Large scale dynamic simulation of plate-like particle suspensions. Part I: Non-Brownian simulation

Meng, Qingjun; Higdon, J. J. L.

doi:10.1122/1.2798236

Cited by 44 publications

(27 citation statements)

References 29 publications

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“…First, Fixman [25,26,30,31] has proposed an approximation to σ iα,jβ by a truncated expansion in Chebyshev polynomials, which has a more favorable scaling than Cholesky decomposition. Second, the long-range hydrodynamic interactions can be calculated by Fast Fourier Transforms [32][33][34][35][36][37], or hierarchical multipole expansions [20]. Accelerated Brownian Dynamics and Stokesian Dynamics algorithms scale close to linearly in the number of particles, and their full potential is not yet explored.…”

Section: Brownian Dynamicsmentioning

confidence: 99%

Lattice Boltzmann Simulations of Soft Matter Systems

Dünweg¹,

Ladd²

2008

Advances in Polymer Science

201

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This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview of the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice-Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice-Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.

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Section: Brownian Dynamicsmentioning

confidence: 99%

Lattice Boltzmann Simulations of Soft Matter Systems

Dünweg¹,

Ladd²

2008

Advances in Polymer Science

201

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“…from an earlier time step. A detailed description of the preconditioner similar to the one employed here can be found in Meng & Higdon (2008a). Figure 10 illustrates the performance of the preconditioned iterative solver for a system of 1000 particles.…”

Section: Pme Stokesian Dynamics For Dicolloidsmentioning

confidence: 99%

“…For the lubrication correction, the previous authors used the asymptotic formulas developed by Claeys & Brady (1989). Meng & Higdon (2008a) developed Stokesian dynamics for plate-like particles by modelling them as rigid planar assemblages of spheres. This technique, which in effect involves constrained motion of spheres, allowed for the use of singularity solutions for spheres in the far-field term and the classic lubrication results for spheres in the nearfield interactions.…”

Section: Introductionmentioning

confidence: 99%

Particle mesh Ewald Stokesian dynamics simulations for suspensions of non-spherical particles

Kumar

Higdon

2011

J. Fluid Mech.

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A particle mesh Ewald (PME) Stokesian dynamics algorithm has been developed to model hydrodynamic interactions in suspensions of non-spherical dicolloidal particles. Dicolloids, which have recently been synthesized by a number of independent research two intersecting spheres of varying radii and centreto-centre separation. One-body resistance tensors and disturbance velocity fields are computed for general linear flows using a superposition of Stokes singularities along the symmetry axis of the dicolloid particles. The coefficients and the locations of the singularities are optimized to minimize the norm of the velocity error on the particle surface. The one-body solution provides all coefficients required for the far-field many-body interactions in the Stokesian dynamics algorithm. These generalize the analytical results for spheres employed in the classic algorithm. Modified lubrication interaction tensors are developed for dicolloids for the singular near-field lubrication interactions. Accuracy of the one-body solutions and two-body generalized Stokesian dynamics solutions are validated by comparison with high-precision numerical solutions computed with the spectral boundary element method of Muldowney & Higdon (J. Fluid Mech., vol. 298, 1995, p. 167). The newly developed PME Stokesian dynamics algorithm was used to study transport properties in dicolloidal suspensions over a range of volume fractions (φ 6 0.5). The effects of the degree of anisotropy on the properties of the suspension are discussed. For these mildly anisotropic particles, the transport properties remain close to those of spheres, however certain interesting trends emerge, with non-monotonic viscosity dependence as a function of increasing aspect ratio. The minimum viscosity in concentrated suspensions is lower than that for spheres with equal volume fraction over a range of volume fractions.

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“…The result of this coincidence is that the grand resistance tensor for the rigid assembly will always be symmetric. In the shorthand notation where translational and rotational velocities are denoted by a single vector, these statements become: ; (33) and Dr ðaAÞ ¼ x ðaÞ À x ðAÞ . For a set of M rigid bodies formed by constraining N particles, the velocities of the particles may be expressed as…”

Section: The Mechanics Of Rigid Assembliesmentioning

confidence: 99%

Modeling hydrodynamic self-propulsion with Stokesian Dynamics. Or teaching Stokesian Dynamics to swim

et al. 2011

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We develop a general framework for modeling the hydrodynamic self-propulsion (i.e., swimming) of bodies (e.g., microorganisms) at low Reynolds number via Stokesian Dynamics simulations. The swimming body is composed of many spherical particles constrained to form an assembly that deforms via relative motion of its constituent particles. The resistance tensor describing the hydrodynamic interactions among the individual particles maps directly onto that for the assembly. Specifying a particular swimming gait and imposing the condition that the swimming body is force-and torque-free determine the propulsive speed. The body's translational and rotational velocities computed via this methodology are identical in form to that from the classical theory for the swimming of arbitrary bodies at low Reynolds number. We illustrate the generality of the method through simulations of a wide array of swimming bodies: pushers and pullers, spinners, the Taylor=Purcell swimming toroid, Taylor's helical swimmer, Purcell's three-link swimmer, and an amoeba-like body undergoing large-scale deformation. An open source code is a part of the supplementary material and can be used to simulate the swimming of a body with arbitrary geometry and swimming gait.

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Large scale dynamic simulation of plate-like particle suspensions. Part I: Non-Brownian simulation

Cited by 44 publications

References 29 publications

Lattice Boltzmann Simulations of Soft Matter Systems

Lattice Boltzmann Simulations of Soft Matter Systems

Particle mesh Ewald Stokesian dynamics simulations for suspensions of non-spherical particles

Modeling hydrodynamic self-propulsion with Stokesian Dynamics. Or teaching Stokesian Dynamics to swim

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