Fluid–solid boundary conditions for multiparticle collision dynamics

The simulation of colloidal particles suspended in solvent requires an accurate representation of the interactions between the colloids and the solvent molecules. Using the multiparticle collision dynamics method, we examine several proposals for stick boundary conditions, studying their properties in both plane Poiseuille flow (where fluid interacts with the boundary of a stationary macroscopic solid) and particle-based colloid simulations (where the boundaries are thermally affected and in motion). In addition, our simulations compare various collision rules designed to remove spurious slip near solid surfaces, and the effects of these rules on the thermal motion of colloidal particles. Furthermore, we demonstrate that stochastic reflection of the fluid at solid boundaries fails to faithfully represent stick boundary conditions, and conclude that bounce-back conditions should be applied at both mobile and stationary surfaces. Finally, we generalize these ideas to create partial slip boundary conditions at both stationary and mobile surfaces.

[1]  R. Kapral.  Multiparticle Collision Dynamics: Simulation of Complex Systems on Mesoscales , 2008 .

[2]  B. Berne,et al.  Molecular hydrodynamics of the partially rough sphere fluid , 1977 .

[3]  Jens Harting,et al.  Shear viscosity of claylike colloids in computer simulations and experiments. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Hiroshi Noguchi,et al.  Dynamics of vesicle self-assembly and dissolution. , 2006, The Journal of chemical physics.

[5]  G. Gompper,et al.  Mesoscopic solvent simulations: multiparticle-collision dynamics of three-dimensional flows. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  H. T. Davis,et al.  Molecular dynamical studies of rough-sphere fluids , 1975 .

[7]  J. Padding,et al.  Hydrodynamic interactions and Brownian forces in colloidal suspensions: coarse-graining over time and length scales. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Hiroshi Noguchi,et al.  Swinging and tumbling of fluid vesicles in shear flow. , 2007, Physical review letters.

[9]  Steve Granick,et al.  Slippery questions about complex fluids flowing past solids , 2003, Nature materials.

[10]  R. Winkler,et al.  Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids , 2008, 0808.2157.

[11]  T Ihle,et al.  Stochastic rotation dynamics. I. Formalism, Galilean invariance, and Green-Kubo relations. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Julia M. Yeomans,et al.  Mesoscale simulations: Lattice Boltzmann and particle algorithms , 2006 .

[13]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[14]  Transport coefficients of multi-particle collision algorithms with velocity-dependent collision rules. , 2008, Journal of physics. Condensed matter : an Institute of Physics journal.

[15]  Hiroshi Noguchi,et al.  Transport coefficients of off-lattice mesoscale-hydrodynamics simulation techniques. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  B. Berne,et al.  A hydrodynamic theory of the angular velocity correlation function with arbitrary slip boundary conditions , 1977 .

[17]  J. F. Ryder,et al.  Transport coefficients of a mesoscopic fluid dynamics model , 2003, cond-mat/0302451.

[18]  Hiroshi Noguchi,et al.  Vesicle dynamics in shear and capillary flows , 2005 .

[19]  Thomas Ihle,et al.  Consistent particle-based algorithm with a non-ideal equation of state , 2006 .

[20]  B. Berne,et al.  The coupling between translational and rotational motions , 1976 .

[21]  Hiroshi Noguchi,et al.  Fluid vesicles with viscous membranes in shear flow. , 2004, Physical review letters.

[22]  J. Padding,et al.  Interplay between hydrodynamic and Brownian fluctuations in sedimenting colloidal suspensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  T Ihle,et al.  Stochastic rotation dynamics. II. Transport coefficients, numerics, and long-time tails. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  B. Berne.  Molecular dynamics of the rough sphere fluid. II. Kinetic models of partially sticky spheres, structured spheres, and rough screwballs , 1977 .

[25]  Raymond Kapral,et al.  Two-particle friction in a mesoscopic solvent. , 2005, The Journal of chemical physics.

[26]  J. F. Ryder,et al.  Modeling microscopic swimmers at low Reynolds number. , 2007, The Journal of chemical physics.

[27]  A Lamura,et al.  Numerical study of the flow around a cylinder using multi-particle collision dynamics , 2002, The European physical journal. E, Soft matter.

[28]  T. Ihle,et al.  Stochastic rotation dynamics: a Galilean-invariant mesoscopic model for fluid flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Eric Lauga,et al.  A note on the stability of slip channel flows , 2005, physics/0503225.

[30]  A. Malevanets,et al.  Mesoscopic model for solvent dynamics , 1999 .

[31]  H. Herrmann,et al.  Simulation of claylike colloids. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  S. Lee,et al.  Molecular Dynamics Simulations of Small n-Alkane Clusters in a Mesoscopic Solvent , 2003 .

[33]  J T Padding,et al.  Hydrodynamic and brownian fluctuations in sedimenting suspensions. , 2004, Physical review letters.

[34]  J. T. Padding,et al.  Stick boundary conditions and rotational velocity auto-correlation functions for colloidal particles in a coarse-grained representation of the solvent , 2005 .

[35]  J. Yeomans,et al.  Polymer translocation: the effect of backflow. , 2005, The Journal of chemical physics.

[36]  Masato Makino,et al.  Simulation of DNA motion in a microchannel using stochastic rotation dynamics. , 2007, The Journal of chemical physics.

[37]  A. Malevanets,et al.  Solute molecular dynamics in a mesoscale solvent , 2000 .

[38]  Bruce J. Berne,et al.  Molecular dynamics of the rough sphere fluid. I. Rotational relaxation , 1975 .

[39]  T. Ihle,et al.  Erratum: Multi-particle collision dynamics: Flow around a circular and a square cylinder , 2001, cond-mat/0110148.

[40]  Hiroshi Noguchi,et al.  Relevance of angular momentum conservation in mesoscale hydrodynamics simulations. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[42]  Hiroshi Noguchi,et al.  Particle-based mesoscale hydrodynamic techniques , 2006, cond-mat/0610890.

[43]  C. Pangali,et al.  Molecular dynamics of the rough sphere fluid. III. The dependence of translational and rotational motion on particle roughness , 1977 .

[44]  T Ihle,et al.  Transport coefficients for stochastic rotation dynamics in three dimensions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Hirotada Ohashi,et al.  Development of a Simulation Model for Solid Objects Suspended in a Fluctuating Fluid , 2002 .

[46]  K. Kremer,et al.  Advanced Computer Simulation Approaches for Soft Matter Sciences III , 2005 .