Fluctuating Hydrodynamics Approaches for Mesoscopic Modeling and Simulation Applications in Soft Materials and Fluidics
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1 Fluctuating Hydrodynamics Approaches for Mesoscopic Modeling and Simulation Applications in Soft Materials and Fluidics Computational Methods and Software Summer School on Multiscale Modeling of Materials Stanford University June 2016 Paul J. Atzberger Department of Mathematics Department of Mechanical Engineering University of California Santa Barbara
2 Fluctuating Hydrodynamics Brownian Motion: Molecular Collisions Hydrodynamics + Fluctuations Continuum Gaussian Random Field Landau-Lifschitz fluctuating hydrodynamics Spontaneous momentum transfer from molecular-level interactions. Thermal fluctuations captured through random stress Σ. Mathematically, equations present challenges since δ-correlation in space-time. Fluid-structure interactions?
3 SELM Fluctuating Hydrodynamics Eulerian-Lagrangian Mechanics Eulerian-Lagrangian Coupling Brownian Motion: Molecular Collisions Continuum Gaussian Random Field SELM Inertial Regime I: hydrodynamics thermal fluctuations microstructure SELM Overdamped Regime IV: microstructure + hydrodynamics (quasi-steady) thermal fluctuations
4 MANGO-SELM Simulation Software MANGO-SELM Software Features: SELM - Simulation Software: SELM fluctuating hydrodynamics : fluid-structure interactions subject to thermal fluctuations. Numerical time-step integrators for inertial and quasi-steady physical regimes(c/c++). Lees-Edwards-style methods for imposing shear. Codes use standardized XML formats for parametrization and data output. Codes use standardized formats VTK for continuum fields and microstructures. MANGO - Modeling Software: Java-based Graphical User Interface (GUI) for setting up models and simulations. Generates scripts and data files for SELM fluctuating hydrodynamics simulations. Extensible object-oriented architecture for inclusion of new SELM methods. Available for download at:
5 MANGO-SELM Simulation Software SELM - Simulation Software: Source codes: C/C++ used with object-oriented classes mirroring parts of SELM Delegator design pattern is used to control work flow. Four main SELM classes correspond to: Eulerian Mechanics Lagrangian Mechanics Fluid-Structure Coupling (Eulerian-Lagrangian communication) Time-Step Integration Additional classes for XML parsing, data generation. Codes designed to be easily extended for new types of SELM formulations and integrators.
6 MANGO - Modeling Software: MANGO-SELM Simulation Software
7 MANGO-SELM Simulation Software MANGO - Modeling Software:
8 MANGO-SELM Simulation Software MANGO - Modeling Software: Source codes: Java-based used with object-oriented classes mirroring parts of SELM. Dynamic object loaders for delegator design pattern for control flow (extension after compiled byte-codes). Four main SELM classes correspond to: Eulerian Mechanics Lagrangian Mechanics Fluid-Structure Coupling (Eulerian-Lagrangian communication) Time-Step Integration Codes designed to be easily extended for new types of SELM formulations and integrators. Custom classes and interface for rendering models in 3D and interactively editing models.
9 MANGO-SELM Simulation Software MANGO - Modeling Software: Source codes: Custom classes and interface for rendering models in 3D and interactively editing models. Interactive editor features allow for interactive views of model adding / removing control points adding / removing bonds between points adding custom force interactions Custom classes implemented for tracking physical units in tables.
10 MANGO-SELM Simulation Software MANGO - Modeling Software: Jython Terminal: Custom classes implement interactive terminal based on Jython. Wrapper jython classes implemented for MANGO interface and SELM data structures. Editor features allow for jython/python scripting to construct models custom GUI windows : interactive components in MANGO post-processing scripts generation of SELM XML files from the constructed MANGO data structures.
