1. MD IMARAN
June 30, 2016
Stokesian dynamics Simulation of Shear
thinning and Shear thickening
Suspensions in bounded shear flow
Department of Chemical Engineering,
Indian Institute of Technology Guwahati,
Guwahati-781039

2. Presentation Flow
June 30, 2016Md Imaran (IITG)
2
 Introduction
 Mechanism of Shear thinning and thickening
 Objectives
 Literature Review
 Simulation Methodology
 Results and Discussion
 Conclusions
 Future work

3. June 30, 2016Md Imaran (IITG)
Introduction
3
Suspension
(Solid particles dispersed in liquid media )
Newtonian
(Linear Rheological behavior )
Non-Newtonian
(Non-Linear Rheological behavior )
Shear Thinning Shear Thickening

4. Applications
June 30, 2016Md Imaran (IITG)
Body Armor3
4
1. http://www.abcsafetymart.com9
2. http://www.onandemirel.com
3. J. Wagner (2003), Army Research Laboratory(US)
4. Google images
Safety gloves
Safety helmet
(a) Neat Kevlar (b) STF-Kevlar
3
1
2
4
Kechup4

5. June 30, 2016Md Imaran(IITG)
STFs which are best suited for the preparation of the Body Armor
Colloidal Particle Liquid Medium Weight
Fraction
1. Spherical silica (120
nm) and fumed silica
(Aerosil 200) (300-400
nm)
Polyethylene Glycol and
Ethylene Glycol
5-65%
2. Colloidal Silica Ethylene Glycol 40%
3. Spherical silica
(120nm) and ellipsoidal
precipitated CaCO3
particles
Polyethylene Glycol 5-50%
Hasanzadeh et.al.2014. JMEPEG:1182-1196
5

6. Properties
June 30, 2016Md Imaran (IITG)
Flow Field
Types
Rate of flow Deformation
Time of flow deformation
Suspending Phase
Viscosity of the medium solvent
Particle Parameter
Shape
Particle size
Concentration
Interaction with other particles
6

7. June 30, 2016Md Imaran(IITG)
Mechanism of Shear thinning
• Inter-particle repulsive
forces keep particles apart
• In shear thinning behavior,
the particles are
streamlined in their
trajectories, and suffer
fewer collisions
7

8. June 30, 2016Md Imaran(IITG)
Mechanism of Shear-Thickening
8
Hydrocluster mechanism
Clusters

9. Objective
June 30, 2016Md Imaran (IITG)
 To study the effect of inter -
particle force, shear rate,
couette gap and particle
concentration on rheological
properties of suspension in
bounded shear flow
H
L
U
- U
- - - - - - - - - - - - - - - -
- - - - - -- - - - - - - - - -
- - - - - - - - - - - - - - - -
- - - - - - - - -- - - -- - - -
- - -- - - - - - - - - - - - -
- - - - - - - -- - - - - - - -
H
9

10. June 30, 2016Md Imaran(IITG)
Literature Review
Author (year) Title Study
Durlofsky and
Brady,(1987)
Dynamic Simulation
of Hydro-
dynamically
Interacting Particle
Computed
interaction between
wall and suspended
particle by SD.
Brady and Bossis,
(1988)
Stokesian Dynamics Theory and
application of SD
method.
Nott and Brady,
(1994)
Pressure Driven
Flow of Suspension:
Simulation and
Theory
SD simulation for
non-Brownian
suspension with
Re=0.
10

11. June 30, 2016Md Imaran(IITG)
Literature Review
Author (year) Title Study
Singh and
Nott,(2000)
Normal stresses and
microstructure in bounded
sheared suspensions via
Stokesian Dynamics
simulations
Reported the normal
stresses in a non-
Brownian suspension in
plane Couette flow and
microstructure of the
suspension.
Lee and
Wagner(2003)
Dynamic properties of
shear thickening colloidal
suspensions
Investigated about the
critical shear rate of the
STFs and its depend of
the Shear thickening
behavior on it
11

12. June 30, 2016Md Imaran(IITG)
Literature Review
Author (year) Title Study
Ahuja and Singh,
(2009)
Slip Velocity of
concentrated
suspensions in
coquette flow
Methodology for
determination of slip
velocity and effect of
suspension properties on it
Mari et.al (2013) Shear thickening,
frictionless and
frictional rheologies in
non-Brownian
Suspensions
study the behavior of shear
thickening fluid by
implementing contact
friction model between
inter particles
12

