Multiscale modelling strategy using the lattice Boltzmann method for polymer dynamics in a turbulent flow

Polymer dynamics in a turbulent flow is a problem spanning several orders of magnitude in length and time scales. A microscopic simulation covering all those scales from the polymer segment to the inertial scale of turbulence remains improbable within the foreseeable future. We propose a multiscale simulation strategy to enhance the spatio-temporal resolution of the local Lagrangian turbulent flow by matching two different simulation techniques, i.e. direct numerical simulation for the flow as a whole, and the lattice Boltzmann method coupled to polymer dynamics at the Kolmogorov dissipation scale. Local turbulent flows sampled by Lagrangian tracer particles in the direct numerical simulation are reproduced in the lattice Boltzmann model with a finer resolution, by supplying the latter with both the correct initial condition as well as the correct time-dependent boundary condition, sampled from the former. When combined with a Molecular Dynamics simulation of a polymer chain in the lattice Boltzmann model, it provides a strategy to simulate the passive dynamics of a polymer chain in a turbulent flow covering all these scales. Although this approach allows for a fairly realistic model of the macromolecule, the back-coupling to the flow on the large scales is missing.

[1]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[2]  A. Ladd,et al.  Lattice Boltzmann Simulations of Soft Matter Systems , 2008, 0803.2826.

[3]  R Everaers,et al.  Screening of hydrodynamic interactions in semidilute polymer solutions: a computer simulation study. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Joerg Schumacher,et al.  Stretching of polymers around the Kolmogorov scale in a turbulent shear flow , 2006 .

[5]  Richard H. Nadolink,et al.  Bibliography on Skin Friction Reduction With Polymers and Other Boundary-Layer Additives , 1995 .

[6]  John L. Lumley,et al.  Drag reduction in turbulent flow by polymer additives , 1973 .

[7]  E. J. Hinch,et al.  Mechanical models of dilute polymer solutions in strong flows , 1977 .

[8]  Parviz Moin,et al.  Simulated polymer stretch in a turbulent flow using Brownian dynamics , 2004, Journal of Fluid Mechanics.

[9]  Victor Yakhot,et al.  Asymptotic exponents from low-Reynolds-number flows , 2006 .

[10]  Marco Martins Afonso,et al.  Nonlinear elastic polymers in random flow , 2005, Journal of Fluid Mechanics.

[11]  Victor K. La Mer,et al.  Proceedings of the International Congress on Rheology: Holland, 1948. Edited by The Organizing Committee. North-Holland Publishing Company, Amsterdam, and Interscience Publishers, Inc., N. Y., 1949. Price $11.00 , 1950 .

[12]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[13]  John L. Lumley,et al.  Drag Reduction by Additives , 1969 .

[14]  Vasil Tiberkevich,et al.  Drag reduction by polymers in wall bounded turbulence. , 2003, Physical review letters.

[15]  Ronald G. Larson,et al.  Brownian dynamics simulations of single DNA molecules in shear flow , 2000 .

[16]  Christopher White,et al.  The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote , 2000, Journal of Fluid Mechanics.

[17]  Michael D. Graham,et al.  Polymer dynamics in a model of the turbulent buffer layer , 2003 .

[18]  P. Ahlrichs,et al.  Simulation of a single polymer chain in solution by combining lattice Boltzmann and molecular dynamics , 1999, cond-mat/9905183.

[19]  Roberto Benzi,et al.  Theory of concentration dependence in drag reduction by polymers and of the maximum drag reduction asymptote. , 2003, Physical review letters.

[20]  G. Fredrickson.  The theory of polymer dynamics , 1996 .

[21]  A Celani,et al.  Dynamical slowdown of polymers in laminar and random flows. , 2006, Physical review letters.

[22]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[23]  P. Gennes.  Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients , 1974 .

[24]  P. G. de Gennes,et al.  A Cascade Theory of Drag Reduction , 1986 .

[25]  Juan J de Pablo,et al.  Shear-induced migration in flowing polymer solutions: simulation of long-chain DNA in microchannels [corrected]. , 2004, The Journal of chemical physics.

[26]  B. A. Toms,et al.  Some Observations on the Flow of Linear Polymer Solutions Through Straight Tubes at Large Reynolds Numbers , 1948 .

[27]  Thomas Peters,et al.  Two-way coupling of finitely extensible nonlinear elastic dumbbells with a turbulent shear flow , 2007 .