Structural transitions and arrest of domain growth in sheared binary immiscible fluids and microemulsions.

We investigate spinodal decomposition and structuring effects in binary immiscible and ternary amphiphilic fluid mixtures under shear by means of three-dimensional lattice Boltzmann simulations. We show that the growth of individual fluid domains can be arrested by adding surfactant to the system, thus forming a bicontinuous microemulsion. We demonstrate that the maximum domain size and the time of arrest depend linearly on the concentration of amphiphile molecules. In addition, we find that for a well-defined threshold value of amphiphile concentration, the maximum domain size and time of complete arrest do not change. For systems under constant and oscillatory shear we analyze domain growth rates in directions parallel and perpendicular to the applied shear. We find a structural transition from a sponge to a lamellar phase by applying a constant shear and the occurrence of tubular structures under oscillatory shear. The size of the resulting lamellae and tubes depends strongly on the amphiphile concentration, shear rate, and shear frequency.

[1]  M Nekovee,et al.  Lattice-Boltzmann simulations of self-assembly of a binary water-surfactant system into ordered bicontinuous cubic and lamellar phases. , 2001, Journal of the American Chemical Society.

[2]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[3]  Yuliang Yang,et al.  Annealing Effects on Orientation in Dynamically Sheared Diblock Copolymers , 1996 .

[4]  D. Rothman.  Complex Rheology in a Model of a Phase-Separating Fluid , 1991 .

[5]  T. Koga,et al.  Effect of oscillatory shear deformation on demixing processes of polymer blends , 1997 .

[6]  P. V. Coveney,et al.  Simulations of amphiphilic fluids using mesoscale lattice-Boltzmann and lattice-gas methods , 2003 .

[7]  S. Edwards,et al.  The computer study of transport processes under extreme conditions , 1972 .

[8]  Hirotada Ohashi,et al.  Formation of micelle in the real-coded lattice gas , 2000 .

[9]  Peter V Coveney,et al.  Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  G. Gompper,et al.  Lattice-Boltzmann model of amphiphilic systems , 1998 .

[11]  T. Narayanan,et al.  Lamellar phases under shear: variation of the layer orientation across the couette gap , 2000 .

[12]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[13]  Chen,et al.  Hydrodynamic spinodal decomposition: Growth kinetics and scaling functions. , 1993, Physical review. B, Condensed matter.

[14]  Aiguo Xu,et al.  Phase separation of incompressible binary fluids with lattice Boltzmann methods , 2004 .

[15]  P. Español,et al.  Statistical Mechanics of Dissipative Particle Dynamics. , 1995 .

[16]  Peter V Coveney,et al.  Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: Lattice-Boltzmann simulations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  M. Kleman,et al.  Rheology of lyotropic and thermotropic lamellar phases , 2000 .

[18]  Krall,et al.  Experimental studies of the rheology of a simple liquid mixture during phase separation. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  G. Gonnella,et al.  Spinodal Decomposition to a Lamellar Phase: Effects of Hydrodynamic Flow , 1997 .

[20]  G. Gonnella,et al.  Phase separation of binary mixtures in shear flow: A numerical study , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Hirotada Ohashi,et al.  Immiscible real-coded lattice gas , 2000 .

[22]  M. E. Cates,et al.  3D spinodal decomposition in the inertial regime , 1999, cond-mat/9902346.

[23]  Flekkoy,et al.  Foundations of dissipative particle dynamics , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Matthaeus,et al.  Lattice Boltzmann model for simulation of magnetohydrodynamics. , 1991, Physical review letters.

[25]  Banavar,et al.  Lattice Boltzmann study of hydrodynamic spinodal decomposition. , 1995, Physical review letters.

[26]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[27]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Moses,et al.  String phase in phase-separating fluids under shear flow. , 1995, Physical review letters.

[29]  Shan,et al.  Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  Krall,et al.  Viscoelasticity of a simple liquid mixture during spinodal decomposition. , 1992, Physical review letters.

