Mesoscale fluid simulation of colloidal systems Mingcheng Yang Institute of Physics, CAS
Outline (I) Background (II) Simulation method (III) Applications and examples (IV) Summary
Background
Soft matter (complex fluid) small perturbation large change energy scale k B T entropy importance multiscale
Colloid simplest soft matter mesoscale particle suspended in solvent mesoscale particle 10 nano - 10 micron thermal fluctuations large surface area/volume ratio (surface effects)
Macrosopic atom Characteristic time 1ms - 1s Characteristic length 1 micron, observed by microscope colloidal fluid colloidal crystal colloidal glass
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!
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
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.
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
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
Coarse graining All-atom to bead-spring polymer All-atom to single-bead colloid
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
Diffusive flux concentration gradient mass diffusion j m D c (Fick's law) temperature gradient heat conduction j q T (Fourier's law)
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
Phoresis electrophoresis diffusiophoresis thermophoresis phoretic force is internal force: f
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
Important coarse graining methods Brownian dynamics Lattice Boltzmann method Dissapative particle dynamics Direct simulation monte carlo Multiparticle collision dynamics
Simulation method
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
Streaming step
Collision step
MPC in 2D
MPC in 3D
Rotational collisin in 3D
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)
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)
Galilean invariance
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
MPC units and parameters
viscosity Viscosity and diffusion
Important dimensionless number (I) Schmidt number (simulation ~ 10)
Velocity distribution and equation of state MPC: liquid-like dynamics, but gas-like thermodynamics
Boundary conditions Periodic boundary Stick (noslip) wall boundary streaming step Slip wall boundary
External flow: capillary flow external force + stick boundary
Thermostat and temperature gardient Define hot and cold layers; rescale particle thermal energy boundary thermostat temperature and density distribution
Chemical reaction and concentration gardient Define reaction layers; change particle species A B B A boundary reaction concentration distribution of species A
Colloid-solvent coupling: molecular dynamics colloid-solvent interaction
Hybrid MPC and MD
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)
Flow field past colloidal sphere with high Re with low Re obtained by hybrid MPC and MD simulation
Important dimensionless number (III)
Important time scales
Important time scales Momentum diffusion: In experiments In simulations
Applications and examples
(I) Colloidal thermophoresis boundary thermostat Luesebrink, Yang, Ripoll (2012) JPCM
Thermophoretic flow field b a flow around thermophoretic colloid comparison with theory thermophoretic force = friction Yang, Ripoll (2013) Soft Matter
flow around fixed thermophoretic colloid nonvanishing thermophoretic force comparison with theory (for infinite system)
(II) Diffusive heat flux-driven microturbine Anisotropic thermophoresis: Yang et al (2014) Nanoscale
Rotation rotational velocity Yang et al (2014) Nanoscale
(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)
Self-thermophoretic microdimer temperature profile trajectory T Self-propelled velocity: Yang, Ripoll (2011) PRE
Puller
Pusher
Pusher and puller pusher puller
force dipole 2 r
Self-diffusiophoretic Janus particle Rotation Phoresis Stick boundary Potential Yang et al, (2014) Soft Matter
Rotational dynamics of passive particle
Self-diffusiophoretic Janus particle concentration map of product flow field
(IV) Ecoli modeling Hu, Yang et al, (2015) Soft Matter
Flow field generated by Ecoli swimming velocity vs rotational frequency rotational frequency vs torque Movie_S1.mov Movie_S2.mov
Flow field generated by Ecoli Ecoli with 4 symmetric flagela
(V) Self-diffusiophoretic microgear gear catalyze chemical reation concentration distribution Yang et al, (2015) JCP
rotation angular angular velocity vs reaction probability
(VI) Thermoosmotic micropump ratchet channel with T difference temperature map fluid flow through channel Yang et al, (2016)
Flow manipulation
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
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!
Random shift with wall