## Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing

## Abstract

It has recently been reported that two types of triaxial electric or magnetic fields can drive vorticity in dielectric or magnetic particle suspensions, respectively. The first type-symmetry -- breaking rational fields -- consists of three mutually orthogonal fields, two alternating and one dc, and the second type -- rational triads -- consists of three mutually orthogonal alternating fields. In each case it can be shown through experiment and theory that the fluid vorticity vector is parallel to one of the three field components. For any given set of field frequencies this axis is invariant, but the sign and magnitude of the vorticity (at constant field strength) can be controlled by the phase angles of the alternating components and, at least for some symmetry-breaking rational fields, the direction of the dc field. In short, the locus of possible vorticity vectors is a 1-d set that is symmetric about zero and is along a field direction. In this paper we show that continuous, 3-d control of the vorticity vector is possible by progressively transitioning the field symmetry by applying a dc bias along one of the principal axes. Such biased rational triads are a combination of symmetry-breaking rational fields and rational triads.more »

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1237676

- Report Number(s):
- SAND-2015-6201J

Journal ID: ISSN 1744-683X; SMOABF; 598633

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Soft Matter

- Additional Journal Information:
- Journal Volume: 12; Journal Issue: 4; Journal ID: ISSN 1744-683X

- Publisher:
- Royal Society of Chemistry

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE

### Citation Formats

```
Martin, James E., and Solis, Kyle Jameson. Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing. United States: N. p., 2015.
Web. doi:10.1039/C5SM01975C.
```

```
Martin, James E., & Solis, Kyle Jameson. Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing. United States. doi:10.1039/C5SM01975C.
```

```
Martin, James E., and Solis, Kyle Jameson. Mon .
"Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing". United States. doi:10.1039/C5SM01975C. https://www.osti.gov/servlets/purl/1237676.
```

```
@article{osti_1237676,
```

title = {Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing},

author = {Martin, James E. and Solis, Kyle Jameson},

abstractNote = {It has recently been reported that two types of triaxial electric or magnetic fields can drive vorticity in dielectric or magnetic particle suspensions, respectively. The first type-symmetry -- breaking rational fields -- consists of three mutually orthogonal fields, two alternating and one dc, and the second type -- rational triads -- consists of three mutually orthogonal alternating fields. In each case it can be shown through experiment and theory that the fluid vorticity vector is parallel to one of the three field components. For any given set of field frequencies this axis is invariant, but the sign and magnitude of the vorticity (at constant field strength) can be controlled by the phase angles of the alternating components and, at least for some symmetry-breaking rational fields, the direction of the dc field. In short, the locus of possible vorticity vectors is a 1-d set that is symmetric about zero and is along a field direction. In this paper we show that continuous, 3-d control of the vorticity vector is possible by progressively transitioning the field symmetry by applying a dc bias along one of the principal axes. Such biased rational triads are a combination of symmetry-breaking rational fields and rational triads. A surprising aspect of these transitions is that the locus of possible vorticity vectors for any given field bias is extremely complex, encompassing all three spatial dimensions. As a result, the evolution of a vorticity vector as the dc bias is increased is complex, with large components occurring along unexpected directions. More remarkable are the elaborate vorticity vector orbits that occur when one or more of the field frequencies are detuned. As a result, these orbits provide the basis for highly effective mixing strategies wherein the vorticity axis periodically explores a range of orientations and magnitudes.},

doi = {10.1039/C5SM01975C},

journal = {Soft Matter},

number = 4,

volume = 12,

place = {United States},

year = {2015},

month = {11}

}

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