DNS of colloidal dispersions using the smoothed profile method: formulation and applications
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1 Hokusai, 1831 Workshop III: High Performance and Parallel Computing Methods and Algorithms for Multiphase/Complex Fluids Institute for Mathematical Sciences, NUS, Singapore 2 6 March 2015 DNS of colloidal dispersions using the smoothed profile method: formulation and applications Ryoichi Yamamoto Dept. Chem. Eng., Kyoto University
2 Contents 1. DNS of colloidal (passive) particles Hydrodynamic interaction (HI) and smoothed profile method (SPM) External force = Gravity -> a falling coin External force = Shear flow -> a tumbling rod 2. DNS of swimming (active) particles Squirmer: spherical model swimmer Collective motion of squirmers -> density wave 2
3 Hydrodynamic Interaction (HI) 1. without HI 2. with HI Gravity Blue: slow Red: fast kt0 3 B
4 PRE 2005 Basic equations of SPM i x Navier-Stokes (Fluid) Newton-Euler (Colloids) 1 Fluid ξ Solid t 2 u u p u f u ξ 1 p, 0 exchange momentum d R i d i d i Vi, m V i Fi, I Ω i N dt dt dt FEM: sharp solid/fluid interface on irregular lattice extremely slow i 0 a R i a x SPM: smeared out interface on fixed square lattice much faster!! 4
5 in External force = Gravity G Gravity: Sedimentation in colloidal disp. Gravity: A falling object at high Re=10 3 5
6 in External force = Shear flow γ γ Shear flow: Tumbling rigid bodies / Rheology AC Shear flow: Complex modulus G' G'' 6
7 in External force = Electric field E Et () DC Electric field: Mobility AC Electric field: Complex mobility ' '' 7
8 Swimming (active) particles Squirmer Soft Matter (2013) Mol. Phys. (2014) Explicit shape mimicking e. coil bacteria (on-going) 8
9 KAPSEL: a DNS code using SPM KAPSEL-3.2 Platform: OCTA compatible (but not in CD!) Supported OS & compiler: Windows (cygwin/gcc) Linux (gcc, intel+omp) Source code available Implemented features: Neutral / Charged colloids Rigid bodies & Chains Swimming particles Brownian motion on / off Gravity on / off Shear flow on / off Electric field on / off kapsel 9
10 Contents 1. DNS of colloidal (passive) particles Hydrodynamic interaction (HI) and smoothed profile method (SPM) External force = Gravity -> a falling coin External force = Shear flow 2. DNS of swimming (active) particles Squirmer: spherical model swimmer Collective motion of squirmers 10
11 Inertia of coin / Inertia of fluid A falling coin in water S. B. Field, M. Klaus, M. G. Moore & F. Nori, Nature 388, 252 (1997). D Tumbling A B C D C Chaotic A Steady falling B Periodic Re of coin in fluid 11
12 In preparation A falling coin in water Simulation system 12
13 Inertia of coin / Inertia of fluid In preparation A falling coin in water A: Steady falling D Tumbling C Chaotic A Steady falling B Periodic Re of coin in fluid 13
14 Inertia of coin / Inertia of fluid In preparation A falling coin in water B: Periodic D Tumbling C Chaotic A Steady falling B Periodic Re of coin in fluid 14
15 Inertia of coin / Inertia of fluid In preparation A falling coin in water C: Chaotic D Tumbling C Chaotic A Steady falling B Periodic Re of coin in fluid 15
16 Inertia of coin / Inertia of fluid In preparation A falling coin in water D: Tumbling D Tumbling C Chaotic A Steady falling B Periodic Re of coin in fluid 16
17 In preparation Angular velocity auto-correlation Body flame coordinate 1) steady falling 2) periodic f f C yz, ω ( f ) Spectral density of angular velocity (y & z) auto-correlation function 3) chaotic f 4)tumbling f 17
