Mesoscale fluid simulation of colloidal systems
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1 Mesoscale fluid simulation of colloidal systems Mingcheng Yang Institute of Physics, CAS
2 Outline (I) Background (II) Simulation method (III) Applications and examples (IV) Summary
3 Background
4 Soft matter (complex fluid) small perturbation large change energy scale k B T entropy importance multiscale
5 Colloid simplest soft matter mesoscale particle suspended in solvent mesoscale particle 10 nano - 10 micron thermal fluctuations large surface area/volume ratio (surface effects)
6 Macrosopic atom Characteristic time 1ms - 1s Characteristic length 1 micron, observed by microscope colloidal fluid colloidal crystal colloidal glass
7 Nonequilibrium state External field driving colloid Active colloid Colloidal glass dilute.mov concentrate.mov Wysocki (2009) Soft matter Jiang et al (2009) PRL Zhang (2013) PNAS Palacci (2013) Science Solvent plays an important role!
8 Colloidal microscale devices micro-valve Terray et al (2002) Science micro-pump optical micro-rotor Bleil et al (2006) APL Zong et al (2015) ACS Nano micro-clutch Williams et al (2015) Nat. phys. micro-heat engine Blickle et al (2011) Nat. phys. self-propelled micro-swimmer Paxton et al (2004) JACS, Howse et al (2007) PRL self-propelled micro-rotor Jiang et al (2010) PRL
9 Solvent in equilibrium colloids colloidal particle + solvent molecule: Partition function: (trace out solvent variables) Expectation: Simulation: Monte Carlo or MD, with effective potential, without explicit solvent.
10 Solvent in non-equilibrium colloids Solvent effects: Thermal fluctuations Hydrodynamic interactions (friction, correlation, driving) Mass transport Heat conduction Nonequilibrium driving force Simulation: - All-atom MD, - Mesoscale method with coarse-grained solvent, - Numerical solution of coupled transport equations f
11 Challenge for simualtion Huge difference in length and time scales between of colloidal particles and solvent molecule. neglect microscopic detail of solvent molecules Coarse grained solvents Hybrid MD-Meso simulation: Solvent dynamics: Coarse graining method Colloid-colloid and colloid-solvent interactions: MD
12 Coarse graining All-atom to bead-spring polymer All-atom to single-bead colloid
13 Essential features of coarse-grained solvent Colloid-solvent direct interactions Thermal fluctuation Dissapation Mass diffussion Heat conduction Hydrodynamic interactions Nonequilibrium driving force Explicit liquid solvent
14 Diffusive flux concentration gradient mass diffusion j m D c (Fick's law) temperature gradient heat conduction j q T (Fourier's law)
15 Hydrodynamics Hydrodynamics interactions are mediated by solvent. Continuum limit: Navier-stokes equation (momentum conservation) incompressible condition (mass conservation) Low Reynolds number hydrodynamics: Re = << 1, external-force free Stokes equation
16 Phoresis electrophoresis diffusiophoresis thermophoresis phoretic force is internal force: f
17 Coarse graining solvent - Colloid-colloid interactions - Colloid-solvent direct interactions - Thermal fluctuation - Dissapation - Mass diffussion - Heat conduction Local conservation of mass, - Hydrodynamic interactions energy and momentum - Correct equilibrium description - H-theorem - Galilean invariance - Isotropy - High efficiency Starting point for construction: basic conserved quantities
18 Important coarse graining methods Brownian dynamics Lattice Boltzmann method Dissapative particle dynamics Direct simulation monte carlo Multiparticle collision dynamics
19 Simulation method
20 Multiparticle collision dynamics method (MPC) N point particles continuous positions continuous velocities discrete time increment Dynamics in two steps: Streaming Collision Malevanets, Kapral (1999) JCP Kapral (2008) Adv. Chem. Phys. Gompper et al (2009) Adv. Polym. Sci. Padding and Louis (2006) PRE
21 Streaming step
22 Collision step
23 MPC in 2D
24 MPC in 3D
25 Rotational collisin in 3D
26 Conservation of mass, momentum and energy Streaming step locally conserves everything! Collision step locally conserves mass In cell level, collision locally conserves momentum In cell level, collision locally conserves energy Hydrodynamic behaviors Heat conduction (microcanonical ensemble) Mass transport Thermal fluctuation (intrinsic)
