Mesoscopic simulations of the rheology of entangled wormlike micelles

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)

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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transient stress• usually large

1st normal stress difference

• overshoots in all transient stresses

• 2nd normal stress difference has a positive overshoot before becoming negative

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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

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simulation and experiment – shear viscosity

8% EHAC

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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)