18 Contents 1. DNS of colloidal (passive) particles Hydrodynamic interaction (HI) and smoothed profile method (SPM) External force = Gravity External force = Shear flow -> a tumbling rod 2. DNS of swimming (active) particles Squirmer: spherical model swimmer Collective motion of squirmers 18
19 Leeds-Edwards PBC Sliding box (boundary driven) Deforming box (SLLOD) Orthogonal Oblique Grid is not periodic Grid is periodic -> FFT 19
20 JCP 2011, Preprint Leeds-Edwards PBC (oblique) Position ˆx x t y ŷ y ẑ z Velocity u u y ˆx ˆ y u u ˆz u u x y z u 2 ( u ) u p u fp K ( ux y) e t fluid/particle interaction external force to maintain shear flow uˆ ˆ ( uˆ ) uˆ ˆ pˆ ˆ uˆ ˆˆ f 2 uˆ eˆ t 2 2 p y x ˆ x
21 Preprint Numerical test: tumbling in shear Simulation vs. Jeffery s orbit 21
22 PRE 2009, EPJE 2010 Numerical test: Rheology Steady shear flow Oscillatory shear flow G G 22
23 Contents 1. DNS of colloidal (passive) particles Hydrodynamic interaction (HI) and smoothed profile method (SPM) External force = Gravity External force = Shear flow 2. DNS of swimming (active) particles Squirmer: spherical model swimmer Collective motion of squirmers 23
24 Physics of swimming Breaststroke Propeller Force free Torque free Swimming = Propulsion without external Force / Torque u( r) r -2 24
25 A spherical model: Squirmer Surface flow velocity down J. R. Blake (1971) u ( s) 1 Ishikawa & Pedley (2006-) B sin sin 2 θˆ up propelling velocity stress against shear flow 25
26 A spherical model: Squirmer Microorganism expansional contractional Bacteria chlamydomonas Squirmer Pusher 0 0 Puller 0 26
27 SM 2013 A single swimmer Externally driven colloid (gravity, tweezers, etc ) Neutral swimmer 0 u( r) r 1 u( r) r 3 Box: 64 x 64 x 64 with PBC, Particle radius: a=6, φ=0.002 Re=0.01, Pe=, Ma=0 27
28 SM 2013 A single swimmer Pusher 2 Neutral 0 Puller 2 u( r) r 2 u( r) r 3 u( r) r 2 Box: 64 x 64 x 64 with PBC, Particle radius: a=6, φ=0.002 Re=0.01, Pe=, Ma=0 28
29 Contents 1. DNS of colloidal (passive) particles Hydrodynamic interaction (HI) and smoothed profile method (SPM) External force = Gravity External force = Shear flow 2. DNS of swimming (active) particles Squirmer: spherical model swimmer Collective motion of squirmers -> density wave 29
30 Collective motion of squirmers confined between hard walls puller with =+0.5 volume fraction = 0.2 Very mysteriously, a standing density wave is observed in such a highly over-dumped dispersion of active particles. 30
31 Dynamic structure factor Summary for bulk liquids c s xd 1 T T (1 x) 2D k ω T Rayleigh mode (diffusion) c dispersion relation with speed of sound: c s s 2 k 2k 2 Brillouin mode (phonon) 31
32 Dynamic structure factor of bulk squirmers (puller with =+0.5) Brillouin mode (phonon-like?) ω c dispersion relation with speed of wave: c s s k ω 32
33 Dynamic structure factor of bulk squirmers (pusher with =-0.5) Similar to the previous puller case with =-0.5 but the intensity of the wave is much suppressed. ω 33
34 Open questions 1. Mechanism of density wave 2. Meaning of phonon-like behavior (propagation with attenuation) 3. Origin of asymmetry between puller and pusher 4. Relation to real phenomena (flying birds or bugs, etc ) c s U U 1 [ LT ]? collision [ L T ]? 34
35 Summary 1. DNS of colloidal (passive) particles Hydrodynamic interaction (HI) and smoothed profile method (SPM) External force = Gravity External force = Shear flow 2. DNS of swimming (active) particles Squirmer: spherical model swimmer Collective motion of squirmers 35
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