Rheological properties of polymer melt between rapidly oscillating plates: - an application of multiscale modeling -

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1 Rheological properties of polymer melt between rapidly oscillating plates: - an application of multiscale modeling - Ryoichi Yamamoto and Shugo Yasuda Dept. Chemical Engineering, Kyoto University (and CREST, Japan Science and Technology Agency) Molecular Simulations: Algorithms, Analysis, and Applications (May 18-22, 2009, IMA) 1

2 contents Multiscale simulations for soft matters - our motivation and strategy Example 1: - flow of polymer melt (1D) Example 2: - flow of simple liquid (2D) 2

3 contents Multiscale simulations for soft matters - our motivation and strategy Example 1: - flow of polymer melt (1D) Example 2: - flow of simple liquid (2D) 3

4 methods for soft matters micro-scale method (MD, MC) meso-scale method (TDGL, DFT, BD, etc) macro-scale method (CFD, etc) multi-scale method (pre-comp, on-demand, etc) nm mm mm m 4

5 why multi-scale for soft matters? polymer flow polymer << flow scale << container colloidal systems ion << colloid << domain, flow scale glasses molecule << collective motion etc... 5

6 KAPSEL v1 (2006), v2 (2009) meso-scale method (SPM) Sedimentation (colloids + fluid) System size 128 x 128 x 2048 Number of particles N = 4000 Particle diameter D = 10 Particle volume fraction Φ = 0.06 Particle Reynolds no. Re = 1.5 Computation time 1 week on 8-core Xeon machine (8,000 USD) 6

7 Kim, Nakayama & RY, PRL (2006) meso-scale mothod (SPM) electrophoresis of charged particles ( solvent + ions + colloids ) Electric field Electric field 7

8 KAPSEL v1 (2006), v2 (2009) meso-scale method (SPM) AC Electric field System size 64 x 64 x 64 Number of particles N = 32 Particle diameter D = 8 Computation time 1 day on Intel 1-core machine (1,000 USD) 8

9 Kim, Nakayama & RY, PRL (2006) EPJE (2008) meso-scale method (SPM) from function / functional to direct numerical evaluation 9

10 MSS ( ) multi-scale method (future) extended MC Sampling a sketch... 10

11 space resolution Dx Space 1. pre-computation simulation to pre-compute parameters to be used in coarse simulation Dt time resolution Time t = 0 coarse simulation

12 Space 2. locally embedded (synchronous) exterior simulation evolving synchronously with coarse simulation point of interest (crack front, nuclei, etc...) Time exterior t = 0 coarse simulation

13 space resolution Dx Space 3. local sampling (synchronous) HMM, Ren & E (2005) etc... simulation l MD MD box size simulation simulation Time t = 0 simulation coarse simulation saving factor = (Dx / l MD ) d

14 Space 3. local sampling (on-demand) HMM, Ren & E (2005) etc... assuming local stationality in simulation t MD : duration of simulation Dt Time t = 0 coarse simulation saving factor = (Dt / t MD )(Dx / l MD ) d

15 related previous works scale bridging algorithms equation-free method, Kevrekidis et. al. (2003) heterogeneous multi-scale modeling, Ren & E (2005)... polymer flow De, Fish, Shephard, Keblinski, & Kumar, PRE (2006) Ren s talk in this workshop... 15

16 related previous works scale bridging algorithms equation-free method, Kevrekidis et. al. (2003) heterogeneous multi-scale modeling, Ren & E (2005)... polymer flow De, Fish, Shephard, Keblinski, & Kumar, PRE (2006) Ren s talk in this workshop... simple catching ideas, but there are still many problems to be overcome, some are very serious 16

17 contents Multiscale simulations for soft matters - our motivation and strategy Example 1: - flow of polymer melt (1D) Example 2: - flow of simple liquid (2D) 17

18 Yasuda & RY, EPL (2009) system under consideration polymer melt between rapidly oscillating plates 2H y x K-G chains (N=10) in severely jammed condition 18

19 Yasuda & RY, EPL (2009) our multi-scale method mid-point (symmetric b.c.) CFD (1D) l = 16 MD (3D) NEMD (SLLOD): Dx > l MD CFD: 1000 beads in a box (N=10 x 100 chains) bottom plate (non-slip b.c.) l = 0 memory space save only Dt CFD = t Sample = 1000Dt MD 19

20 Yasuda & RY, EPL (2009) polymer vs. Newtonian velocity saving factor = 5 Dx / l MD = 5 Dt CFD / t Sample = 1 Newtonian case Thickness of the boundary layer becomes thinner for polymer melt due to shear thinning taking place near the plate. 20

21 Yasuda & RY, EPL (2009) local complex rhology strain amplitude phase retardation elastic stress viscous stress storage modulus (elastic response) loss modulus (viscous response) local complex modulus 21

22 Yasuda & RY, EPL (2009) local complex rheology visco-elastic solid G >G visco-elastic fluid G > G viscous fluid G >> G 22

23 Yasuda & RY, EPL (2009) local complex rheology visco-elastic solid G >G visco-elastic fluid G > G viscous fluid G >> G 23

24 contents Multiscale simulations for soft matters - our motivation and strategy Example 1: - flow of polymer melt (1D) Example 2: - flow of simple liquid (2D) 24

25 Yasuda & RY, Phys. Fluids (2008) system under consideration Driven Cavity Flow (2D) sliding velocity U w simple Lennard-Jones (WCA) fluid Reynolds number non-slip b.c. 25

26 Yasuda & RY, Phys. Fluids (2008) our multi-scale method CFD: CFD (2D) y MD (3D) NEMD: q 256 particles / box 32 x 32 box x space-time save rotation, q 26

27 Yasuda & RY, Phys. Fluids (2008) multi-scale vs. CFD multi-scale CFD saving factor = 64 (Dx / l MD ) 2 = 16 Dt CFD / t Sample = 4 snapshot at 27

28 Yasuda & RY, unpublished more cost-saving time evolution steady state profile (color represents pressure) pressure saving factor = 512 (Dx / l MD ) 2 = 64 Dt CFD / t Sample = 8 28

29 Yasuda & RY, Phys. Fluids (2008) fluctuation analysis fluctuating local stress Foulier transform. y spectrum density x 29

30 Yasuda & RY, Phys. Fluids (2008) multi-scale vs. fluct. hydro. comparison with fluctuating hydrodynamics for saving factor = 1 ( Δx / l MD =1, Δt / t MD =1 ) Re = 59 saving factor = 1 signal + (white) noise 30

31 Yasuda & RY, Phys. Fluids (2008) a scaling hypothesis (CLT) Re = 235 saving factor = 8 saving factor = 5 saving factor = 2.5 thermally fluctuating local stress artificial fluctuation 31

32 summary and outlook simple fluid (1D, 2D, 3D) complex fluid (1D) complex fluid (2D, 3D) space-time save MD + grid-based CFD space save MD + grid-based CFD need effective N.R. to make more saving!! -> low-pass filter? space save MD + off-grid CFD (SPH,etc) 32