Multiscale modeling of active fluids: selfpropellers and molecular motors. I. Pagonabarraga University of Barcelona

Transcription

1 Multiscale modeling of active fluids: selfpropellers and molecular motors I. Pagonabarraga University of Barcelona

2 Introduction Soft materials weak interactions Self-assembly Emergence large scale structures Entropy plays a relevant role Sensitive to external deformations Mechanical proerties from building blocks Sepration of sclaes Heterogeneous materials

3 Introduction Heterogeneity both in Space Time Need to coarse grain select relevant degrees of freedom Decrease separation of sclaes computational feasibility

4 Aims? Controlling materials through external fields shearing gravity electric/magnetic fields Use internal capabilities of materials Temperature quench internal structure length/time scale competition emerging structures Spontaneous internal motion actuated/internal propulsion interaction with actuating fields K. Stratford et al. Science (2005)

5 Active matter Living systems internal activity metabolism Micro-robots synthetic self propelling particles Intrinsically out-of-equilibrium energy pumped from small scales

6 Mesoscopic modelling: Ludwig Lattice kinetic model: microscopic dynamics Lattice Boltzmann f i = ρ f i c i = ρv f i c i c i = ρvv + P Conserved variables Proper symmetries Colloid rigid hollow surface f i (r + c i,t + 1) = f i (r,t) ω[ f i (r,t) f i eq (r,t)] Hydrodynamic equations collision bounce-back molecular dynamics Hybrid scheme: Pre-selection of relevant degrees of freedom

7 Smooth interface approximation Mesoscopic modelling Mesoscopic approach to thin film dynamics Free energy functional of a binary fluid Volume Interface Surface 7

8 Mesoscopic modelling How to bridge scales? reduce separation τ=r/c s << τ=r 2 /ν <<τ=r 2 /D Importance to keep proper hierarchy length time scales Impossibility to capture real parameters how far can we take it? slow speed of sound wide interfaces finite Reynolds numbers Despite all concerns, consistent results Effect of finite Re Re=Uσ/ν<<1 Pe=Uσ/D<1 Sedimen8ng sphere

9 Mesoscopic modelling Lattice Boltzmann algorithm for multiphase fluids + (resolved) particles Colloidal particles Suspended particles are defined by a set of of links between lattice nodes Particle characteristic unit vector bounce-back-on-links algorithm: mass/momentum conservation between particle and fluid (AJC Ladd, J. Fluid Mech. 271, 285 (1994)) + position dependent slip velocity at the particle surface

10 Mesoscopic modelling What if par8cles might generate concentra8on gradients? self- propulsion!!! (Paxton et al, JACS 126, (2004)) (Golestanian et al, PRL 94, (2005)) ac8vity modelled by simple upda8ng rule non- conserved dynamics for φ! par8cle surface ac8vity Inclusion of a global source term (mimicks coupling with an external bath of concentra8on field)

11 Filament instability: drop emission Forced thin film or rivulet Stabilized by incoming flow Localized by wetting mismatch Due to substrate hydrophobicity/hydrophilicity Different from Rayleigh-Plateau R. Ledesma-Aguilar et al. Nature Materials (2011) 11

12 Filament instability: drop emission Forced thin film or rivulet Stabilized by incoming flow Localized by wetting mismatch Due to substrate hydrophobicity/hydrophilicity Different from Rayleigh-Plateau 12

13 Squirmer suspensions Time scales: analogous to passive colloids τ r R 2 /ν τ << τ m << τ D τ m R/u τ D R 2 / Diffusion induced by collisions τ D/ τ m = u R/ Pe Size~ µm Speeds < 100 µm/s Neglect thermal fluctuations fluid inertia (Re<0.01) Paramecium Opalina u ~1000 µm/s u ~100 µm/s R ~200 µm R ~200 µm Re ~ 0.2 Re ~ 0.02

14 chlamydomonas v~1/r 2 β>0 Contrac8le/Puller β<0 Extensile/pusher 1/β=0 (B 1 =0 B 2 0) Apolar β=0 (B 2 =0 B 1 0) Passive squirmer v~1/r 3

15 Squirmer suspensions Emerging clusters no characteristic size Super diffusive regime alignment-induced acceleration

16 Squirmer suspensions v w Shearing forces structure across the gap nematic order induced by shear L Impact in rheological response -v non-netownian behavior w Shear-thinning Shear-thickening Associated to active stresses

17 Squirmer suspensions Streamlines Polar Passive Apolar

18 Chemical swimmer suspensions Number density variance indicator for clustering Transition controlled by chemical attraction/repulsion Hydrodynamics slows down aggregation smaller sizes lost or orientation induce by walls dynamic heterogeneities Changes in cluser morphology?

19 µ = (without hydrodynamics)

20 µ = (with hydrodynamics)

21 Percolating emerging structures active gels? Chemical swimmer suspensions

22 Computational performance Local moves suitable for MPI Excellent scalability various platforms Extended objects non-locality additional costs load imbalance Sensitivity to Surface/volume ratio Small fraction overall computational time

23 Long simulation runs identify emerging structures cover relevant length scales Computational needs Particle size limits domain decomposition ~8000 particles 16/1024 CPU s Long range correlations long relaxation times compromise size/time regimes Domain sizes recover emerging structures / finite size effects

24 Acknowledgements Andrea Scagliarini Francisco Alarcón Paolo Malgaretti University of Barcelona Ricard Matas-Navarro University of Durham Rodrigo Ledesma-Aguilar University of Oxford 24