O' Berk Usta

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Simulations of Polymer Solutions in Periodic and
Confined GeometriesA Lattice-Boltzmann Approach

O. Berk Usta Anthony J. C. Ladd Jason E. Butler
Supported by the National Science Foundation
(CTS-0505929)
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Overview Lattice-Boltzmann Method for
Polymer Simulations

• Solve Navier-Stokes equations with Brownian
  stresses using lattice-Boltzmann method.
• Represent polymers by a micromechanical model
  which is coupled with the solution for the flow
  field.
• Simulate polymer as point particles having
  excluded volume (Ahlrichs and Duenweg J. Chem.
  Phys, 1999).
• Connect point particles with potentials of choice
  (FENE, Hookean, etc.).
• Addition of walls through simple bounce-back
  rules for the fluid-wall interactions.

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Verification of the Model

• Hydrodynamic Interactions
• Fluid Response
• Two Particle Mobility
• Polymer Properties
• Scaling of end-to-end distance and radius of
  gyration (RE, RG) with chain length (N)
• Scaling of center of mass diffusion coefficient
  (DCM) with (N)
• Effect of Schmidt number

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Single Chain Simulations (Periodic)
O. B. Usta, A. J. C. Ladd, and J. E. Butler J.
Chem. Phys., 122, 094902, (2005)
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Advantages of the Lattice-Boltzmann Method for
Polymer Simulations

• Computation (primarily) scales with number of
  fluid nodes, not number of particles.
• No need to calculate the Greens function for each
  new geometry.
• Ideal for studying confined flows and can be
  extended to simulate semi-dilute polymer
  solutions.
• Easy to code a basic Lattice-Boltzmann
  simulation.
• Implementation of a parallel code is
  straightforward due to the local nature of the
  calculations.

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Problems in Confined Geometries

• Unidirectional Flows in Microchannels
• Pressure Driven Flow
• Lateral Migration
• Dispersion and Separation
• Simple Shear Flow
• Lateral Migration
• External Field Driven Flows
• Combined Flows

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Pressure Driven Flow
y
Vmax
H
x
z
Low Re
Flow Peclet Number
Confinement Level
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Results

• Wide Channels, Center of Mass Distribution

Wall
Center
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The Mechanism (Ma Graham 2005)
Forces Polymer in tension.
Velocities Hydrodynamic lift away from wall.
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External Forces
Particle Peclet Number
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External Forces - Results
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External Forces Effect of Hydrodynamic
Interactions
H/Rg8
Wall
Center
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Mechanism 2 External Forces

• Kinetic theory predicts a rotation of the polymer
  near the wall to a preferential orientation as
  shown.
• Subsequently, the polymer drifts away from the
  wall due to the external force and hydrodynamic
  interactions between the beads.

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Combined Flow
Concurrent
P1
P2
F
Countercurrent
H
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Three Mechanisms
Rotation Due to Force Drift Due to Force
Lift Due to Shear
Rotation Due to Shear and Drift Due to Force (no
wall needed!)
F
U
F
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Concurrent Application
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Countercurrent Application
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Conclusions and Continuing Work

• The fluctuating lattice-Boltzmann method coupled
  to point particles is a flexible and efficient
  alternative for simulating polymers in solution.
• Hydrodynamic interactions in bounded geometries
  can give rise to unexpected behavior such as
  migration.
• Several different driving forces can induce
  migration.
• Combination of these forces can be used to
  manipulate the migration.
• Couple the current simulation capabilities with a
  detailed micromechanical model to predict the
  dynamics and viscoelastic properties actin
  filaments.
• Combine with molecular scale models to simulate
  force generation by actin polymerization.