Transcript Molecular Dynamics simulations of Visco

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
(3)
of Cambridge, UK
University of Twente, NL
acknowledgments: V.Anderson, J.Crawshaw, M.Stukan, J.R.A.Pearson
oil-responsive surfactant fluids
+salt
+oil
wormlike micelles
H
H
CH 2 –CH 2 –OH
C
CH 3 –(CH 2 ) 7
C
Cl
visco-elastic network of
wormlike micelles
—
+
spherical micelles
or micro-emulsions
(CH 2 ) 11 –CH 2 –N–CH 3
EHAC
CH 2 –CH 2 –OH
erucyl bis-(hydroxyethyl)methylammonium chloride
hydraulic fracturing
1.00E+02
Viscosity (Pa.s)
1.00E+01
1.00E+00
40 oC (104 oF)
70 oC (158 oF)
1.00E-01
90 oC (194 oF)
130 oC (266 oF)
150 oC (302 oF)
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)
2 ESB
7/22/2015
other applications: food products, personal care (shampoo, …)
available REoS are inadequate
Step up in shear rate
d
dt

1
λ

 0     k  
 τ : D
param eters G 0 ,  0 ,   , λ,λ J ,  1 ...(   solvent )
 0 ,   , kλ determ ined from steady state expt
•
1.
Problems:
poor fit to transient data
(Anderson et
al. 2006)
2.
extensional viscosity (Boek, Pearson et al.,
JNNFM 126, 39-46 (2005)
3
3.
normal stresses
ESB
7/22/2015
Instantaneous shear stress / Pa

2

τ
τ   D  λJ D 
G 0
 

1
/ Pa
stress
shear
Instantaneous
Instantaneous
Instantaneous shear stress / Pa
shear stress
/ Pa
Bautista-Manero:
 == 11s Step up down shear rate
4
10
2
10
0
10
0
10
20
30
40
100
50
Time / s
120
140
160
180
100
120
140
160
180
120
140
160
180
 == 1010s
4
10
2
10
0
10
0
10
20
30
40
50
 == 100
100
s
Time / s
4
10
2
10
0
10
0
10
20
30
40
50
100
Time / s
Time / s
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
4 ESB
7/22/2015
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
5 ESB
7/22/2015
mesoscopic simulation model (2/4)
• Bonded interaction:
• Mesoscopic property input:
–
–
–
–
6 ESB
7/22/2015
Persistence length lp
Elastic modulus K
Scission energy Esc
Activation barrier Ea
b 
1K
2 lp
r  l 
p
2
 E sc
mesoscopic simulation model (3/4)
• Brownian Dynamics
(overdamped) of rigid rods of
dimension lp x d in a solvent of
viscosity hs
1
r  t  t   r  t     t   FS  t  t   r
 r r  2kBT  1  t  t

1
t  
ln  l p / d 
4hs l p
 ˆI  uˆ  t  uˆ  t  
• Additional mesoscopic input:
7 ESB
7/22/2015
– Solvent viscosity hs


Total systematic force on unit
Anisotropic random
displacement and friction which
depend on rod orientation
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
8 ESB
7/22/2015
mechanical properties from MD
simulation of worm-like micelle
• lp = 30 nm
lp
• d = 4.8 nm
• K = 2 nJ/m
•
d
J.T. Padding, E.S. Boek and W.J. Briels, J. Phys.: Condens. Matter 17, S3347–S3353
(2005).
•
solvent is water: hs = 10-3 Pa s
•
experimentally Esc = 20-50 and Ea = 10-25 kBT
– scission-recombination extremely rare!
– preliminary results with Esc = 17 kBT
9 ESB
7/22/2015
• 12 kBT + 2.5 kBT ln (lp / d)
– and lower Ea (1.5 kBT)
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)
Ly = 340 nm
lp = 30 nm
10 ESB
7/22/2015
– Computational speed:
0.1 – 1 ms/week on one
2.8 GHz Pentium 4
processor
linear rheology

shear relaxation modulus
(measured from equilibrium
stress fluctuations)
G t  
S 
V
kBT
1
r   r  F


V
i,
i j
11 ESB
7/22/2015
Sxy  t  Sxy  0 
j,
ij , 
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 react
to flow velocity of wormlike micellar
material
12 ESB
7/22/2015
transient stress
• usually large
1st normal stress
difference
• overshoots in all
transient stresses
• 2nd normal stress
difference has a
positive overshoot
before becoming
negative
13 ESB
7/22/2015
shear thinning
• average length of WLM
decreases with shear
rate
• average breaking time
decreases with shear
1
rate: opposite
effect
from
L

 
break
c1L
• viscosity decreases
rapidly with shear rate
14 ESB
7/22/2015
simulation and experiment – shear viscosity
8% EHAC
15 ESB
7/22/2015
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-
16 ESB
7/22/2015
255 (2006).
•
E.S. Boek, V. Anderson, J.T. Padding, W.J. Briels and J. Crawshaw, submitted for publication