Simulating colloid hydrodynamics with lattice Boltzmann methods

Cates, Michael E.; Stratford, Kevin; Adhikari, R.; Stansell, Paul; Desplat, J. C.; Pagonabarraga, Ignacio; Wagner, A. James

doi:10.1088/0953-8984/16/38/009

Cited by 85 publications

(108 citation statements)

References 42 publications

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“…Another useful approach is the lattice Boltzmann (LB) method. 18,19) LB is a grid-based method that operates at the level of the reduced phase space distribution function. The LB approach is capable of handling large system sizes efficiently.…”

Section: Introductionmentioning

confidence: 99%

On the Role of Hydrodynamic Interactions in Colloidal Gelation

et al. 2008

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In this letter, we investigate several aspects related to the effect of hydrodynamic interactions on phase separation-induced gelation of colloidal particles. We explain physically the observation of hydrodynamic stabilization of cellular network structures in two dimensions. We demonstrate that hydrodynamic interactions have only a minor quantitative influence on the structure of transient gels in three dimensions. We discuss some experimental implications of our results.

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Section: Introductionmentioning

confidence: 99%

On the Role of Hydrodynamic Interactions in Colloidal Gelation

et al. 2008

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“…(Without shear, subtle non-scaling effects arise in 2D from the formation of disconnected droplets [8], but shear seems to suppress these [9].) Performing simulations in 2D is therefore a fair compromise, especially given the extreme computational demands of the full 3D problem [3,10]. But, apart from [9,11], most numerical studies of binary fluids under steady shear, even in 2D, neglect hydrodynamics altogether [12,13,14].…”

mentioning

confidence: 99%

“…Unlike previous authors, we are able to give clear evidence of true dynamical steady states, uncontaminated by finite size effects or other artifacts. (Finite size effects typically result in quasi-laminar stripe domains which connect with themselves after one or more circuits of the periodic boundary conditions [9,10].) We then combine datasets using a quantitative scaling methodology developed for the unsheared problem in [15]; this allows scaling exponents to be estimated using combined multi-decade fits.…”

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confidence: 99%

Nonequilibrium Steady States in Sheared Binary Fluids

et al. 2006

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We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths Lx,y in the directions (x, y) of velocity and velocity gradient. Apparent scaling exponents are estimated as Lx ∼γ −2/3 and Ly ∼γ −3/4 . We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.PACS numbers: 47.11.+jSystems that are not in thermal equilibrium play a central role in modern statistical physics, and arise in areas ranging from soap manufacture to subcellular biology [1]. Such systems include two important classes: those that are evolving towards Boltzmann equilibrium (e.g., by phase separation following a temperature quench), and those that are maintained in nonequilibrium by continuous driving (such as a shear flow). Of fundamental interest, and surprising physical subtlety, are systems combining both features -such as a binary fluid undergoing phase separation in the presence of shear. Here it is not known [2,3] whether coarsening continues indefinitely, as it does without shear, or whether a steady state is reached, in which the characteristic length scales L x,y,z of the fluid domain structure attain finiteγ-dependent values at late times. (We define the mean velocity as u x =γy so that x, y, z are velocity, velocity gradient and vorticity directions respectively;γ is the shear rate.) Experimentally, saturating length scales are reportedly reached after a period of anisotropic domain growth [2,4]. However, the extreme elongation of domains along the flow direction means that, even in experiments, finite size effects could play an essential role in such saturation [5]. Theories in which the velocity does not fluctuate, but does advect the diffusive fluctuations of the concentration field, predict instead indefinite coarsening, with length scales L y,z scaling asγ-independent powers of the time t since quench, and (typically) L x ∼γtL y [5]. In real fluids, however, the velocity fluctuates strongly in nonlinear response to the advected concentration field, and hydrodynamic scaling arguments, balancing either interfacial and viscous or interfacial and inertial forces, predict saturation (e.g., L ∼γ −1 or L ∼γ −2/3 ) [3,6,7]. Given these experimental and theoretical differences of opinion, computer simulations of sheared binary fluids, with full hydrodynamics, are of major interest.The aforementioned scaling arguments cannot really distinguish one Cartesian direction from another, but even in theories that can do so, a two dimensional (2D) representation, suppressing z, is expected to capture the main physics [5]. (Without shear, subtle non-scaling effects arise in 2D from the formation of disconnected droplets [8], but shear seems to suppress these [9].) Performing simulations in 2D is therefore a fair compromise, especially given the extreme computational demands of the full 3D problem [3,10]. But, apart from [9,11]...

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“…Both Reynolds and electrolyte Péclet numbers are much smaller than unity in the simulations described below, ensuring a realistic setting of dimensionless numbers ͑see, e.g., Ref. 16 for a discussion on the relevance of dimensionless numbers in LB͒. In our simulations the diffusion coefficient has a value which corresponds to nanometric electrolytes ͑again for monovalent ions in water͒.…”

Section: A Simulation Methodsmentioning

confidence: 91%

Lattice-Boltzmann simulation of the sedimentation of charged disks

Capuani

Pagonabarraga²,

Frenkel

2006

The Journal of Chemical Physics

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We report a series of lattice-Boltzmann simulations of the sedimentation velocity of charged disks. In these simulations, we explicitly account for the hydrodynamic and electrostatic forces on disks and on their electrical double layer. By comparing our results with those for spheres with equal surface and charge, we can clarify the effect of the particle shape on the sedimentation process. We find that disks and spheres exhibit a different dependence of the sedimentation velocity on the Debye screening length. An analysis of the behavior of highly charged disks ͑beyond the scope of the linearized Poisson-Boltzmann equation͒ shows that, in that regime, the charge dependence of the sedimentation velocity of disks and spheres is similar. This suggests that, at high charge, the effective hydrodynamic shape of the disks becomes more spherical.

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Simulating colloid hydrodynamics with lattice Boltzmann methods

Cited by 85 publications

References 42 publications

On the Role of Hydrodynamic Interactions in Colloidal Gelation

On the Role of Hydrodynamic Interactions in Colloidal Gelation

Nonequilibrium Steady States in Sheared Binary Fluids

Lattice-Boltzmann simulation of the sedimentation of charged disks

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