Pairwise Force Smoothed Particle Hydrodynamics model for multiphase flow: Surface tension and contact line dynamics

We present a novel formulation of the Pairwise Force Smoothed Particle Hydrodynamics (PF-SPH) model and use it to simulate two- and three-phase flows in bounded domains. In the PF-SPH model, the Navier-Stokes equations are discretized with the Smoothed Particle Hydrodynamics (SPH) method, and the Young-Laplace boundary condition at the fluid-fluid interface and the Young boundary condition at the fluid-fluid-solid interface are replaced with pairwise forces added into the Navier-Stokes equations. We derive a relationship between the parameters in the pairwise forces and the surface tension and static contact angle. Next, we demonstrate the model's accuracy under static and dynamic conditions. Finally, we use the Pf-SPH model to simulate three phase flow in a porous medium.

[1]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[2]  D. Bonn,et al.  Wetting and Spreading , 2009 .

[3]  Zhou,et al.  Immiscible-fluid displacement: Contact-line dynamics and the velocity-dependent capillary pressure. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[4]  J. Morris,et al.  Modeling Low Reynolds Number Incompressible Flows Using SPH , 1997 .

[5]  P. Gennes.  Wetting: statics and dynamics , 1985 .

[6]  Alexandre M. Tartakovsky,et al.  Smoothed Particle Hydrodynamics Model of Non-Aqueous Phase Liquid Flow and Dissolution , 2008 .

[7]  Ali Q. Raeini,et al.  Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method , 2012, J. Comput. Phys..

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

[9]  Hai Huang,et al.  Dissipative particle dynamics simulation of fluid motion through an unsaturated fracture and fracture junction , 2007, J. Comput. Phys..

[10]  Maria Ines Dragila,et al.  Fluid motion through an unsaturated fracture junction , 2004 .

[11]  Nikolaus A. Adams,et al.  A multi-phase SPH method for macroscopic and mesoscopic flows , 2006, J. Comput. Phys..

[12]  P. Meakin,et al.  Modeling and simulation of pore‐scale multiphase fluid flow and reactive transport in fractured and porous media , 2009 .

[13]  John S. Rowlinson,et al.  Molecular Theory of Capillarity , 1983 .

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

[15]  J. Morris.  Simulating surface tension with smoothed particle hydrodynamics , 2000 .

[16]  Paul Meakin,et al.  Modeling of surface tension and contact angles with smoothed particle hydrodynamics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[18]  L. Scriven,et al.  Hydrodynamic Model of Steady Movement of a Solid / Liquid / Fluid Contact Line , 1971 .

[19]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[20]  Alexandre M. Tartakovsky,et al.  Simulation of Unsaturated Flow in Complex Fractures Using Smoothed Particle Hydrodynamics , 2005 .

[21]  Bruce J. Palmer,et al.  Smoothed particle hydrodynamics pore-scale simulations of unstable immiscible flow in porous media , 2013 .

[22]  P. Meakin,et al.  Pore scale modeling of immiscible and miscible fluid flows using smoothed particle hydrodynamics , 2006 .

[23]  R. Hardy,et al.  Formulas for determining local properties in molecular‐dynamics simulations: Shock waves , 1982 .

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

[25]  Paul Meakin,et al.  Three‐dimensional simulation of liquid drop dynamics within unsaturated vertical Hele‐Shaw cells , 2008 .

[26]  Alexandre M. Tartakovsky,et al.  A smoothed particle hydrodynamics model for droplet and film flow on smooth and rough fracture surfaces , 2013 .

[27]  Kim F. Ferris,et al.  Lagrangian particle model for multiphase flows , 2009, Comput. Phys. Commun..

[28]  M. Lastiwka,et al.  Truncation error in mesh‐free particle methods , 2006 .

[29]  Alexandre M. Tartakovsky,et al.  Pore-scale simulations of drainage of heterogeneous and anisotropic porous media , 2007 .

[30]  Ivan Lunati,et al.  Hybrid Multiscale Finite Volume method for two-phase flow in porous media , 2013, J. Comput. Phys..

[31]  E. B. Dussan,et al.  LIQUIDS ON SOLID SURFACES: STATIC AND DYNAMIC CONTACT LINES , 1979 .

[32]  Nikolaus A. Adams,et al.  A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation , 2010, J. Comput. Phys..

[33]  John R. Williams,et al.  Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media , 2011 .