Sedimentation of magnetorheological fluids measured using an automated vertical axis inductance monitoring system

Magnetorheological fluids (MRFs) consist of magnetic particles randomly dispersed in a non-magnetic carrier fluid. When the external magnetic field is applied, the magnetic particles are coupled along the direction of the external magnetic field, and MRFs change to semi-solids rapidly and reversibly. Semi-active devices based on the principle of MRF have been applied and developed, such as aircraft landing gear systems,^1–3 wearable exoskeleton,⁴ soft crawling robots,⁵ earthquake mitigation systems,⁶ and semi-active vehicle dampers.^7,8 However, the settlement problem is the main reason limiting the application of magnetorheological devices that needs long-term standing.⁹ If effective measures are not taken to prevent sedimentation, magnetic particles will gather at the bottom of the device. When the impact load comes, it will affect the energy absorption of magnetorheological devices, resulting in failure to achieve the expected effect and safety in accidents.

The sedimentation of MRFs is driven by gravity due to the large density difference between the dispersed phase and the continuous phase.¹⁰ However, because MRFs are opaque, only the change of the supernatant zone can be visually observed.¹¹ In fact, there will be a supernatant zone, original concentration zone, variable concentration zone, and sediment zone in the sedimentation process of MRFs. In the initial stage of sedimentation, there will be an observable boundary between the supernatant zone and the original concentration zone, which is called the mud-line.¹² The boundary between the original concentration zone and the variable concentration zone is called the gel-line. The boundary between the variable concentration zone and the sedimentation zone is called the cake-line.¹³ After a period of time, the mud-line coincides with the gel-line, and the original concentration zone disappears. Finally, the mud-line coincides with the cake line, leaving only the supernatant zone and the sedimentation zone, in which the upper limit of particle concentration is manifested. It is necessary to characterize the time evolution of these four zones in order to better understand the physics of hindered settling. In addition, it is of interest to know how the position of the boundaries evolves with time. Therefore, the primary objective of this study is to develop an optimized inductance sensor and a sedimentation zone boundary identification procedure to locate these boundaries.

For the study of MRFs, there is no unified standard to evaluate their stability. In prior studies,^14–16 the visual observation method was adopted and sedimentation measurements were performed under the influence of gravity. To evaluate the sedimentation rate of MRFs more accurately, the effects of magnetic particle concentration on the physical properties of MRFs (i.e., capacitance, thermal conductivity, inductance, etc.) were studied. Fan et al.¹⁷ proposed a method to evaluate the suspension stability of MRFS by establishing the correlation model between dispersed particle concentration and capacitance strength. Zhang et al.¹⁸ designed an in situ sensing method (i.e, Bayesian network) for MRF sedimentation detection by using the relationship between dispersed particle concentration and capacitance, which can effectively reflect the state of MRF sedimentation. Qiu et al.¹⁹ and Cheng et al.²⁰ experimentally observed that the thermal conductivity of MRFs was linearly related to the volume fraction of dispersed particles, and the sedimentation rate of dispersed particles was determined by monitoring particle volume fraction as a function of time. However, the control units of these two kinds of measuring systems need to be improved. Chen and Chen²¹ made a highly sensitive but immovable inductance sensor using permalloy and measured a highly linear relationship between the inductance and column height. Based on this technique, Ngatu and Wereley¹² developed an inductive sensor to track the descent rate of mud-line. Iglesias et al.²² realized the coil translation using a stepper motor and monitored the change of the local volume fraction of magnetic particles through the change of inductance. The University of Maryland^13,23 developed the automated vertical axis inductance monitoring system (AVAIMS), which can effectively detect the change of MRFs concentration and fully automates the process of characterizing sedimentation in an MRF column. Wen et al.²⁴ developed an improved low aspect ratio inductive sensor (LARS) and proposed a recognition algorithm for the sedimentation zone boundaries in order to improve their detection accuracy.

In this study, the design and identification method of the AVAIMS previously developed at the University of Maryland was improved. The structure of the inductance sensor was newly designed, and the shell and coil frame structure of the inductance sensor was optimized by a finite element method (FEM) to improve the sensitivity of the inductive sensor to the change of MRF particle concentration in this study. This optimized inductance sensor was used to improve the identification accuracy of the sedimentation zone boundaries in a vertical column of MRF.

The measurement system (Fig. 1) was comprised of an inductance sensor and an LCR meter connected in a closed-loop circuit. The electromagnetic coil was the key component of the inductance sensor. More detailed information about the measurement system can be found in our previous papers.^13,23

The inductance sensor consisted of a coil, a shell, and a coil bobbin. The MRF column surrounded by the coil is the magnetic core of the coil. The magnetic particles dispersed in the carrier liquid will settle by gravity, so the particle concentration changes, resulting in the change of the coil inductance. The inductance, L of the coil can be calculated by Eq. (1).

where N is the turn number of the coil, S is the cross-sectional area of the coil, l is the length of the coil, μ₀ is the vacuum permeability, and k_l is the correction factor introduced considering that the coil length is much smaller than its diameter. The MRF relative permeability, μ_r, can be determined graphically from the B − H curve of a given MRF for different magnetic fields. The empirical magnetic relationship of an MRF can be given by:^25,26

where ϕ is the iron particle volume percentage in the MRF and H_MR is the applied magnetic field. Then, the relative permeability μ_r can be defined as:

Here, B is in Tesla, H_MR is in a unit of A/m, and

From Eqs. (1) and (3), the magnetic particle concentration, ϕ can be determined by the coil inductance, L.

