skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Large scale Brownian dynamics of confined suspensions of rigid particles

 [1]; ORCiD logo [2];  [1];  [3]
  1. McCormick School of Engineering, Northwestern University, Evanston, Illinois 60208, USA
  2. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA, Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, New York 10010, USA
  3. Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 24; Related Information: CHORUS Timestamp: 2018-02-14 10:18:23; Journal ID: ISSN 0021-9606
American Institute of Physics
Country of Publication:
United States

Citation Formats

Sprinkle, Brennan, Balboa Usabiaga, Florencio, Patankar, Neelesh A., and Donev, Aleksandar. Large scale Brownian dynamics of confined suspensions of rigid particles. United States: N. p., 2017. Web. doi:10.1063/1.5003833.
Sprinkle, Brennan, Balboa Usabiaga, Florencio, Patankar, Neelesh A., & Donev, Aleksandar. Large scale Brownian dynamics of confined suspensions of rigid particles. United States. doi:10.1063/1.5003833.
Sprinkle, Brennan, Balboa Usabiaga, Florencio, Patankar, Neelesh A., and Donev, Aleksandar. 2017. "Large scale Brownian dynamics of confined suspensions of rigid particles". United States. doi:10.1063/1.5003833.
title = {Large scale Brownian dynamics of confined suspensions of rigid particles},
author = {Sprinkle, Brennan and Balboa Usabiaga, Florencio and Patankar, Neelesh A. and Donev, Aleksandar},
abstractNote = {},
doi = {10.1063/1.5003833},
journal = {Journal of Chemical Physics},
number = 24,
volume = 147,
place = {United States},
year = 2017,
month =

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on December 22, 2018
Publisher's Accepted Manuscript

Save / Share:
  • Cited by 4
  • We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the othermore » based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.« less
  • We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest numbermore » of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blob-blob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the Rotne-Prager-Yamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single no-slip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently developed rigid-body immersed boundary method by B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev (Commun. Appl. Math. Comput. Sci. 11 (2016), no. 1, 79-141) to suspensions of freely moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid-body equations converges in a bounded number of iterations regardless of the system size. In our approach, each iteration only requires a few cycles of a geometric multigrid solver for the Poisson equation, and an application of the block-diagonal preconditioner, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.« less
  • This paper proposes an iterative method that can simulate mechanical systems featuring a large number of contacts and joints between rigid bodies. The numerical method behaves as a contractive mapping that converges to the solution of a cone complementarity problem by means of iterated fixed-point steps with separable projections onto convex manifolds. Since computational speed and robustness are important issues when dealing with a large number of frictional contacts, we have performed special algorithmic optimizations in order to translate the numerical scheme into a matrix-free algorithm with O(n) space complexity and easy implementation. A modified version, that can run onmore » parallel computers is discussed. A multithreaded version of the method has been used to simulate systems with more than a million contacts with friction.« less
  • There is considerable interest in Brownian motion in a nondilute suspension, in which the Brownian particles can influence the motion of one another both as a consequence of direct long-range interactions and indirectly by means of the disturbance of the medium caused by the motion of each Brownian particle. The authors examined the second effect; therefore, they investigated the case in which there is no long-range Brownian-particle-Brownian-particle interaction. The direct encounters of the Brownian particles with one another were also disregarded, since their consideration is impossible without consideration of the influence of the long-range forces.