13. June 30, 2016Md Imaran(IITG)
Literature Review
Author (year) Title Study
Ding et.al (2013) Review on Shear
Thickening Fluids and
Applications
Reviewed Basic models
used to describe shear
behavior and applications,
particularly in the area of
body armor, as well as
other industrial
applications.
Hasanzadeh et.al
(2014)
The Role of Shear-
Thickening Fluids (STFs)
in Ballistic and Stab-
Resistance Improvement
of Flexible Armor
Study the properties of
STFs and how to improve
their impact resistance
13

14. June 30, 2016Md Imaran(IITG)
John F. Brady .1988. Stokesian Dynamics .Ann. Rev. Fluid Mech. :111-157
Atoms and molecule, L-J
potential, Hard sphere,
Electrostatic force
Protein molecule or
polymer chain
Sand gravel,
seeds, high Re
Suspension flow,
Hydrodynamic and
non –hydrodynamic
forces Planet ,
galaxies, stars
are interacting
through
vacuum
14

15. June 30, 2016Md Imaran(IITG)
Simulation Methodology
Stokesian Dynamics
𝛻𝑝 = 𝜂𝛻2
𝑢
𝛻. 𝑢 = 0
No slip Boundary condition
u =
u U x 
.U x E x  
  
15
Stoke’s Equation
At far away points
u - velocity fields
P - pressure field
U - translation velocity
Ω - rotational velocity

16. June 30, 2016Md Imaran(IITG)
F=𝜼A.(U∞-U)+ 𝜼B’.(Ω∞-Ω)+ 𝜼G’.E ∞
T=𝜼B.(U∞-U)+ 𝜼C.(Ω∞-Ω)+ 𝜼H’.E ∞
S=𝜼G.(U∞-U)+ 𝜼H.(Ω∞-Ω)+ 𝜼M.E ∞
𝑭
𝑻
𝑺
= 𝜼 ∗
𝑨 𝑩′ G′
𝑩 𝑪 𝑯′
𝑮 𝑯 𝑴
*
𝑼∞ − 𝑼
𝜴∞ − 𝜴
𝑬 ∞
Singh et.al. 2000J.Fluid Mech. Vol. 412:279-301
16

17. June 30, 2016Md Imaran(IITG)
R =
𝑨 𝑩′ G′
𝑩 𝑪 𝑯′
𝑮 𝑯 𝑴
A, B ,C - Second order tensor
G ,H - Third order tensor
M - Fourth order tensor
Symmetric and
positive definite
matrix .
17
Grand mobility matrix .
symmetric and positive definite.
M

18. June 30, 2016Md Imaran(IITG)
R = M-1+ R2B - R2B
∞
R2B = two body interactions
R2B
∞ =Far-field effect of the body interactions
Inversion and
Addition of two body
Interactions
Captures
far field
interactions
18
Durlofsky et al.1987,Journal of Fluid Mechanics, 180, 21–49.

19. June 30, 2016Md Imaran(IITG)
To obtain the position of the particle we know that
m*
𝑑𝑈
𝑑𝑡
= FH + FP +FB
FH = Hydrodynamic force
FP= Inter-particle interaction
FB= Brownian force
19
𝑑𝑋𝑖
𝑑𝑡
= Ui
Xi(t=0)

20. Result and Discussions
June 30, 2016Md Imaran(IITG)
1. Effect of DLVO force
𝐹αβ = Force exerted by sphere β on sphere α
τ = Range of interaction force
Fo = Strength of interaction force
𝜀 = Separation between surface of spheres
𝑒 𝛼𝛽= Unit vector connecting the sphere centers
𝐹αβ = 𝐹0
𝜏𝑒−𝜏𝜀
1 − 𝑒−𝜏𝜀
𝑒 𝛼𝛽
Derjaguin. and Landau (1941) , Acta Phys. Chim., 14, 633-662
Verwey and Overbeek. (1948) Elsevier Amsterdam,
20

21. Result and Discussions
June 30, 2016Md Imaran(IITG)
21
Validation of method
F0 = 100
τ= 0.001

22. Result and Discussions
June 30, 2016Md Imaran(IITG)
Simulation Parameters
22
τ Fo Fo *τ
100 0.001 0.1
100 0.3 30
100 1 100
100 5 500
100 10 1000
1. (a) Effect of Simulation Parameters

23. Result and Discussions
June 30, 2016Md Imaran(IITG)
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(a) F0=0.001, τ =100 (b)F0=1,τ =100
Viscosity Profile for different concentration

24. Result and Discussions
June 30, 2016Md Imaran(IITG)
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(c) F0=5, τ =100 (d) F0=10,τ =100
Viscosity Profile

