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Mesoscopic simulations of the rheology of entangled wormlike micelles

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## Mesoscopic simulations of the rheology of entangled wormlike micelles

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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 acknowledgments: V.Anderson, J.Crawshaw, M.Stukan, J.R.A.Pearson (SCR)**+**+ + + + + + hydraulic fracturing + + + oil-responsive surfactant fluids +salt +oil wormlike micelles spherical micelles or micro-emulsions visco-elastic network of wormlike micelles EHAC erucyl bis-(hydroxyethyl)methylammonium chloride other applications: food products, personal care (shampoo, …)**available REoS are inadequate**l = 1 Bautista-Manero: l = 10 • Problems: • poor fit to transient data (Anderson et al. 2006) • extensional viscosity (Boek, Pearson et al., JNNFM 126, 39-46 (2005) • normal stresses Instantaneous shear stress / Pa l = 100 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**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**mesoscopic simulation model (2/4)**• Bonded interaction: • Mesoscopic property input: • Persistence length lp • Elastic modulus K • Scission energy Esc • Activation barrier Ea**mesoscopic simulation model (3/4)**• Brownian Dynamics (overdamped) of rigid rods of dimension lp x d in a solvent of viscosity hs • Additional mesoscopic input: • 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**mechanical properties from MD simulationof 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: hs= 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)**Ly = 340 nm**lp = 30 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 (mm) • Computational speed: 0.1 – 1 ms/week on one 2.8 GHz Pentium 4 processor**linear rheology**• shear relaxation modulus(measured from equilibriumstress fluctuations)**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**transient stress**• usually large1st normal stress difference • overshoots in all transient stresses • 2nd normal stress difference has a positive overshoot before becoming negative**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**references**• J.T. Padding and E.S. Boek, ``Evidence for diffusion controlled recombination kinetics in model wormlike micelles’‘, Europhysics Letters66, 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. E70, 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)