Stress tensors of multiparticle collision dynamics fluids.

Stress tensors are derived for the multiparticle collision dynamics algorithm, a particle-based mesoscale simulation method for fluctuating fluids, resembling those of atomistic or molecular systems. Systems with periodic boundary conditions as well as fluids confined in a slit are considered. For every case, two equivalent expressions for the tensor are provided, the internal stress tensor, which involves all degrees of freedom of a system, and the external stress, which only includes the interactions with the confining surfaces. In addition, stress tensors for a system with embedded particles are determined. Based on the derived stress tensors, analytical expressions are calculated for the shear viscosity. Simulations illustrate the difference in fluctuations between the various derived expressions and yield very good agreement between the numerical results and the analytically derived expression for the viscosity.

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

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

[3]  W. C. Swope,et al.  A computer simulation method for the calculation of equilibrium constants for the formation of physi , 1981 .

[4]  Gerhard Gompper,et al.  Multiparticle collision dynamics modeling of viscoelastic fluids. , 2008, The Journal of chemical physics.

[5]  J. M. Yeomans,et al.  Dynamics of short polymer chains in solution , 2000 .

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

[7]  H. Noguchi,et al.  Shape transitions of fluid vesicles and red blood cells in capillary flows. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[8]  R. Winkler.  Virial pressure of periodic systems with long range forces , 2002 .

[9]  D. Theodorou,et al.  Stress tensor in model polymer systems with periodic boundaries , 1993 .

[10]  Gerhard Gompper,et al.  Low-Reynolds-number hydrodynamics of complex fluids by multi-particle-collision dynamics , 2004 .

[11]  H. S. Green,et al.  A general kinetic theory of liquids. II. Equilibrium properties , 1947, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  T Ihle,et al.  Equilibrium calculation of transport coefficients for a fluid-particle model. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  J. F. Ryder,et al.  Shear thinning in dilute polymer solutions. , 2006, The Journal of chemical physics.

[14]  R. Winkler,et al.  Star polymers in shear flow. , 2006, Physical review letters.

[15]  H. Ted Davis,et al.  Statistical Mechanics of Phases, Interfaces and Thin Films , 1996 .

[16]  D. Y. Yoon,et al.  Novel molecular dynamics simulations at constant pressure , 1992 .

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

[18]  Roland G. Winkler,et al.  Polyelectrolyte electrophoresis: Field effects and hydrodynamic interactions , 2008 .

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

[20]  R. Winkler,et al.  Liquid benzene confined between graphite surfaces. A constant pressure molecular dynamics study , 1993 .

[21]  G. Gompper,et al.  Mesoscale simulations of polymer dynamics in microchannel flows , 2007, 0709.3822.

[22]  G Gompper,et al.  Dynamic regimes of fluids simulated by multiparticle-collision dynamics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  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.

[24]  T Ihle,et al.  Resummed Green-Kubo relations for a fluctuating fluid-particle model. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Raymond Kapral,et al.  Friction and diffusion of a Brownian particle in a mesoscopic solvent. , 2004, The Journal of chemical physics.

[26]  C M Pooley,et al.  Kinetic theory derivation of the transport coefficients of stochastic rotation dynamics. , 2005, The journal of physical chemistry. B.

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

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

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

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

[31]  J. Yeomans,et al.  Statistical mechanics of phase transitions , 1992 .

[32]  R. Becker,et al.  Theory of Heat , 1967 .

[33]  J. F. Ryder,et al.  Kinetics of the polymer collapse transition: the role of hydrodynamics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  R. Winkler,et al.  Dynamics of polymers in a particle-based mesoscopic solvent. , 2005, The Journal of chemical physics.

[35]  On the Equivalence of Atomic and Molecular Pressure , 2004 .

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