. Comput. Phys..

[20]  Moving Contact Line with Balanced Stress Singularities , 2008, 0806.3847.

[21]  Stéphane Zaleski,et al.  A mesh-dependent model for applying dynamic contact angles to VOF simulations , 2008, J. Comput. Phys..

[22]  S. Kalliadasis,et al.  Dynamics of moving contact lines: A comparison between slip and precursor film models , 2011 .

[23]  F. Schönfeld,et al.  Dynamic contact angles in CFD simulations , 2009 .

[24]  D. Ahn,et al.  Spreading of an inkjet droplet on a solid surface with a controlled contact angle at low Weber and Reynolds numbers. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[25]  Xiangyu Hu,et al.  An interface interaction method for compressible multifluids , 2004 .

[26]  J. Li,et al.  Numerical simulation of moving contact line problems using a volume-of-fluid method , 2001 .

[27]  Nikolaus A. Adams,et al.  A conservative sharp interface method for incompressible multiphase flows , 2015, J. Comput. Phys..

[28]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[29]  C. Tropea,et al.  3D computation of an incipient motion of a sessile drop on a rigid surface with contact angle hysteresis , 2015 .

[30]  M. Griebel,et al.  Simulation of Droplet Impact with Dynamic Contact Angle Boundary Conditions , 2014 .

[31]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[32]  C. Naraynan,et al.  Simulation of filling of microfluidic devices using a coarse-grained continuum contact angle model , 2006 .

[33]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[34]  Wei Lu,et al.  A Local Semi-Implicit Level-Set Method for Interface Motion , 2008, J. Sci. Comput..

[35]  E Weinan,et al.  Continuum models for the contact line problem , 2010 .

[36]  A. Zosel,et al.  Studies of the wetting kinetics of liquid drops on solid surfaces , 1993 .

[37]  B. Andreotti,et al.  Moving Contact Lines: Scales, Regimes, and Dynamical Transitions , 2013 .

[38]  Dominique Legendre,et al.  Numerical simulation of static and sliding drop with contact angle hysteresis , 2010, J. Comput. Phys..

[39]  Mark Sussman,et al.  A method for overcoming the surface tension time step constraint in multiphase flows II , 2012 .

[40]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[41]  L. Tanner,et al.  The spreading of silicone oil drops on horizontal surfaces , 1979 .

[42]  Guillaume Blanquart,et al.  Level set reinitialization at a contact line , 2014, J. Comput. Phys..

[43]  Gihun Son,et al.  A Level-Set Method for Simulation of a Thermal Inkjet Process , 2008 .

[44]  J. E. Sprittles,et al.  Finite element simulation of dynamic wetting flows as an interface formation process , 2012, J. Comput. Phys..

[45]  H. Udaykumar,et al.  Sharp interface Cartesian grid method II: A technique for simulating droplet interactions with surfaces of arbitrary shape , 2005 .

[46]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[47]  B. Müller,et al.  Contact line treatment with the sharp interface method , 2013 .