Generalized lattice Boltzmann method with multirange pseudopotential.

The physical behavior of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudopotential method is developed, which permits to tune the equation of state and surface tension independently of each other. The spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and/or high order isotropy. Higher order schemes to implement self-consistent forcings are rigorously computed for 2d and 3d models. The extended scenario developed in this work clarifies the theoretical foundations of the Shan-Chen methodology for the lattice Boltzmann method and enhances its applicability and flexibility to the simulation of multiphase flows to density ratios up to O(100).

[1]  J. Harting,et al.  On the effect of surfactant adsorption and viscosity change on apparent slip in hydrophobic microchannels , 2006, cond-mat/0610034.

[2]  X. Shan.  Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Laura Schaefer,et al.  Equations of state in a lattice Boltzmann model , 2006 .

[4]  D. Quéré,et al.  Bouncing transitions on microtextured materials , 2006 .

[5]  J. Horbach,et al.  Lattice boltzmann versus molecular dynamics simulation of nanoscale hydrodynamic flows. , 2006, Physical review letters.

[6]  S Succi,et al.  Mesoscopic modeling of a two-phase flow in the presence of boundaries: The contact angle. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  J. Yeomans,et al.  Drop dynamics on chemically patterned surfaces , 2006, cond-mat/0601541.

[8]  A. Buguin,et al.  Bouncing or sticky droplets: Impalement transitions on superhydrophobic micropatterned surfaces , 2005, cond-mat/0510773.

[9]  S. Quake,et al.  Microfluidics: Fluid physics at the nanoliter scale , 2005 .

[10]  Hans Jürgen Herrmann,et al.  Lattice Boltzmann simulations of apparent slip in hydrophobic microchannels , 2005, physics/0509035.

[11]  J. Yeomans,et al.  Modeling droplets on superhydrophobic surfaces: equilibrium states and transitions. , 2005, Langmuir : the ACS journal of surfaces and colloids.

[12]  Junfeng Zhang,et al.  Lattice boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces. , 2004, Langmuir : the ACS journal of surfaces and colloids.

[13]  T. Inamuro,et al.  A lattice Boltzmann method for incompressible two-phase flows with large density differences , 2004 .

[14]  J. Yeomans,et al.  Lattice Boltzmann simulations of contact line motion. II. Binary fluids. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  A. Wagner,et al.  Lattice Boltzmann simulations of contact line motion. I. Liquid-gas systems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  V. Sofonea,et al.  Reduction of Spurious Velocity in Finite Difference Lattice Boltzmann Models for Liquid-Vapor Systems , 2003, nlin/0305013.

[17]  A. Wagner.  The Origin of Spurious Velocities in Lattice Boltzmann , 2002, cond-mat/0207558.

[18]  C. Clanet,et al.  Surface phenomena: Contact time of a bouncing drop , 2002, Nature.

[19]  B. Shi,et al.  Discrete lattice effects on the forcing term in the lattice Boltzmann method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Xiaoyi He,et al.  Thermodynamic Foundations of Kinetic Theory and Lattice Boltzmann Models for Multiphase Flows , 2002 .

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

[22]  Sauro Succi,et al.  Applying the lattice Boltzmann equation to multiscale fluid problems , 2001, Comput. Sci. Eng..

[23]  A. Ladd,et al.  Lattice-Boltzmann Simulations of Particle-Fluid Suspensions , 2001 .

[24]  J. Chun,et al.  The recoiling of liquid droplets upon collision with solid surfaces , 2001 .

[25]  Chen,et al.  Lattice-boltzmann model for interacting amphiphilic fluids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  D. Quéré,et al.  Bouncing water drops , 2000 .

[27]  J. Buick,et al.  Gravity in a lattice Boltzmann model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  D. Wolf-Gladrow.  Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , 2000 .

[29]  Yeomans,et al.  Lattice Boltzmann simulation of nonideal fluids. , 1995, Physical review letters.

[30]  Shan,et al.  Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[33]  S. Wolfram.  Cellular automaton fluids 1: Basic theory , 1986 .

[34]  A. Yarin.  Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing ... , 2006 .

[35]  John Ellis,et al.  Int. J. Mod. Phys. , 2005 .

[36]  Theo G. Theofanous,et al.  The lattice Boltzmann equation method: theoretical interpretation, numerics and implications , 2003 .

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

[38]  K. N. Dollman,et al.  - 1 , 1743 .