# 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:

- 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. Fri .
"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 = {Fri Jul 15 00:00:00 EDT 2016},

month = {Fri Jul 15 00:00:00 EDT 2016}

}