A FEM software (i.e., COMSOL) was used to simulate the two-dimensional axisymmetric electromagnetic field of the inductance sensor. The quarter equivalent model of the inductance sensor is shown in Fig. 2. The MRF column is equivalent to a cylinder with uniform permeability distribution, the air field was equivalent to a sphere, and the inductance sensor was equivalent to a two-dimensional axisymmetric structure. The diameter of the measured liquid column, R = 25 mm, and the height, h = 100 mm. The thicknesses of the coil bobbin (d₁) and the shell (d₂) were 5 mm and 6 mm, respectively, and the diameter of the wire is 0.2 mm. The coil was wound with 4 layers of wire, each with 10 turns, and the current (i.e., 9 mA) was applied to the coil.

The inductance was obtained by parametric scanning of the uniform concentration MRF column with a Fe solids loading of 20 vol. %. Figure 3 shows the inductance at different heights of the MRF column. The sensitivity, P of the sensor can be measured by the change rate of the inductance between A(x_a, y_a) and B(x_b, y_b), which was calculated as follows:

The material properties of the coil frame and shell determine whether the sensor can accurately perceive the permeability change of the MRF column. After trying a variety of material combinations, representative resin, AISI1045 steel, and permalloy were selected as the coil bobbin materials, and AISI1045 steel and permalloy were selected as the shell materials. It can be seen from Fig. 4 that the sensitivity could be increased by up to 3 times when the shell was changed from steel to permalloy, while the change of sensitivity was not apparent when the coil bobbin was made of the resin (i.e., 0.721), AISI1045 (i.e., 0.7845) or permalloy (i.e., 0.789). Using metal as a coil bobbin increased the sensitivity by only 9%. In this study, the resin was used to make the coil bobbin because of its easy workability, and permalloy was used to make the shell because it can shield the external magnetic field well and reduce the sensor boundary effect. With the number of coil turns, the sum (d₁ + d₂) of the coil bobbin thickness (d₁) and shell thickness (d₂) remained unchanged, the FEM simulation results were shown in Fig. 5, which indicated that with the decrease of coil bobbin thickness (i.e. increasing the shell thickness), the coil inductance value increased approximately linearly, and its sensitivity was also improved.

MRF samples were prepared by suspending carbonyl Fe powders (particle size: 1–3 μm and density 7.86 g cm⁻³) into a silicone oil (viscosity: 100 cSt and density: 0.965 g cm⁻³). MRF samples had an initial particle concentration of 5 vol. %, 10 vol. %, 15 vol. %, 20 vol. %, 30 vol. % and 40 vol. %, without additives. Each sample was stirred with an electric stirrer for 2 h at high speed to ensure uniform particle dispersion and minimum particle agglomeration. Each MRF sample was tested with a fluid column height of 160 mm, and the inductance value in the middle section of the fluid column (i.e., 40 mm–60 mm) was used. The inductance sensor scanned vertically along the tube from top to bottom. Before each scan, the sensor position was reset by moving to the bottom of the motion system stroke to contact the limit switch, ensuring that each test starts in the same position. The calibration curve of the sensor was obtained by measuring samples with different particle volume fractions as shown in Fig. 6. It shows that particle concentration and inductance are highly linearly dependent. The calibration curve for this sensor is:

where the measured inductance, L is in a unit of μH and the particle concentration, ϕ is in a unit of vol. %. It should be noted that the calibration curve should be measured for the particular inductance sensor configuration and MRF composition used.

The sensor design was validated by examining a uniformly mixed MRF column with an initial particle concentration of 20 vol. % for seven consecutive days. Figure 7 shows a concentration profile that was measured at 0 h, 24 h, 48 h, and 72 h. It shows from Fig. 7(b) that the particles of the MRF settled at a constant rate, and they began to deposit at the bottom MRF column. It can be observed from Fig. 7(c) that the original concentration zone completely disappeared with the continuous sedimentation of the particles and that the particle concentration of the bottom MRF column reached a peak and the sediment zone appeared. Figure 7(d) shows only the remaining supernatant zone and the sediment zone. In addition, the coil sensitivity calculated using the test data in Fig. 7(a) is 0.713, which was close to the sensitivity (i.e., 0.721) calculated using the FEM data in Fig. 4.

Figure 8 shows a concentration gradient profile using data measured after 16 h. There are distinguishing features that can be used to determine sedimentation zone boundaries. The mud-line and the fluid bottom can be determined by identifying the locations of the maximum gradient and minimum gradient. Another two peak points fall between the mud-line and bottom which define the gel-line and the cake-line. These results show that the AVAIMS can detect subtle changes in the concentration of MRF and localize sedimentation zone boundaries using the concentration gradient profile method.

This study focused on ensuring the sensitivity and design effectiveness of the inductance sensor in the AVAIM system, which ensures the accurate identification of the sedimentation zone boundaries of an MRF column. This study analyzed the sensitivity of the inductance sensor by material selection and geometry. Then, the performance of the sensor was tested and sedimentation zone boundaries were identified based on the particle concentration gradient.

The results showed that the key factor affecting the sensor was the shell, which should be made of high magnetic conductivity metal materials (that was permalloy in this study). The high permeability material could shield the external magnetic field from interfering with the coil magnetic field in the sensor. As a result, the sensitivity of the inductance sensor was greatly improved. When both the coil bobbin and the shell were made of the high magnetic conductivity material, the inductance curve was smoother because of the weaker distortion of the magnetic field. In addition, the sensor sensitivity could be improved apparently with the smaller thickness of the coil bobbin or the larger thickness of the shell. As a future work, the analytical design optimization to minimize or maximize a desired objective function will be conducted.

The authors have no conflicts to disclose.

Ran Ma: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (lead); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Norman M. Wereley: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.