11 SELM Fluctuating Hydrodynamics Eulerian-Lagrangian Mechanics Eulerian-Lagrangian Coupling Brownian Motion: Molecular Collisions Continuum Gaussian Random Field SELM Inertial Regime I: hydrodynamics thermal fluctuations microstructure SELM Overdamped Regime IV: microstructure + hydrodynamics (quasi-steady) thermal fluctuations
12 MANGO-SELM Simulation Software SELM Inertial Regime I (Verlet-stye temporal integration): microstructure microstructure hydrodynamics hydrodynamics thermal fluctuations
13 MANGO-SELM Simulation Software SELM Coupling: adjoint condition IB-Kernel coupling: Generalized Coupling (Faxen)
14 Rheological Properties and Microstructure Dynamics Rheomety Device
15 MANGO-SELM Simulation Software Lees-Edwards Boundary Conditions: Material Stress Microscopic Forces Stress Tensor Estimator: Fluctuating hydrodynamics (moving frame):
16 MANGO-SELM Simulation Software Example System : Finitely Extensible Nonlinear Elastic (FENE) Dimers: Potential Energy: Q Q 0 = 200
17 MANGO - Modeling Software: MANGO-SELM Simulation Software
18 MANGO-SELM Simulation Software MANGO-SELM Download:
19 MANGO-SELM Simulation Software Demo Live: FENE_Dimer Steps: 1. Use File Open project. 2. Load: Fene_Dimer/FeneModel.SELM_Builder_Project 3. Adjust coupling operator table to /common/couplingop_t_kernel_1.selm_cou plingoperator_weighttable 4. Gear Icon generate SELM simulation files. 5. Link executable in ln s./common/ SELM_LAMMPS_serial_x86_Ubuntu run 6. run in Fene_Dimer.LAMMPS_script 7. Generates output data.dcd file. 8. Run./vis_FENE.vmd to visualize the model. Important files: FENE_Dimer.LAMMPS_script FENE_Dimer.LAMMPS_read_data FENE_Dimer.SELM_Info FENE_Dimer.SELM_InfoExtra FENE_Dimer.SELM_params FENE-bonds.SELM_Interaction CouplingOp.SELM_CouplingOperator CouplingOp_T_KERNEL_1.SELM_CouplingOperator_weightTable LAMMPS_SHEAR_QUASI_STEADY1_FFTW3.SELM_Integrator LAMMPS_SHEAR_UNIFORM1_FFTW3.SELM_Eulerian Particles.SELM_Lagrangian SELM_LAMMPS_serial_x86_Ubuntu *.dcd vis1.vmd
20 Demo Live: FENE MANGO-SELM Simulation Software
21 MANGO-SELM Simulation Software Finitely Extensible Nonlinear Elastic (FENE) Dimers: Shear Viscosity First Normal Stress.
22 MANGO-SELM Simulation Software Other Demos: Sheared FENE Dimer FENE Fluid Polymer Chain Polymer Knot
23
24 Fluidics Transport Fluidic Devices Electrokinetics Geometry / Confinement Fluidic Devices Developed to miniaturize and automate many laboratory tests, diagnostics, characterization. Hydrodynamic transport at such scales must grapple with dissipation / friction. Electrokinetic effects utilized to drive flow. Key Features Large surface area to volume. Ionic double-layers can be comparable to channel width. Brownian motion plays important role in ion distribution and analyte diffusion across channel. Hydrodynamic flow effected by close proximity to walls or other geometric features. Ionic concentrations often in regime with significant discrete correlations /density fluctuations. Challenges Develop theory and methods beyond mean-field Poisson-Boltzmann theory. Methods capable of handling hydrodynamics, fluctuations, geometry/confinement.
25 Mesoscale Simulations : Fluidics Channel Considerations: FEM-SELM approach used to study advection-diffusion in microfluidic device geometry. Particle interactions with walls and post-obstacles (gel-free electrophoresis / sorting). Hydrodynamic responses and diffusivity augmented by proximity to walls / obstacles.
26 Mesoscale Simulations : Fluidics Channel Considerations: FEM-SELM approach used to study advection-diffusion in microfluidic device geometry. Particle interactions with walls and post-obstacles (gel-free electrophoresis / sorting). Hydrodynamic responses and diffusivity augmented by proximity to walls / obstacles.
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28 Coarse-Grained Lipid Model Lipid Interactions Interaction Potentials Lipid Bilayer Membranes Steric Repulsion: Weeks-Chandler Anderson Self-Assembled Bilayers Coarse-Grained Model Head Tail Bonds: FENE Bending Tail-Tail Attraction: Hydrophobic-Hydrophilic Effect Self Assembles Deserno Deserno Atzberger Key Features Atomic details coarse-grained to obtain simplified model. Lipids represented by a few beads. Hydrophobic-hydrophilic effect drives bilayer formation. Solvent treated implicitly through free energy of interactions. Long-range tail-tail interaction drives self-assembly (important to obtain fluid phase). IS-CG models widely used for equilibrium. What about kinetics? Phases gas fluid gel Deserno 2005.
