Molecular simulation of fluid dynamics on the nanoscale

Transcription

1 VI. International Conference on Computational Fluid Dynamics Molecular simulation of fluid dynamics on the nanoscale St. Petersburg, July 16, 2010 M. Horsch, Y.-Tz. Hsiang, Z. Liu, S. K. Miroshnichenko, J. Zhai, J. Vrabec Universität Paderborn (IVT) Universität Stuttgart (ITT), National Cheng Kung University ( 國 立 成 功 大 學 )

2 Simulation scenario: Poiseuille flow z z Poiseuille flow: The fluid and a single wall are accelerated in opposite directions Couette flow: -z Two walls are accelerated in opposite directions

3 Simulation scenario: Couette flow z Poiseuille flow: The fluid and a single wall are accelerated in opposite directions Couette flow: -z Two walls are accelerated in opposite directions

4 Short-range ordering in a nanochannel fluid density in units of mol/l T = 175 K; r = 18.4 mol/l; h = 3 nm; W = 0.353; d = LJTS (CH 4 ) THERMODYNAMIK UND ENERGIETECHNIK ns ns y coordinate in units of nm

5 Flow regulation fluid acceleration in LJ units average fluid velocity in LJ units THERMODYNAMIK UND ENERGIETECHNIK Poiseuille flow of LJTS (Argon) in a graphite slit pore, T = 0.85 /k, h = 24, / da/dt = -2 [U + v(t-t ) - 2v(t)]; t = 61.2 d /dt = 1/2 ; = simulation time step (corresponding to 1.0 fs) = s

6 Poiseuille flow of methane in a graphite channel

7 Poiseuille flow: Velocity profile d center wall density in units of mol/l velocity in units of m/s y coordinate in units of nm 0 THERMODYNAMIK UND ENERGIETECHNIK

8 Poiseuille flow: Velocity profile wall d center wall density in units of mol/l velocity in units of m/s y coordinate in units of nm THERMODYNAMIK UND ENERGIETECHNIK 0

9 Poiseuille flow: Velocity profile 60 wall d wall velocity in units of m/s r slip = 3.7 nm v slip = 40 m/s y coordinate in units of nm THERMODYNAMIK UND ENERGIETECHNIK

10 Couette flow: Velocity profile 0.25 wall d wall 0.20 velocity in units of m 1/2-1/ r slip = 23 v slip = m 1/2-1/2 Argon (LJTS) T = 0.85 ε 0.00 THERMODYNAMIK UND ENERGIETECHNIK y coordinate in units of μ = μ s (T)

11 Properties of nanoscopic Poiseuille flow

12 Grand canonical MD simulation Grand canonical molecular dynamics (GCMD) : Specification of μ, V, and T Test insertions and deletions of single particles in alternation with canonical MD steps: P ins μ ΔU max1, exp μ ΔU P max1, exp T ins del T del Application: Chemical potential gradient induced Poiseuille flow μmax μmin

13 Fluid flow induced by a chemical potential gradient

14 GCMD simulation of adsorption -3 fluid density in units of heterogeneous system: h = 24 h = 72 saturated bulk liquid y coordinate in units of THERMODYNAMIK UND ENERGIETECHNIK Graphite + argon (LJTS), T = 0.85 ε/k, μ = μ s (T) Γ y min dy ρ( y) ρ'

15 Scenario: Slit pore with a cylindrical cavity u σ σ 12 fw( r ) 4ε C r r 6

16 Rotation inside the cavity induced by stationary Poiseuille flow: J 1 N r i p i i 2D v = 0.8 C = 0.5 Oliver et al. (2006) 3D v = 0.82 C = 0.5 (present)

17 Massively parallel MD simulation Spatial domain decomposition: processors calculate interactions within spatially defined subdomains Linked cell communication: each subdomain exchanges information with its 26 neighbours Halo bins: contain relevant molecules from adjoining subdomains excellent scalability of the MD software Concurrency in space but NOT in time!

18 Scaling of the ls1 mardyn program homogeneous truncated-shifted LJ system methane + graphite HLRS nehalem cluster Baku/Laki 100 computing time in units of s simulation loop input/output 2 000, 4 000, 8 000, and particles per process number of processes speedup processes uniform subdomains static load balancing

19 Communication and load balance OpenMPI, gcc-4.1.2, HLRS nehalem cluster Baku/Laki.

20 Innovative HPC-Methoden und Einsatz für hochskalierbare Molekulare Simulation (IMEMO) Participants: Associated enterprises:

21 Conclusion Based on a uniform additional force, Couette and Poiseuille flow can be simulated for real fluids in nanoscopic channels. The velocity profile remains approximately linear (Couette) or parabolic (Poiseuille) and Darcy s law holds down to the molecular length scale. However, boundary slip cannot be neglected for diameters below 100 nm. By grand canonical MD simulation, adsorbed layers and the behaviour of the confined fluid can be investigated as if they were in equilibrium with a specified state of the bulk fluid. The present approach is viable for more elaborate geometries as well. High performance computing permits MD simulation of systems with characteristic volumes up to (100 nm) 3 or interfaces up to 1 μm 2.