25. Result and Discussions
June 30, 2016Md Imaran(IITG)
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Viscosity Profile for different repulsive force

26. Result and Discussions
June 30, 2016Md Imaran(IITG)
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Concentration Profile (φA=0.648)

27. Result and Discussions
June 30, 2016Md Imaran(IITG)
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(a) F0=0.3, τ =100 (b) F0=10, τ =100
Velocity Profile and particle configuration(φv=0.5)
Shear rate(γ) = 0.428

28. Result and Discussions
June 30, 2016Md Imaran(IITG)
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Viscosity variation with time (φv=0.5)
Shear rate(ϓ) = 0.428

29. Result and Discussions
June 30, 2016Md Imaran(IITG)
29
1. (b) Effect of Couette Gap
Viscosity profile for different DLVO force and couette gap
фv = 0.35
(a) F0=0.001, τ =100 (b) F0=10, τ =100

30. Result and Discussions
June 30, 2016Md Imaran(IITG)
30
Viscosity profile for different concentration and couette gap
фv = 0.5фv = 0.35

31. Result and Discussions
June 30, 2016Md Imaran(IITG)
Shear rate(ϓ) = 0.4
Velocity profile and configuration at different coquette gap
H-30
H-20
фv = 0.5

32. Result and Discussions
June 30, 2016Md Imaran(IITG)
Double exponential model
𝐹 𝑆𝑅 = 𝑅[𝐴1 𝑒
−𝐷
𝑑1 + 𝐴2 𝑒
−𝐷
𝑑2 ]
𝐴1 = 0.1055
𝑑1 = 0.563
𝐴2 = 11.67155
𝑑2 = 0.057
Fitting Parameters
R = Particle radius,
D = Separation distance
DLVO parameters
Fo = 0.001
τ = 100
32
Franks et al. (2000)..
2. Effect of Double layer exponential and DLVO force

33. Result and Discussions
June 30, 2016Md Imaran(IITG)
33
Viscosity profile

34. Result and Discussions
June 30, 2016Md Imaran(IITG)
34
Concentration and velocity Profile (φv=0.5)
Shear rate(γ) = 0.0714 Shear rate(γ) = 0.5714

35. Result and Discussions
June 30, 2016Md Imaran(IITG)
35
Shear rate(ϓ) = 0.0714 Shear rate(ϓ) = 0.5714
Particle configuration and velocity profile

36. Result and Discussions
June 30, 2016Md Imaran(IITG)
36
фv = 0.5
Effect of coquette gap

37. Effect of DLVO and frictional forces
June 30, 2016Md Imaran(IITG)
Contact friction Model (Based on the friction between the
particles):-
𝐹 𝐶, 𝑛𝑜𝑟
𝑖, 𝑗
= 𝑘 𝑛ℎ𝑛𝑖𝑗
𝐹 𝐶, tan
𝑖, 𝑗
= 𝑘 𝑡ξ
( 𝑖, 𝑗)
𝑇 𝐶
𝑖, 𝑗
= 𝑎𝑖 𝑛𝑖𝑗 ∗ 𝐹 𝐶, tan
𝑖, 𝑗
𝑘𝑡 , 𝑘 𝑛 = Spring Constant
ξ = Tangential spring stretch
ξ(𝑖,𝑗)(t0) = 0
Un
(i,j) = Pnij(U(j) – U(i) )
Ut
(i,j) = P’nij [U(j) – U(i) – ( aiΩ(i) + ajΩ(j))*nij]
ξ(𝑖,𝑗)(t0) = 0
ξ(𝑖,𝑗)(t)
Mari et al . (2014). J. of Rheology :1693-1724.
37
3. Effect of DLVO and Frictional forces

38. June 30, 2016Md Imaran(IITG)
F’C,tan
(i,j)(t+dt) =𝑘𝑡ξ’(𝑖,𝑗)(t+dt) +tUt
(i,j)(t+dt)
ξ’(𝑖,𝑗)(t+dt) = ξ(𝑖,𝑗)(t)+ Ut
(i,j)(t)dr
if F’C,tan
(i,j)(t+dt) ≤ μ FC,tan
(i,j)(t+dt)
ξ(𝑖,𝑗)(t+dt) = ξ’(𝑖,𝑗)(t+dt)
Else
ξ(𝑖,𝑗)(t+dt) = (1/kt) (μ FC, nor
(i,j)(t+dt) tij - tUt
(i,j)(t))
tij = F’C,tan
(i,j)(t+dt) / F’C,tan
(i,j)(t+dt)
Slide Friction
Static Friction
38
μ=1 , kt=1 and kn=5. DLVO force parameters are Fo = 10 and τ = 1000.