29 Extending IS-CG Models with Fluctuating Hydrodynamics Lipid Interactions Fluctuating Hydrodynamics Particle Dynamics: Stochastic Eulerian-Lagrangian Method Coarse-Grained Model Head Tail Deserno Fluctuating Hydrodynamics (SELM): Thermal Fluctuations SELM-CG Bilayer Model Coupling by Immersed Boundary Method Atzberger Atzberger 2007 Extending Implicit Solvent Models for Kinetics Solvent treated implicitly (free energy contributions). Hydrodynamic Coupling Missing momentum transport through solvent. Saffman-Delbruck diffusion shows solvent important! We introduce fluctuating hydrodynamics to thermostat system. Extends IS-CG models for kinetic studies (SELM-CG).
30 SELM-CG Bilayer Model SELM-CG Bilayer Model Lipid Vesicles Correlation Analysis Lipid Vesicle Lipid Dynamics within Vesicle Bilayers Saffman-Delbruck diffusion shows solvent is important! Cluster lipid cluster displacement Lipid motions correlated through direct contacts and solvent flow. Langevin dynamics models momentum transfer as local. Cluster Correlation: Dynamics Results: SELM vs Langevin Stokes Lipid dynamics: consider correlations within a cluster. SELM-CG vs Langevin dynamics (Stokes drag). Langevin drag suppresses lateral correlations. SELM exhibits long-range correlations. Atzberger 2013
31 SELM-CG Bilayer Model SELM-CG Bilayer Model Lipid Vesicles Results Langevin:Stokes Drag Correlation Analysis Two-point correlation Displacement Δt Spatial Correlation SELM: Fluctuating Hydrodynamics Langevin: Small Drag Lipid Dynamics within Vesicle Bilayers Spatial analysis of lipid motions (passive fluctuations). Two point correlations (linear response to point force). SELM vs Langevin Dynamics. Atzberger et al, 2013, 2016
32 Conclusions Coarse-Grained Lipid Models Fluctuating Hydrodynamics Approaches Continuum Mechanics of Bilayer Membranes Fluctuating Hydrodynamics Approaches Hybrid Descriptions for Fluidics Fluctuating Hydrodynamics Approaches SELM Fluctuating Hydrodynamics Software Packages Summary Stochastic Eulerian Lagrangian Method (SELM) for fluctuating hydrodynamic descriptions of mesoscale systems. SELM incorporates into traditional hydrodynamic and CFD approaches the role of thermal fluctuations. Developed both coarse-grained and continuum approaches for soft-materials and fluidics. Many applications: polymeric fluids, colloidal systems, lipid bilayer membranes, electrokinetics, fluidics. Open source package in LAMMPS MD for SELM simulations: Recent Students / Post-docs B. Gross J. K. Sigurdsson Y. Wang P. Plunkett G. Tabak M. Gong I. Sidhu CM4 Collaborators C. Siefert, J. Hu, M. Parks (Sandia) A. Frischknecht (Sandia) H. Lei, G. Schenter, N. Baker (PNNL) N. Trask (Brown / Sandia) More information: Funding NSF CAREER DOE CM4 Keck Foundation
33 Publications Hydrodynamic Coupling of Particle Inclusions Embedded in Curved Lipid Bilayer Membranes, J.K. Sigurdsson and P.J. Atzberger, (submitted), (2016) Fluctuating Hydrodynamics Methods for Dynamic Coarse-Grained Implicit-Solvent Simulations in LAMMPS, Y. Wang, J. K. Sigurdsson, and P.J. Atzberger, SIAM J. Sci. Comp. (accepted), (2016). Systematic Stochastic Reduction of Inertial Fluid-Structure Interactions subject to Thermal Fluctuations, G. Tabak and P.J. Atzberger, SIAM J. Appl. Math., 75(4), , (2015). Spatially Adaptive Stochastic Methods for Fluid-Structure Interactions Subject to Thermal Fluctuations in Domains with Complex Geometries,P. Plunkett, J. Hu, C. Siefert, P.J. Atzberger, Journal of Computational Physics, Vol. 277, 15 Nov. 2014, pg , (2014). Dynamic Implicit-Solvent Coarse-Grained Models of Lipid Bilayer Membranes : Fluctuating Hydrodynamics Thermostat, Y. Wang, J. K. Sigurdsson, E. Brandt, and P.J. Atzberger, Phys. Rev. E 88, , (2013). Incorporating Shear into Stochastic Eulerian Lagrangian Methods for Rheological Studies of Complex Fluids and Soft Materials, P.J. Atzberger, Physica D, Vol. 265, pg , (2013). Stochastic Eulerian Lagrangian Methods for Fluid Structure Interactions with Thermal Fluctuations, P.J. Atzberger, J. of Comp. Phys., 230, pp , (2011). A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales, P.J. Atzberger, P.R. Kramer, and C.S. Peskin, J. Comp. Phys., Vol. 224, Iss. 2, (2007). More information:
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