Core Modified DPD Simulations of Colloids

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Core Modified DPD Simulations of Colloids

• Martin Whittle Karl P. Travis
• Department of Engineering Materials
• University of Sheffield

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Legacy Sludge

• Legacy wastes at Sellafield Site
• Sludges in storage tanks and ponds
• Recovery/ storage operations
• Pumping/ Squeezing
• Understanding rheology is key to optimising
  mobilisation

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Sludge samples
Yield stress up to 12 kPa Viscosity 200 Pas _at_
100 s-1
J.J. Hastings et al. / Powder Technology 174
(2007) 1824
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Modelling approaches to simulate retrieval
Binary phase modelling for pipe flow
J.J. Hastings et al. / Powder Technology 174
(2007) 1824
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Dissipative particle dynamics (DPD)
Each DPD particle represents a number of fluid
particles

• Forces all short- ranged

• Conservative interaction very soft.

• Dissipative depends on relative velocities vij
  (vi vj)

• Random only acts between centres

Where
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Core Modified DPD
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Periodic boundaries
The system is surrounded with 26 images of
itself
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Radial Distribution Function
Very sharp peak Indicates clustering
90 Colloid particles in a fluid of 59910
GW-water particles
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Depletion interaction
Coarse graining of fluid leads to a spurious
depletion force at short range
Osmotic pressure
FD
FD
This causes rapid aggregation and has to be
compensated to obtain a stabilised colloid model
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Measured depletion force
f2
f1
f1-f2
Theory
Agrees with theory providing a solvent size
parameter 0.5rc is used
A. Vrij, Pure Appl.Chem 48, 471, 1976
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Depletion balance disperses clusters
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Other interactions

• Depletion
• Lubrication (pair drag)
• Core

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Radial distribution functions
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Relative viscosity vs. volume fraction
Equilibrium Green-Kubo viscosities
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Lees-Edwards shearing boundaries
Steady state linear velocity profile
Dimensionless shear rate
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Temperature rise under shear
GW-Water
Colloid/GW-water
Needs an auxiliary thermostat
Polynomial
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Dependence on auxiliary thermostat
R 3.0, Vf 0.3374
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Shows main features of colloid rheology
R 3.0, Vf 0.3374
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Change with volume fraction
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Literature results
Foss, D. R. Brady, J. F. J. Fluid. Mech.
(2000), 407, 167-200
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Stress response
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Problem water-water RDFs
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Summary

• Spurious depletion interaction can be compensated
• Core DPD code can represent a colloidal system
  semi-quantitative comparison with SD/expt.
• Rheology is Newtonian or pseudoplastic
• We could now investigate suitable colloidal
  potentials aggregated networks that could
  develop yield stress
• Problems thermostatting temperature
  dependence, pressure increase with f, changing
  fluid phase structure with f. Can the method
  reproduce macroscopic dynamic response to
  external stress?

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Acknowledgments

• Scott L. Owens, Mark Bankhead Nexia
  Solutions Ltd.

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Relative viscosity vs. volume fraction I
Equilibrium Green-Kubo viscosities
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RDF at low Pe
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Non-equilibrium viscosity