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Mesoscopic simulations of the rheology of entangled wormlike micelles. Edo Boek ( 1 ) Johan Padding ( 1,2,3 ) Wim Briels ( 3 ). ( 1 ) Schlumberger Cambridge Research, UK ( 2 ) University of Cambridge, UK ( 3 ) University of Twente, NL - PowerPoint PPT Presentation
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Mesoscopic simulations of the rheology of entangled wormlike micelles
Edo Boek(1)
Johan Padding(1,2,3)
Wim Briels(3)(1) Schlumberger Cambridge Research, UK(2) University of Cambridge, UK(3) University of Twente, NLacknowledgments: V.Anderson, J.Crawshaw, M.Stukan, J.R.A.Pearson (SCR)
2 ESB04/22/23
oil-responsive surfactant fluids
+ +
+
++ +
+ + +
+
wormlike micellesvisco-elastic network of
wormlike micelles
1.00E-02
1.00E-01
1.00E+00
1.00E+01
1.00E+02
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03
Shear Rate (s-1)
Vis
cosi
ty (P
a.s)
40 oC (104 oF)
70 oC (158 oF)
90 oC (194 oF)
130 oC (266 oF)
150 oC (302 oF)
+oil
spherical micelles or micro-emulsions
+salt
hydraulic fracturing
other applications: food products, personal care (shampoo, …)
CH3–(CH2)7
C C
HH
(CH2)11–CH2–N–CH3
CH2–CH2–OH
CH2–CH2–OH
+
—Cl
EHACerucyl bis-(hydroxyethyl)methylammonium chloride
3 ESB04/22/23
available REoS are inadequate
0 10 20 30 40 50
100
102
104
Inst
anta
neou
s sh
ear
stre
ss /
Pa
100 120 140 160 180
0 10 20 30 40 50
100
102
104
Inst
anta
neou
s sh
ear
stre
ss /
Pa
100 120 140 160 180
0 10 20 30 40 50
100
102
104
Inst
anta
neou
s sh
ear
stre
ss /
Pa
100 120 140 160 180
= 1 s
= 10 s
= 100 s
Step up down shear rateStep up in shear rate
Time / s
Time / s
Time / s
J0
0
1 2τ τ D λ DG
d 1 k τ : Ddt λ
Bautista-Manero:
Inst
anta
neou
s she
ar st
ress
/ Pa
Time / s
= 1
= 100
= 10
• Problems:
1. poor fit to transient data (Anderson et al. 2006)
2. extensional viscosity (Boek, Pearson et
al., JNNFM 126, 39-46 (2005)
3. normal stresses
0 0 J 1
0
parameters G , , , λ,λ , ...( ), , kλ determined from steady state expt
solvent
4 ESB04/22/23
predictive multi-scale simulation model:chemistry to rheology
• Level 1:Microscopic Molecular Dynamics (MD) yields mesoscopic properties
• Level 2:Mesoscopic (Brownian Dynamics) simulation model yields rheological properties
5 ESB04/22/23
mesoscopic simulation model (1/4)• each unit (red sphere)
represents the midpoint of one persistence length lp– conservation of mass
• the endpoints (blue spheres) of the WLM are found by extrapolating from the first / last bonds– orientation of “monomer”
must be traced explicitly
6 ESB04/22/23
mesoscopic simulation model (2/4)
• Bonded interaction:
• Mesoscopic property input:– Persistence length lp– Elastic modulus K– Scission energy Esc
– Activation barrier Ea
212b p sc
p
K r l El
7 ESB04/22/23
mesoscopic simulation model (3/4)• Brownian Dynamics
(overdamped) of rigid rods of dimension lp x d in a solvent of viscosity s
• Additional mesoscopic input:– Solvent viscosity s
1
1
1
2
ln / ˆ ˆ ˆ4
S
B
p
s p
t t t t t t
k T t t
l dt t t
l
r r F r
r r
I u u
Total systematic force on unitAnisotropic random displacement and friction which depend on rod orientation
8 ESB04/22/23
mesoscopic simulation model (4/4)• Charge interactions are ignored
– Uncharged or charged system with small screening length.• Excluded volume interactions are ignored
– WLMs as long thin threads. No spontaneous nematic phase.• Uncrossability of threadlike wormlike micelles is treated by
TWENTANGLEMENT
9 ESB04/22/23
mechanical properties from MD simulation of worm-like micelle
• lp = 30 nm• d = 4.8 nm• K = 2 nJ/m• J.T. Padding, E.S. Boek and W.J. Briels, J. Phys.: Condens. Matter 17, S3347–S3353 (2005).
• solvent is water: s = 10-3 Pa s
• experimentally Esc = 20-50 and Ea = 10-25 kBT– scission-recombination extremely rare!– preliminary results with Esc = 17 kBT
• 12 kBT + 2.5 kBT ln (lp / d)– and lower Ea (1.5 kBT)
pl
d
10 ESB04/22/23
llpp = 30 nm = 30 nm
Ly = 340 nm
example: 8% EHAC + 3% KCl
• Typical simulation:– Total 4.000 – 32.000
persistence length units
– Box size 300-600 nm– Average worm contour
length O (m)– Computational speed:
0.1 – 1 ms/week on one 2.8 GHz Pentium 4 processor
11 ESB04/22/23
linear rheology shear relaxation modulusshear relaxation modulus
(measured from equilibrium(measured from equilibriumstress fluctuations)stress fluctuations)
, , ,
0
1
xy xyB
i j iji j
VG t S t Sk T
S r r FV
12 ESB04/22/23
non-linear rheology• impose constant shear rate between upper and
lower face of the periodic box• do not assume affine solvent flow field
– instead, let solvent reactto flow velocity of wormlike micellarmaterial
13 ESB04/22/23
transient stress• usually large
1st normal stress difference
• overshoots in all transient stresses
• 2nd normal stress difference has a positive overshoot before becoming negative
14 ESB04/22/23
shear thinning• average length of WLM
decreases with shear rate
• average breaking time decreases with shear rate: opposite effect from
• viscosity decreases rapidly with shear rate
1
1break L
c L
15 ESB04/22/23
simulation and experiment – shear viscosity
8% EHAC
16 ESB04/22/23
references• J.T. Padding and E.S. Boek, ``Evidence for diffusion controlled recombination kinetics in model wormlike micelles’‘,
Europhysics Letters 66, 756-762 (2004).
• J.T. Padding and E.S. Boek, ``The influence of shear flow on the formation of rings in wormlike micelles: a nonequilibrium molecular dynamics study'‘, Phys. Rev. E 70, 031502 (2004).
• E.S. Boek, J.T. Padding, V. Anderson, P. Tardy, J. Crawshaw and J.R.A. Pearson, ``Constitutive Equations for Extensional flow of wormlike micelles: Stability analysis of the Bautista-Manero model'', J. Non-Newtonian Fluid Mech. 126, 39-46 (2005).
• J.T. Padding, E.S. Boek and W.J. Briels, ``Rheology of wormlike micellar fluids from Brownian and Molecular Dynamics simulations'', J. Phys.: Condens. Matter 17, S3347–S3353 (2005).
• V. Anderson, J.R.A. Pearson and E.S. Boek, ``The rheology of worm-like micellar fluids'', in Rheology Reviews 2006, D.M. Binding and K. Walters (Eds.), British Society of Rheology, 217-255 (2006).
• E.S. Boek, V. Anderson, J.T. Padding, W.J. Briels and J. Crawshaw, submitted for publication (2006)