The influence of the viscosity on the oscillations of the element of magnetic fluid in the magnetic field

The article describes a study of the viscoelastic parameters of the system based on a element of magnetic fluid bounded by the surface of a horizontal plexiglass tube located in the field of an electromagnet. A element of magnetic fluid makes damped oscillations. A mechanism is proposed for interpreting the experimental results to determine the dependence of the viscosity of a magnetic fluid on the magnetic field strength.


Introduction
Due to the ability to control the physical parameters, first of all, viscosity and fluidity, using an external magnetic field, magnetic fluids (MF) are widely used in various devices for vibration damping, control of friction characteristics, in shock absorbers and dampers. Of particular interest is the study of the dependence of the viscosity of the MF on the strength of an external magnetic field. In most studies, the research of the dependence of viscosity on the magnitude of the magnetic field was based on the Brookfield rotary rheometers, in which the shaft, disk or cone rotates in the liquid under study [1][2][3][4]. Various ferrofluids under shear flow were investigated in [5]. Experiments have shown that an increase in the magnetic field strength leads to an increase in the viscosity of the liquid, the so-called «magneto-viscous effect». However, in most of the MF-based damping devices, the active element, most often the cylinder, makes oscillatory movements, therefore, it is of particular interest to study the dependence of the viscosity of the MF on the external magnetic field strength in such systems. The block diagram of the experimental setup for measuring the oscillation frequency of the MF element ν is shown in Figure 1. We used a laboratory FL-1 electromagnet with a pole diameter of 100 mm. The design of the electromagnet FL-1 and technical data are described in [6]. A transparent tube 1 with an internal diameter d = 12 mm, made of plexiglass, is placed between the pole pieces. The axis of the tube passes horizontally through the center of the interpolar gap parallel to the surface of the pole pieces. When the magnetic field strength is ≥ 100 kA / m, the tube is filled with magnetic fluid 2, which is captured by the field and hangs in it. The piston 3 is used to excite vibrations. In the gap between the tube and the pole tip at the level of the free surface of the element MF installed vibration indicator -inductor 4. The inductor has 5000 turns, wound with a copper wire with a diameter of 0.071 mm, on the frame of Plexiglas. The signal from the oscillation indicator is fed to a Selective Nanovoltmeter type 237 5 amplifier. After amplification, the signal is transmitted to the GwInstek GOS-72074 6 oscilloscope, and then to a computer (not shown in the figure) for further processing.
Elastic vibrations of the magnetic fluid were excited by pulling out the rubber stopper from the free end of the tube. During the experiment, a tube with a hole was used to excite oscillations, which was opened during the process of screwing it into the tube, then the hole was sealed and the tube was pulled out of the tube, thus exciting the magnetic fluid. The oscillogram of the received oscillations was recorded using a digital oscilloscope.

The theory and experiment results
Expression (17) in [7] can be rewritten as: where µ 0 is the magnetic constant, M x and ∂H x /∂z are the magnetization and the gradient of the magnetic field strength at the location of the base of the MF element, respectively.
In the left part of (1), the first term represents the dynamic coefficient of elasticity, k dω , the second term is the correction for the motion of a viscous fluid |δ η |, and the right part is the coefficient of ponderomotive elasticity, k p , obtained in [8].
The coefficient of ponderomotive elasticity k p is due to the interaction of the MF with a non-uniform magnetic field [9][10]. In the works [11,12], an amendment to the coefficient of elasticity is obtained, associated with the flow of a viscous fluid: However, the formula obtained for δ η gives an estimate "from above" (the maximum value after the expiration of a quarter of a period). The coefficient of viscous elasticity k η represents the "average half-period" harmonic function of the maximum value, i.e. k η= 2δ η / π. Therefore: In addition, it was previously assumed that the viscosity of the MF does not depend on the magnetic field strength. Assuming this dependence, make the replacement of η by η Н . Then the expression (1) takes the form:  The results obtained are preliminary in nature and require the continuation of experimental and theoretical studies, primarily in the methodological aspect. First, the reduced and subtracted in brackets of the formula (6) is much larger than the resulting difference, which requires upgrading the installation to more accurately determine the parameters. Secondly, the calculations do not take into account the transient thin layer of the passage of a viscous wave. It is assumed that the entire MF element is involved in the oscillatory motion.
To refine the estimate of viscosity, we will need to expand the applicability of the relations obtained, for example, by increasing the magnetic field gradient, which allows us to obtain a higher frequency of oscillations of the MF element.
The work was carried out with the financial support of the basic part of the state task of the Ministry of Education and Science of the Russian Federation. Project code 3.8949.2017 / BP.