# Influence of High Viscosity and Magnetoviscous Effect on the Washout Resistance of Magnetic Fluid

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## Abstract

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## 1. Introduction

## 2. Materials and Method

#### 2.1. Materials

_{3}O

_{4}nanoparticles were synthesized by coprecipitation without protective gas in air. The particles coated with the surfactant were dispersed in different types of engine oil by stirring. Polyisobutylene succinimide (OLOA) and cido erucico were used as surfactants to steadily disperse nanoparticles. The three kinds of carrier fluids belong to total loss system oil, so their components and structures are similar, and they also possess similar densities and surface tension values. The quality of Fe

_{3}O

_{4}nanoparticles was controlled and the difference in saturation magnetization of magnetic fluids was no more than 20%. The size of the magnet was 15 mm × 10 mm × 5 mm and the direction of magnetization was along the shortest side. The type and material were, respectively, N35 and NdFeB.

#### 2.2. Viscosity Measurement

#### 2.3. Washout Test and Experimental Platform

#### 2.4. Theory and Calculation

#### 2.4.1. Ferrohydrodynamic Analysis of the Washout

_{max}and H

_{min}are the maximum and minimum magnetic field intensities on the horizontal line of half the height of the magnetic droplet; B

_{max}and B

_{min}are the maximum and minimum magnetic flux densities on the horizontal line of half the height of the magnetic droplet.

#### 2.4.2. Mechanism of Magnetic Fluid Washout

_{a}and U

_{b}are the fluid velocities; ${\rho}_{a}$ and ${\rho}_{b}$ are the densities; ${\mu}_{a}$ and ${\mu}_{b}$ are the relative permeabilities of fluid a and b; $\alpha $ is the interfacial surface tension; g is the gravity constant; and H

_{y}is the applied magnetic field intensity parallel to the unperturbed surface.

#### 2.4.3. Chain Model of Magnetoviscous Effect

_{n}represents the chain length distribution function, m

_{chain}is the magnetic moment of a particular chain interacting with the field, k is the Boltzmann constant, T is the absolute temperature, ${\mu}_{0}$ represents the permeability of vacuum. The first term in the bracket in Equation (4) is the free energy of the ideal gas and the second term accounts for the interaction with the field. Hence, the maximum length of a chain can be treated as a function of shear rate, and the maximum number of particles in a chain can be calculated in the following equation [19]:

_{0}represents the spontaneous magnetization of the magnetic fluid, $\stackrel{\cdot}{{\displaystyle \gamma}}$ is the shear rate, d is the mean diameter of magnetic particles and $\delta $ is the surfactant layer thickness.

## 3. Results and Discussion

#### 3.1. Magnetoviscous Property of Magnetic Fluids

_{max}increases with a decrease in shear rate $\stackrel{\cdot}{{\displaystyle \gamma}}$, which contributes to the rise of the viscosity at an applied field ${\eta}_{\mathrm{H}}$. Due to the high saturation magnetization and magnetization tendency shown in Figure 1 and the relationship between M

_{0}and n

_{max}, the M

_{0}increases obviously with the magnetic intensity before 40,000 A/m so that ${\eta}_{\mathrm{H}}$ has a rapid growth. It is concluded that the three samples of magnetic fluid have a strong magnetoviscous effect under a low shear rate.

#### 3.2. Washout Test of Magnetic Fluid

## 4. Conclusions

- (1)
- The high-viscosity magnetic fluids were prepared with three kinds of mineral oil and the magnetoviscous effect of the three samples was studied. The viscosity of the three samples decreased at most by about 100 times with the shear rate increasing.
- (2)
- We designed and built a washout experimental platform and observed and summarized three phases of magnetic fluid washout. The magnetic fluid of higher viscosity can resist the same water flow with as little as 0.148 times the magnetic force than that of lower viscosity. Magnetic fluid of higher viscosity requires lower magnetic force to remain stationary. We also studied the relationship between viscosity and residual volume after washout in a quantitative way. From this research, it can be concluded that the viscosity of the magnetic fluid has a significant influence on washout resistance.
- (3)
- The ability to modify viscosity of magnetic fluid and resist washout in diverse operating environments is a crucial ingredient in developing liquid seals based on ferrofluids.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Experimental platform for washout test. 1—Pump. 2—Flow meter. 3—Pump flow regulator. 4—Flow indicator. 5—Black and white camera. 6—Square tube. 7—Backlight. 8—Manual lift guide rail. 9—Computer. 10—Water tank. 11—Height adjustment knob.

**Figure 4.**The magnetic droplet state with different distances between the magnet and magnetic fluid.

**Figure 16.**Residual volume with different initial volumes (distance between magnetic fluid and magnet is 5 mm).

Sample No. | Density (g/mL) | Zero Magnetic Field Viscosity (mPa·s) (100/s) | Saturation Magnetization (KA/m) |
---|---|---|---|

1 | 1.4057 | 297.4 | 44.5 |

2 | 1.3569 | 377.9 | 38.7 |

3 | 1.4140 | 1456.9 | 37.0 |

4 | 0.8176 | 1.9 | - |

5 | 0.8343 | 14.5 | - |

6 | 0.8744 | 46.2 | - |

Sample No. | The Distance from Magnet to MF When Magnetic Fluid Started Being Washed Away (mm) | The Magnetic Force on Magnetic Fluid (Pa) |
---|---|---|

1 | 4.66 | 90.08 |

2 | 4.62 | 91.79 |

3 | 7.5 | 13.49 |

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**MDPI and ACS Style**

Li, Z.; Li, D.; Li, Y.; Han, S.
Influence of High Viscosity and Magnetoviscous Effect on the Washout Resistance of Magnetic Fluid. *Magnetochemistry* **2023**, *9*, 134.
https://doi.org/10.3390/magnetochemistry9050134

**AMA Style**

Li Z, Li D, Li Y, Han S.
Influence of High Viscosity and Magnetoviscous Effect on the Washout Resistance of Magnetic Fluid. *Magnetochemistry*. 2023; 9(5):134.
https://doi.org/10.3390/magnetochemistry9050134

**Chicago/Turabian Style**

Li, Zixian, Decai Li, Yanwen Li, and Shuntao Han.
2023. "Influence of High Viscosity and Magnetoviscous Effect on the Washout Resistance of Magnetic Fluid" *Magnetochemistry* 9, no. 5: 134.
https://doi.org/10.3390/magnetochemistry9050134