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

Title: A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

Abstract

Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.

Authors:
;  [1]
  1. Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton St. (MC 110), Chicago, Illinois 60607-4408 (United States)
Publication Date:
OSTI Identifier:
22598923
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids; Journal Volume: 28; Journal Issue: 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; BROWNIAN MOVEMENT; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DISPERSIONS; ITERATIVE METHODS; LENGTH; LIMITING VALUES; LIQUIDS; MAGNETIC FIELDS; MAGNETIC MATERIALS; MAGNETISM; MAXWELL EQUATIONS; MONTE CARLO METHOD; PARTICLE INTERACTIONS; PARTICULATES; SHEAR

Citation Formats

Dubina, Sean Hyun, E-mail: sdubin2@uic.edu, and Wedgewood, Lewis Edward, E-mail: wedge@uic.edu. A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations. United States: N. p., 2016. Web. doi:10.1063/1.4955014.
Dubina, Sean Hyun, E-mail: sdubin2@uic.edu, & Wedgewood, Lewis Edward, E-mail: wedge@uic.edu. A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations. United States. doi:10.1063/1.4955014.
Dubina, Sean Hyun, E-mail: sdubin2@uic.edu, and Wedgewood, Lewis Edward, E-mail: wedge@uic.edu. 2016. "A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations". United States. doi:10.1063/1.4955014.
@article{osti_22598923,
title = {A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations},
author = {Dubina, Sean Hyun, E-mail: sdubin2@uic.edu and Wedgewood, Lewis Edward, E-mail: wedge@uic.edu},
abstractNote = {Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.},
doi = {10.1063/1.4955014},
journal = {Physics of Fluids},
number = 7,
volume = 28,
place = {United States},
year = 2016,
month = 7
}
  • As computational fluid dynamics (CFD) continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics. One key to accomplishing this goal is recognition of the dual role assumed by the pressure, i.e., a mechanism for instantaneously enforcing conservation of mass and a force in the mechanical balance law for conservation of momentum. Proving this assertion has motivated the development of a new, primitive-variable, incompressible, CFD algorithm called the continuity constraint method (CCM). The theoretical basis for the CCM consistsmore » of a finite-element spatial semidiscretization of a Galerkin weak statement, equal-order interpolation for all state variables, a {theta}-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor weak statement formulation for dispersion error control. This paper presents: the formulation of the unsteady evolution of the divergence error; an investigation of the role of nonsmoothness in the discretized continuity-constraint function; the development of a uniformly H{sup 1} Galerkin weak statement for the Reynolds-averaged Navier-Stokes pressure Poisson equation; and a derivation of physically and numerically well-posed boundary conditions. In contrast to the general family of pressure-relaxation incompressible CFD algorithms, in the CCM, the mathematically smooth and physically motivated genuine pressure is an underlying replacement for the nonsmooth continuity-constraint function to control inherent dispersive-error mechanisms. The genuine pressure is calculated by the diagnostic pressure Poisson equation, evaluated using the verified solenoidal velocity field. This produces a clear view of the distinct boundary conditions required for the continuity-constraint function and genuine pressure.« less
  • We have carried out Brownian-dynamics simulations of a charged colloidal suspension under oscillatory shear flow with both Couette and Poiseuille velocity profiles. We show that in the steady-shear'' limit, for both of the velocity profiles, the enhancement of the self-diffusion coefficient in directions transverse to the flow shows a crossover from a [dot [gamma]][sup 2] dependence to a [dot [gamma]][sup 1/2] dependence as the shear rate [dot [gamma]] increases. The magnitude of the enhancement is a function of the interparticle interaction strength. There is a layering tendency in the direction of the velocity gradient for Couette flow, while such amore » tendency is not that prominent for Poiseuille flow.« less
  • The shear thinning behavior of a sterically stabilized nonaqueous colloidal suspension was investigated using nonequilibrium Brownian dynamics simulations of systems with 108 and 256 particles. At a volume fraction of 0.4, the suspension is thixotropic: it has a reversible shear thinning transition from a disordered state to an ordered, lamellar state with triangularly packed strings of particles. The time scale for the transition is set by the free particle diffusion constant. For the smaller system, the transition occurs gradually with increasing shear rate. For the larger system, the transition is sharp and discontinuous shear thinning is found. 34 refs., 9more » figs., 1 tab.« less
  • One application where microstructure plays a critical role is in the production of specialty ceramics, where colloidal suspensions act as precursors; here the microstructure influences the structural, thermal, optical and electrical properties of the ceramic products. Using Brownian dynamics, equilibrium and dynamic properties are calculated for colloidal suspensions that are stabilized through the Milner, Witten and Cates (1988) steric potential. Results are reported for osmotic pressures, radial distributions functions, static structure factors, and self-diffusion coefficients. The sterically-stabilized systems are also approximated by equivalent hard spheres, with good agreement for osmotic pressure and long-range structure. The suitability of the potential tomore » model the behavior of a real system is explored by comparing static structure factors calculated from Brownian dynamics simulations to those measured using SANS. Finally, the effects of Hamaker and hydrodynamic forces on calculated properties are investigated.« less