[31]  P. Coveney,et al.  Erratum: Lattice-gas simulations of domain growth, saturation, and self-assembly in immiscible fluids and microemulsions [Phys. Rev. E55, 708 (1997)] , 1997 .

[32]  P V Coveney,et al.  Three-dimensional hydrodynamic lattice-gas simulations of domain growth and self-assembly in binary immiscible and ternary amphiphilic fluids. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  G. Gonnella,et al.  Steady state of microemulsions in shear flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  P. Coveney,et al.  Chirality and domain growth in the gyroid mesophase , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[35]  R. Benzi,et al.  Lattice Gas Dynamics with Enhanced Collisions , 1989 .

[36]  M. E. Cates,et al.  Inertia, coarsening and fluid motion in binary mixtures , 1999 .

[37]  A. Lamura,et al.  A lattice Boltzmann model of ternary fluid mixtures , 1995 .

[38]  Michael E. Cates,et al.  Simulation of amphiphilic mesophases using dissipative particle dynamics , 1999 .

[39]  Alexander J. Wagner,et al.  Breakdown of Scale Invariance in the Coarsening of Phase-Separating Binary Fluids , 1998 .

[40]  Peter V Coveney,et al.  Stress response and structural transitions in sheared gyroidal and lamellar amphiphilic mesophases: Lattice-Boltzmann simulations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  I. Pagonabarraga,et al.  Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study , 2001, Journal of Fluid Mechanics.

[42]  Richard A. L. Jones.  Soft Condensed Matter , 2002 .

[43]  Jean-Pierre Rivet,et al.  Lattice Gas Hydrodynamics , 1987 .

[44]  A. Lamura,et al.  Spinodal Decomposition of Binary Mixtures in Uniform Shear Flow , 1998 .

[45]  Aiguo Xu,et al.  Phase-separating binary fluids under oscillatory shear. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Peter V Coveney,et al.  Lattice Boltzmann study of spinodal decomposition in two dimensions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  P. V. Coveney,et al.  Emergence of rheological properties in lattice Boltzmann simulations of gyroid mesophases , 2006 .

[48]  Ignacio Pagonabarraga,et al.  Lees–Edwards Boundary Conditions for Lattice Boltzmann , 2001 .

[49]  Peter V. Coveney,et al.  Self-assembly of the gyroid cubic mesophase: Lattice-Boltzmann simulations , 2003, cond-mat/0310390.

[50]  Two-Scale Competition in Phase Separation with Shear , 1999, cond-mat/9904423.

[51]  Peter V. Coveney,et al.  Detection and tracking of defects in the gyroid mesophase , 2005, Comput. Phys. Commun..

[52]  M. Cates,et al.  Interfacial dynamics in 3D binary fluid demixing: animation studies* , 2001 .

[53]  Peter V. Coveney,et al.  A ternary lattice Boltzmann model for amphiphilic fluids , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[54]  Peter V. Coveney,et al.  Large-scale lattice Boltzmann simulations of complex fluids: advances through the advent of computational Grids , 2005, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[55]  A. Wagner,et al.  Phase Separation under Shear in Two-dimensional Binary Fluids , 1999, cond-mat/9904033.

[56]  Chen,et al.  Lattice-boltzmann model for interacting amphiphilic fluids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[57]  M E Cates,et al.  Nonequilibrium steady states in sheared binary fluids. , 2006, Physical review letters.

[58]  A. Chakrabarti,et al.  Ordering of viscous liquid mixtures under a steady shear flow , 2000 .

[59]  Paschalis Alexandridis,et al.  Shear induced structures in lamellar phases of amphiphilic block copolymers , 1999 .

[60]  Raymond Kapral,et al.  Continuous-velocity lattice-gas model for fluid flow , 1998 .

[61]  A. Bray.  Theory of phase-ordering kinetics , 1994, cond-mat/9501089.