Parallel <i>O</i>(<i>N</i>) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai; Karpeev, Dmitry; Heinonen, Olle; Barry, Smith; Hernández-Ortiz, Juan P.; Pablo, Juan J. de

doi:10.1063/1.4989545

Cited by 19 publications

(22 citation statements)

References 82 publications

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“…Our simulation method, denoted by IB-pFE-GgEm, is an O(N) algorithm that includes hydrodynamic interactions for confined, large-scale suspensions of finite-size particles of arbitrary shape. Details can be found in our previous work 38 . Briefly, the O(N) algorithm consists of three major components: (a) pFE-GgEm routines to calculate the Green's function (Stokeslet) for any geometry, (b) Fixman's mid-point algorithm for time integration and (c) the Chebyshev polynomial approximation for the fluctuation dissipation theorem.…”

Section: Mathematical Model and Systemmentioning

confidence: 99%

“…We have developed an efficient computational framework to perform BD simulations of arbitrarily shaped particles confined in any type of geometry. We use an Immersed-Boundary (IB) method to represent the suspended particles, a parallel Finite Element General geometry Ewald-like method (pFE-GgEm) 38 to calculate the confined Green's functions, and a Chebyshev polynomial approximation to satisfy the fluctuation-dissipation theorem. In this work, we use this methodology to study how steric repulsion, short-and longrange hydrodynamic interactions, confinement, particle volume fraction and particle shape affect the structure and the diffusion of spherical and cylindrical finite-size particles confined in a spherical cavity.…”

Section: Introductionmentioning

confidence: 99%

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Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: spheres and cylinders

Li,

Jiang,

Singh

et al. 2020

Preprint

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The structure and dynamics of confined suspensions of particles of arbitrary shape is of interest in multiple disciplines, from biology to engineering. Theoretical studies are often limited by the complexity of long-range particle-particle and particle-wall forces, including many-body fluctuating hydrodynamic interactions. Here, we report a computational study on the diffusion of spherical and cylindrical particles confined in a spherical cavity. We rely on an Immersed-Boundary General geometry Ewald-like method to capture lubrication and long-range hydrodynamics, and include appropriate non-slip conditions at the confining walls. A Chebyshev polynomial approximation is used to satisfy the fluctuation-dissipation theorem for the Brownian suspension. We explore how lubrication, long-range hydrodynamics, particle volume fraction and shape affect the equilibrium structure and the diffusion of the particles. It is found that once the particle volume fraction is greater than 10%, the particles start to form layered aggregates that greatly influence particle dynamics. Hydrodynamic interactions strongly influence the particle diffusion by inducing spatially dependent short-time diffusion coefficients, stronger wall effects on the particle diffusion towards the walls, and a sub-diffusive regime -caused by crowding-in the long-time particle mobility. The level of asymmetry of the cylindrical particles considered here is enough to induce an orientational order in the layered structure, decreasing the diffusion rate and facilitating a transition to the crowded mobility regime at low particle concentrations. Our results offer fundamental insights into the diffusion and distribution of globular and fibrillar proteins inside cells.

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Section: Mathematical Model and Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: spheres and cylinders

Li,

Jiang,

Singh

et al. 2020

Preprint

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“…Both types of omitted terms will be indicated by an ellipsis to shorten notation. The first goal now is to recover integrals over the full unit cell surface ∂Γ instead of only over ∂ Γ in equation (76). For this we exploit a + b = 0 and b + a = 0 for the single-or double-layer kernels.…”

Section: B1 the Boundary Integral Equation With Cut Objectsmentioning

confidence: 99%

A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles

Guckenberger

Gekle

2017

J. Fluid Mech.

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A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof contains as a subset the simpler boundary integral equation without volume-changing objects (such as red blood cell or capsule suspensions) which is widely used but for which a formal proof in periodic domains has not been published to date.In the second part, we apply our method to study microbubbles for targeted drug delivery. The ideal drug delivery agent should stay away from the biochemically active vessel walls during circulation. However, upon reaching its target it should attain a near-wall position for efficient drug uptake. Though seemingly contradictory, we show that lipid-coated microbubbles in conjunction with a localized ultrasound pulse possess precisely these two properties. This ultrasound-triggered margination is due to hydrodynamic interactions between the red blood cells and the oscillating lipid-coated microbubbles which alternate between a soft and a stiff state. We find that the effect is very robust, existing even if the duration in the stiff state is more than three times lower than the opposing time in the soft state.

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“…Recently, we have introduced an efficient computational approach in order to overcome some of the limitations of other available numerical approaches for hydrodynamic interactions. In particular, this approach can be easily extended to particles of arbitrary shape dispersed in a confined geometry also of arbitrary shape [24][25][26] . An Immersed-Boundary (IB) method is used to represent the suspended finite-sized particles.…”

Section: Introductionmentioning

confidence: 99%

“…An Immersed-Boundary (IB) method is used to represent the suspended finite-sized particles. A parallel Finite Element General geometry Ewald-like method (pFE-GgEm) 24 is used to calculate the confined Green's functions, which relies on a Chebyshev polynomial approximation to satisfy the fluctuation-dissipation theorem. In recent work 26 , we relied on this approach to compare the structure of pure spherical and pure cylindrical particles confined in a spherical cavity.…”

Section: Introductionmentioning

confidence: 99%

Shape induced segregation and anomalous particle transport under spherical confinement

Singh,

Li,

Jiang

et al. 2020

Preprint

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Colloid or nanoparticle mobility under confinement is of central importance to a wide range of physical and biological processes. Here, we introduce a minimal model of particles in a hydrodynamic continuum to examine how particle shape and concentration affect the transport of particles in spherical confinement. Specifically, an immersed boundary-General geometry Ewald-like approach is adopted to simulate the dynamics of spheres and cylinders under the influence of short-and long-range fluctuating hydrodynamic interactions with appropriate non-slip conditions at the confining walls. An efficient O(N) parallel finite element algorithm is used, thereby allowing simulations at high concentrations, while a Chebyshev polynomial approximation is implemented in order to satisfy the fluctuation-dissipation theorem. A concentration-dependent anomalous diffusion is observed for suspended particles. It is found that introducing cylinders in a background of spheres, i.e. particles with a simple degree of anisotropy, has a pronounced influence on the structure and dynamics of the particles. First, increasing the fraction of cylinders induces a particle segregation effect, where spheres are pushed towards the wall and cylinders remain near the center of the cavity. This segregation leads to a lower mobility for the spheres relative to that encountered in a system of pure spheres at the same volume fraction. Second, the diffusive-to-anomalous transition and the degree of anomaly -quantified by the power law exponent in the mean square displacement vs. time relation -both increase as the fraction of cylinders becomes larger. These findings are of relevance for studies of diffusion in the cytoplasm, where proteins exhibit a distribution of size and shapes that could lead to some of the effects identified in the simulations reported here.

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Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

Cited by 19 publications

References 82 publications

Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: spheres and cylinders

Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: spheres and cylinders

A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles

Shape induced segregation and anomalous particle transport under spherical confinement

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