39. June 30, 2016Md Imaran(IITG)
Result and discussions
39
фv = 0.5
Relative viscosity vs shear rate
Polymethylmethacrylate particles suspensions in
glycerine–water mixtures (Jiang et.al ,2010)
Present simulation work

40. Result and discussions(c)
June 30, 2016Md Imaran(IITG)
40
Viscosity profile with time фv = 0.5

41. Result and discussions(c)
June 30, 2016Md Imaran(IITG)
41
Shear rate(ϓ) = 0.14 Shear rate(ϓ) = 0.35 Shear rate(ϓ) = 0.57
Particle configuration and velocity profile

42. Suspension velocity profile
June 30, 2016Md Imaran(IITG)
42
Shear rate(ϓ) = 0.14 Shear rate(ϓ) = 0.35 Shear rate(ϓ) = 0.57

43. Result and discussions(c)
June 30, 2016Md Imaran(IITG)
43
Viscosity profile with varying gap
фv = 0.5

44. Conclusions
June 30, 2016Md Imaran(IITG)
 Inter-particle forces are deciding factor in rheology of
suspension.
 Suspension viscosity decreases with increasing the DLVO
force.
 Effect of inter-particle force is negligible at low concentration.
 Couette gap effect is negligible for low inter-particle force.
 Suspension viscosity increases with couette gap for high inter-
particle force.
 Shear thinning behavior is achieved with double layer
repulsive force.
 Shear thickening behavior is observed with frictional forces.
44

45. Future Work
June 30, 2016Md Imaran(IITG)
• Present work is done for 2-D Stokesian dynamics simulation
of suspension. It can be extended for 3-D simulation with
added interparticle force models.
• Parametric analysis of frictional forces can be done.
• Inter particle forces can be added to study the rod, plate and
dumbbell shape particle suspension.
45

46. References
June 30, 2016Md Imaran(IITG)
• http://www.ammoland.com/2012/10/revolutionary-liquid-body-armor
• Ahuja A., & Singh, A. (2011). Slip velocity of concentrated suspensions in Couette
flow, Journal of Rheology 53, 1461
• Brady, J. (1988). Stokesian Dynamics. Annual Review of Fluid Mechanics, 20(1),
111–157.
• Ding, J., Tracey, P., Li, W., Peng, G., Whitten, P. G., & Wallace, G. G. (2013). Review
on Shear Thickening Fluids and Applications, XX (Xx), 1–12.
• Dratler, D. I., Schowalter, W. R., & Hoffman, R. L. (1997). Dynamic simulation of
shear thickening in concentrated colloidal suspensions. Journal of Fluid Mechanics,
353, 1–30.
• Durlofsky, L., Brady, J. F., & Bossis, G. (1987). Dynamic simulation of
hydrodynamically interacting particles. Journal of Fluid Mechanics, 180, 21–49.
• Franks, G. V, Zhou, Z., Duin, N. J., Boger, D. V, Franks, G. V, Zhou, Z., & Duin, N. J.
(2000). ,Journal of Rheology 44, 759.
• Hasanzadeh, M., & Mottaghitalab, V. (2014). The Role of Shear-Thickening Fluids
(STFs) in Ballistic and Stab-Resistance Improvement of Flexible Armor. Journal of
Materials Engineering and Performance, 23(April), 1–15.

47. References
June 30, 2016Md Imaran(IITG)
• Lee, Y., & Wagner, N. (2003). Dynamic properties of shear thickening colloidal
suspensions. Rheologica Acta, 42, 199–208.
• Mari, R., Seto, R., Morris, J. F., & Denn, M. M. (2013). Shear thickening, frictionless
and frictional rheologies, 1693, 32.
• Nott and Brady (1994). Pressure-driven flow of suspensions: simulation and
theory. Journal of Fluid Mechanics, 275, 157-199.
• Singh, A., & Nott, P. R. (2000). Normal stresses and microstructure in bounded
sheared suspensions via Stokesian Dynamics simulations. Journal of Fluid
Mechanics, 412, 279–301.
• Zhang, X. Z., Li, W. H., & Gong, X. L. (2008). The rheology of shear thickening fluid
(STF) and the dynamic performance of an STF-filled damper. Smart Materials and
Structures, 17(3), 035027.

48. THANK YOU!
June 30, 2016Md Imaran(IITG)
48