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Mesoscopic simulations of the rheology of entangled wormlike micelles

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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  1. 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)

  2. + + + + + + + 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, …)

  3. 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

  4. 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. 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. mesoscopic simulation model (2/4) • Bonded interaction: • Mesoscopic property input: • Persistence length lp • Elastic modulus K • Scission energy Esc • Activation barrier Ea

  7. 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

  8. 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. 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)

  10. 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

  11. linear rheology • shear relaxation modulus(measured from equilibriumstress fluctuations)

  12. 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. transient stress • usually large1st normal stress difference • overshoots in all transient stresses • 2nd normal stress difference has a positive overshoot before becoming negative

  14. 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

  15. simulation and experiment – shear viscosity 8% EHAC

  16. 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)