27 Anderson thermostat MPC Collision rule: random number from Maxwellian distribution the number of particles in collision cell Locally conserve mass and momentum, but not energy (canonical ensemble)
28 Galilean invariance
29 Random shift Galilean invariance is recovered Collisional transfer of momentum is enhanced Collisional interaction is smoothed (uniform) T. Ihle and D. M. Kroll (2001) PRE
30 MPC units and parameters
31 viscosity Viscosity and diffusion
32 Important dimensionless number (I) Schmidt number (simulation ~ 10)
33 Velocity distribution and equation of state MPC: liquid-like dynamics, but gas-like thermodynamics
34 Boundary conditions Periodic boundary Stick (noslip) wall boundary streaming step Slip wall boundary
35 External flow: capillary flow external force + stick boundary
36 Thermostat and temperature gardient Define hot and cold layers; rescale particle thermal energy boundary thermostat temperature and density distribution
37 Chemical reaction and concentration gardient Define reaction layers; change particle species A B B A boundary reaction concentration distribution of species A
38 Colloid-solvent coupling: molecular dynamics colloid-solvent interaction
39 Hybrid MPC and MD
40 Important dimensionless number (II) Reynolds number inertial force / viscous force Low Re region (simulation < 0.1) Knudsen number mean free path / particle size Liquid (continuum) (simulation < 0.05)
41 Flow field past colloidal sphere with high Re with low Re obtained by hybrid MPC and MD simulation
42 Important dimensionless number (III)
43 Important time scales
44 Important time scales Momentum diffusion: In experiments In simulations
45 Applications and examples
46 (I) Colloidal thermophoresis boundary thermostat Luesebrink, Yang, Ripoll (2012) JPCM
47 Thermophoretic flow field b a flow around thermophoretic colloid comparison with theory thermophoretic force = friction Yang, Ripoll (2013) Soft Matter
48 flow around fixed thermophoretic colloid nonvanishing thermophoretic force comparison with theory (for infinite system)
49 (II) Diffusive heat flux-driven microturbine Anisotropic thermophoresis: Yang et al (2014) Nanoscale
50
51 Rotation rotational velocity Yang et al (2014) Nanoscale
52 (III) Self-phoresis microswimmer Howse et al (2007) PRL Jiang et al (2010) PRL self-generated gradient external gradient self-diffusiophoresis (catalytic chemical reaction) self-thermophoresis (heat solvent)
53 Self-thermophoretic microdimer temperature profile trajectory T Self-propelled velocity: Yang, Ripoll (2011) PRE
54 Puller
55 Pusher
56 Pusher and puller pusher puller
57 force dipole 2 r
58 Self-diffusiophoretic Janus particle Rotation Phoresis Stick boundary Potential Yang et al, (2014) Soft Matter
59 Rotational dynamics of passive particle
60 Self-diffusiophoretic Janus particle concentration map of product flow field
61
62 (IV) Ecoli modeling Hu, Yang et al, (2015) Soft Matter
63 Flow field generated by Ecoli swimming velocity vs rotational frequency rotational frequency vs torque Movie_S1.mov Movie_S2.mov
64 Flow field generated by Ecoli Ecoli with 4 symmetric flagela
65 (V) Self-diffusiophoretic microgear gear catalyze chemical reation concentration distribution Yang et al, (2015) JCP
66
67 rotation angular angular velocity vs reaction probability
68 (VI) Thermoosmotic micropump ratchet channel with T difference temperature map fluid flow through channel Yang et al, (2016)
69 Flow manipulation
70 Conclusion Hybrid mesoscale simulation MPC solvent Thermal noise, hydrodynamic interactions, dissapation, mass diffussion, heat conduction, nonequilibrium force, H-theorem, Galilean invariance, isotropy, high efficiency Simulation of non-equilibrium colloids thermphoretic colloid, diffusive flux-driven microturbine, self-propelled dimmer, Ecoli, self-propelled microrotor, thermal ratchet microfluidic pump
71 Collaborators: Dr. Marisol Ripoll Forschungszentrum Juelich, Germany Dr. Adam Wysocki Forschungszentrum Juelich, Germany Dr. Daniel Lüsebrink Universitat de les Illes Balears Palma de Mallorca, Spain Dr. Ke Chen Institute of physics, CAS, China Dr. Rui Liu Institute of physics, CAS, China Jinglei Hu Nanjing University, China Acknowledgements Thank You for your attention!
72 Random shift with wall
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