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 )
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
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
Short-range ordering in a nanochannel fluid density in units of mol/l 30 20 10 0 T = 175 K; r = 18.4 mol/l; h = 3 nm; W = 0.353; d = 0.947 LJTS (CH 4 ) THERMODYNAMIK UND ENERGIETECHNIK 0.06-0.12 ns 0.42-0.48 ns 2 4 6 y coordinate in units of nm
Flow regulation fluid acceleration in LJ units average fluid velocity in LJ units 0.0010 0.0005 0.0000-0.0005 0.10 THERMODYNAMIK UND ENERGIETECHNIK Poiseuille flow of LJTS (Argon) in a graphite slit pore, T = 0.85 /k, h = 24, 1000000 2000000 3000000 0.05 1/32 0.00-0.05 da/dt = -2 [U + v(t-t ) - 2v(t)]; t = 61.2 d /dt = 1/2 ; = 0.00361 1000000 2000000 3000000 simulation time step (corresponding to 1.0 fs) = s
Poiseuille flow of methane in a graphite channel
Poiseuille flow: Velocity profile 60 50 d center wall 60 50 density in units of mol/l 40 30 20 40 30 20 velocity in units of m/s 10 10 0 0 2 4 6 8 y coordinate in units of nm 0 THERMODYNAMIK UND ENERGIETECHNIK
Poiseuille flow: Velocity profile 60 50 wall d center wall 60 50 density in units of mol/l 40 30 20 40 30 20 velocity in units of m/s 10 10 0-4 -2 0 2 4 6 8 y coordinate in units of nm THERMODYNAMIK UND ENERGIETECHNIK 0
Poiseuille flow: Velocity profile 60 wall d wall velocity in units of m/s 50 40 30 20 r slip = 3.7 nm v slip = 40 m/s 10 0-4 -2 0 2 4 6 8 y coordinate in units of nm THERMODYNAMIK UND ENERGIETECHNIK
Couette flow: Velocity profile 0.25 wall d wall 0.20 velocity in units of m 1/2-1/2 0.15 0.10 0.05 r slip = 23 v slip = 0.091 m 1/2-1/2 Argon (LJTS) T = 0.85 ε 0.00 THERMODYNAMIK UND ENERGIETECHNIK 20 30 40 50 60 y coordinate in units of μ = μ s (T)
Properties of nanoscopic Poiseuille flow
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
Fluid flow induced by a chemical potential gradient
GCMD simulation of adsorption -3 fluid density in units of 3 2 1 0 heterogeneous system: h = 24 h = 72 saturated bulk liquid -15-10 -5 0 5 10 15 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'
Scenario: Slit pore with a cylindrical cavity u σ σ 12 fw( r ) 4ε C r r 6
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)
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!
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 100 10 1 simulation loop input/output 2 000, 4 000, 8 000, and 16 000 particles per process 8 32 128 512 2048 number of processes speedup 75 50 25 50 100 150 processes uniform subdomains static load balancing
Communication and load balance OpenMPI, gcc-4.1.2, HLRS nehalem cluster Baku/Laki.
Innovative HPC-Methoden und Einsatz für hochskalierbare Molekulare Simulation (IMEMO) 2008 2011 Participants: Associated enterprises:
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.