Hybrid continuum-atomistic simulation of singular corner flow

A hybrid numerical method is used to study cavity flow driven by a moving wall. Continuum equations with no-slip boundary conditions predict singular stresses at the corners between moving and static walls. Molecular dynamics simulations are used to resolve these singular regions, and the flow field in the remainder of the cavity is obtained from the Navier-Stokes (NS) equations. This hybrid solution agrees well with fully atomistic simulations on small systems, and allows calculations to be accelerated by orders of magnitude in larger systems. Fully continuum and hybrid solutions for the stress and velocity also agree over most of the cavity. Both yield a shear stress that scales as the inverse of the distance from the corner over almost two orders of magnitude. However, in the hybrid solution, this divergence is cut off within a distance S from the corners. In the limit of low wall velocities U, S is a few molecular diameters and corresponds to the length over which slip occurs. By comparing the hybrid ...

[1]  Banavar,et al.  Molecular dynamics of Poiseuille flow and moving contact lines. , 1988, Physical review letters.

[2]  J. Rowlinson.  Virial expansions in an inhomogeneous system , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  Keith E. Gubbins,et al.  Poiseuille flow of Lennard-Jones fluids in narrow slit pores , 2000 .

[4]  A. Patera,et al.  Heterogeneous Atomistic-Continuum Representations for Dense Fluid Systems , 1997 .

[5]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[6]  Bocquet,et al.  Hydrodynamic boundary conditions and correlation functions of confined fluids. , 1993, Physical review letters.

[7]  H. Kapitza,et al.  A 3-d poisson solver based on conjugate gradients compared to standard iterative methods and its performance on vector computers , 1987 .

[8]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

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

[10]  George Keith Batchelor,et al.  An Introduction to Fluid Dynamics. , 1969 .

[11]  L. Mistura.  The definition of the pressure tensor in the statistical mechanics of nonuniform classical fluids , 1987 .

[12]  Evans,et al.  Pressure tensor for inhomogeneous fluids. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Kremer,et al.  Molecular dynamics simulation for polymers in the presence of a heat bath. , 1986, Physical review. A, General physics.

[14]  Robbins,et al.  Simulations of contact-line motion: Slip and the dynamic contact angle. , 1989, Physical review letters.

[15]  David B. Bogy,et al.  On the problem of edge-bonded elastic quarter-planes loaded at the boundary , 1970 .

[16]  Eirik Grude Flekkøy,et al.  Hybrid model for combined particle and continuum dynamics , 2000 .

[17]  S. Hess,et al.  Rheology of dense model fluids via nonequilibrium molecular dynamics: Shear thinning and ordering transition , 1989 .

[18]  Mapping molecular models to continuum theories for partially miscible fluids. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  M. Plischke,et al.  Density profiles and pair correlation functions of Lennard‐Jones fluids near a hard wall , 1986 .

[20]  Gene H. Golub,et al.  Matrix computations , 1983 .

[21]  E. W. Hart.  Thermodynamics of Inhomogeneous Systems , 1959 .

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

[23]  E. Wajnryb,et al.  Uniqueness of the microscopic stress tensor , 1995 .

[24]  Andrea Prosperetti,et al.  A Method for Particle Simulation , 2003 .

[25]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics , 1950 .

[26]  E. Dussan,et al.  On the interpretation of dynamic contact angles in capillaries , 1979, Journal of Fluid Mechanics.

[27]  F. Abraham,et al.  The interfacial density profile of a Lennard‐Jones fluid in contact with a (100) Lennard‐Jones wall and its relationship to idealized fluid/wall systems: A Monte Carlo simulation , 1978 .

[28]  L. Mistura.  The pressure tensor in nonuniform fluids , 1985 .

[29]  J. Banavar,et al.  Corner flow in the sliding plate problem , 1995 .

[30]  Xiaobo Nie,et al.  A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow , 2004, Journal of Fluid Mechanics.

[31]  Robbins,et al.  Shear flow near solids: Epitaxial order and flow boundary conditions. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[32]  Joel Koplik,et al.  Continuum Deductions from Molecular Hydrodynamics , 1997 .

[33]  Søren Toxvaerd.  The structure and thermodynamics of a solid–fluid interface , 1981 .

[34]  O'Connell,et al.  Molecular dynamics-continuum hybrid computations: A tool for studying complex fluid flows. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.