1. MESOSCOPIC SIMULATIONS

2. OUTLINE
• Introduction
• Methods
• Lattice Boltzmann (LB) Color
Method
• Dissipative Particle Dynamics (DPD)
• Examples
• LB Simulations of >2 Immiscible
fluids
• DPD Simulations of Wetting, Multiple
Fluids, Particulates, Drop Impact, etc.
• Summary

3. Lattice Boltzmann
• Discrete solution of the
Boltzmann kinetic
equation
• Boundary conditions are
easy (sort of)
• Multiphase versions

4. LB Method for >2 Fluids
• Color LB method due to
Spencer, Halliday, Care:
• “A local lattice Boltzmann
method for multiple
immiscible fluids and dense
suspensions of drops”, Royal
Society (submitted).
• “Lattice Boltzmann equation
method of multiple
immiscible continuum fluids”,
PRE 82, 066701 (2010)

5. Surface Tension

6. Large Symbols: τB = τR = 0.5
Small Symbols: τB = 1.0 τR = 0.5
Red Symbols: A = 0.01 β = 1.0
Blue Symbols: A = 0.02 β = 1.0
Laplace Pressure - Simulation & Theory
∆P = cs
2∆ρ
σ = cs
2ρA/2β

7. γbg < γrb = γrg
γbg = γrb = γrg γrg < γrb = γbgThree Fluids

8. γrg = γrb = γrm = γbg = γbm = γgm
γrb = γrm = γbg = γgm = γ0
γrg = γbm = γ0 / 2
Four Fluids

9. Wetting

10. Wetting - Multiple Fluids

11. Pressure Driven Flow
Viscosity Ratio = 40

12. Drop Deformation

13. Summary
• LB method of Spencer,
et al can simulate
multiple, immiscible
fluids, wetting,
compound drops, etc.
• Some issues at large Ca
• Could be used to
investigate emulsions of
>2 fluids

14. Dissipative Particle
Dynamics
• Coarse-Grain Particle
Method
• Multi-body Dissipative
Particle Dynamics
(MDPD) due to P.
Warren.
• Accounts for
thermodynamics,
Brownian motion &
hydrodynamics

15. Dissipative Particle
Dynamics
Group of atoms
Single “Bead” or Particle
Atoms “smeared out so interactions
become “soft”
Include friction to represent
dissipation
“Hard” Interactions “Soft” Interactions

16. Viscous Flow

17. Surface Tension

18. ASL = 0.94 ALL ASL = 0.75 ALL
ASL = 0.50 ALL ASL = 0.38 ALL
Wetting

19. Multiple, Immiscible Fluids
A12 = 0.50 A11
A12 = 0.63 A11 A12 = 0.75 A11

20. Tail
Head
Surfactants
Distribution of Tails Surface Tension

21. Initial State Isotropic Phase φ = 18%
Hexagonal Phase φ = 54% Lamellar Phase φ = 83%
Micelles

22. Tie many
DPD particles
together to
form a single
colloid or
particulate.
Aggregating Colloids in DPD
Potential
Interaction

23. Capillary Absorption with
Aggregation

47. Fraction of Fluids & Colloids Absorbed
Fluids Colloids

48. Drop Impact on Surfaces
Vdrop Vdrop
Fluid Drop Fluid Drop + Colloids
Re = 64
We = 260

52. DPD Simulations of
Sliding Drops
• No Particulates
• Particulates that don’t
favor substrate
• Particulates that favor
substrate

53. No Particulates

54. Gravity

60. Particulates Don’t Favor Substrate

67. Particulates Favor Substrate

76. No Particulates
Particulates don’t
favor substrate
Particulates favor
substrate

77. Drop Impact onto
Porous Substrate
• No Particulates
• Particulates don’t favor
substrate
• Particulates favor
substrate

81. Particulates Don’t Favor Substrate

85. Particles Favor Substrate

89. No Particulates Particulates Don’t Favor Substrate
Particulates Favor Substrate

90. No Particulates Particulates Don’t Favor Substrate
Particulates Favor Substrate

91. Summary
• DPD Simulations show rolling
motion of sliding drops
• Particulates that favor the fluid over
the substrate doesn’t significantly
affect drop motion
• Particulates that favor substrate
cause the drop to pin (at slow
velocities)
• Drop impacts onto porous media
at ink jet velocities show no
differences in behavior for the same
interactions where particulates
favor/don’t favor substrate

92. Summary
• DPD simulations can
simulate: Surface tension,
wetting, multiple
immiscible fluids,
surfactants, micelles,
colloids, colloidal
aggregation, capillary
flows, etc.
• DPD is a powerful
technique for exploring
complex fluids

93. Dennis’s Law of
Computer Programs
There is no such thing as
an error-free program.
The more certain you are
that the program is error-
free, the less it does.
Strong
Formulation
Weak
Formulation