Theory analyses and applications of magnetic fluids in sealing

Magnetic fluids are the suspensions composed of magnetic nanoparticles, surfactants, and non-magnetic carrier liquids. Magnetic fluids are widely used in various fields, especially in sealing, because of their excellent features, including rapid magnetic response, flexible flow ability, tunable magneto-viscous effect, and reliable self-repairing capability. Here, we provide an in-depth, comprehensive insight into the theoretical analyses and diverse applications of magnetic fluids in sealing from three categories: static sealing, rotary sealing, and reciprocating sealing. We summarize the magnetic fluid sealing mechanisms and the development of magnetic fluid seals from 1960s to the present, particularly focusing on the recent progress of magnetic fluid seals. Although magnetic fluid sealing technology has been commercialized and industrialized, many difficulties still exist in its applications. At the end of the review, the present challenges and future prospects in the progress of magnetic fluid seals are also outlined.


Introduction
Magnetic fluids are a new type of functional materials consisting of non-magnetic base liquids and magnetic nanoparticles coated with surfactant layers. The diameters of magnetic nanoparticles range from 5 to 15 nm [1], and the magnetic fluid composition is shown in Fig. 1. Surfactants covering the particles prevent particle-to-particle agglomeration, and Brownian motion prevents particle sedimentation in gravitational or magnetic fields [2]. Unlike magnetorheological fluids which solidify in intense high-gradient magnetic fields, coating surfactants, such as oleic acid, allow magnetic fluids to maintain fluidity in the same condition [3]. Magnetic fluids possess outstanding characteristics of both the magnetic properties of solids and also the fluid properties of liquids [4]. As magnetic fluids exhibit great characteristics, they can be applied in many fields, such as micro/ nanoelectromechanical sensors [5], dampers [6], seals [7,8], micro/nanofluidic devices [9], targeted drugdelivery [10], hyperthermia [11], magnetic resonance imaging [12], lubricants [13], etc. After exploring more than twenty years, our team has prepared several magnetic fluids, as shown in Table 1 [14]. Practical applications of these magnetic fluids for years have proved that these magnetic fluids have superior performance. The study and applications of them have gone through three periods. The first period of magnetic fluids is mainly used in the military industry. In the early 1960s, scientists of the National Aeronautics and Space Administration (NASA), USA, investigated liquid manipulation in order to solve the sealing problem of movable joints in space suits. In 1963, for the first time, Papell [15] devised a stable magnetic fluid in the NASA laboratory, and then obtained the world's first practical patent for the production of magnetic fluids two years later. The second period started in the late 1960s. The preparation technology of magnetic fluids made breakthrough development, and magnetic fluids began to apply in many fields at the same time. With the rapid development of nanotechnology, many countries, such as USA, the former Soviet Union, Japan, and UK, successively carried out research on magnetic fluids. Khalafalla and Reimers [16,17] developed chemical precipitation syntheses suited for rapid production in the mid-1970s. Based on rapid production, research on magnetic fluid applications in the fields of sensors [18][19][20], dampers [21,23], and lubricants [24][25][26] all began in this period. The third period is from the 1990s to the present, and magnetic fluids have entered multidisciplinary development, involving chemistry [27], fluid mechanics [28], magnetism [29], optics [30], etc. With modern advances in understanding nanoscience and nanotechnology, current research has focused on synthesis, characterization, and functionalization. Meanwhile, magnetic fluids have been promoted and applied in many fields. At present, magnetic fluids have become a hot research interest. In turn, research on magnetic fluids will prospectively improve the development of nanoscience [31], vacuum technology [32], colloidal chemistry [33], physical chemistry [34], surfactants [35], and other related disciplines.
Odenbach [36] focused on rheological investigations of magnetic fluids and briefly mentioned magnetic fluid seal (MFS) based on magnetic response to magnetic field of magnetic fluids. Torres-Díaz and Rinaldi [37] summarized recent advances in established and emerging applications of magnetic fluids, involving sensors, seals, optics, actuators, lubrication, and static/dynamic magnetically driven assembly of structures, with emphasis on contributions since 2005. Li and Hao [38] reviewed the latest progress in major Table 1 Types and physical parameters of magnetic fluids [14]. 2 Magnetic fluid preparation and sealing mechanism

Magnetic fluid preparation
According to different kinds of magnetic particles, magnetic fluids can be divided into ferrite magnetic fluids, metallic magnetic fluids, and nitride iron magnetic fluids. Tables 2 and 3 introduce the characteristics and main preparation methods of the three kinds of magnetic fluids, respectively.

Magnetic fluid sealing mechanism
The internal structure of the magnetic fluid changes with the variation of the external magnetic field, which leads to the transformation in the physical and   [47] 1999 Nitride iron magnetic fluids High saturation magnetization and good dispersion of prepared magnetic fluids Complex equipment, strict preparation conditions, long preparation time, and high cost chemical characteristics of the magnetic fluid, such as rheology [48,49], thermal effect [50], and optical property [51]. Theoretical research on magnetic fluids, involving magnetization [52], magnetoviscosity [53], stability [54], etc., has promoted the development of magnetic fluid applications. It is obvious that the utilization of magnetic fluids for sealing is one of the earliest and most successful applications, and has already achieved industrialization and commercialization. Magnetic fluid seals (MFSs) are different from mechanical seals, which are contactless. Their sealing ability does not depend on the mutual compression between the sealing surfaces, so the friction is comparatively much lower than that of mechanical contact seals [55]. When there is relative movement between the sealing surfaces, MFSs can avoid the wear problem of traditional dynamic seals, such as abrasive particles, which are produced by wear [56]. Compared with other sealing methods such as labyrinth seal [57], mechanical seal [58], and brush seal [59], MFS has the advantages of no leakage, high reliability, good durability, and simple structure.
Based on magnetization characteristic, magnetic fluids can be moved with the help of a magnetic field, so they can be positioned at the desired point very precisely [60]. The schematic of the main structure of the general magnetic fluid sealing is shown in Fig. 2. Magnetic fluids form discrete liquid rings when injected into the gaps between sealing surfaces, and can be held at the sealing stage by applying an external magnetic field, so that they can sustain a pressure difference without any leakage [40]. The shape change of the magnetic fluid film during the pressure process is shown in Fig. 3 [61]. When the pressure difference between the two sides is zero, that is 1 2 P P  , the boundary of the fluid film coincides with the contour of the magnetic induction intensity, and the boundary is symmetrically distributed. If 1 2 P P  , the magnetic fluid will be pulled to the side with low pressure until reaching a new pressure equilibrium.

Magnetic fluid motion equation
In 1964, Neuringer and Rosensweig [62] assumed that the relaxation time of magnetization of magnetic fluids is much shorter than that of hydrodynamics of magnetic fluids. The magnetization of magnetic fluids can be thought to be determined by only a few thermodynamic parameters and magnetic field strength.
The value of these thermodynamic parameters varies with time and space changes. Under the framework of this method, magnetic fluids are regarded as a single component and single phase continuous medium, and the basic dynamics equation of magnetic fluids is obtained.
According to the general hydrodynamic continuity equation, the mass conservation equation of magnetic fluids is as Eq. (1): where f  is the density of magnetic fluids, V is the flow velocity of magnetic fluids, and t is the time.
The body force term of the motion equation of a homogeneous magnetic fluid is different from that of an ordinary fluid. Generally, the body force of an ordinary fluid is gravity. In addition to gravity, the magnetic fluid is also subjected to magnetic force generated by an external magnetic field. The magnetic www.Springer.com/journal/40544 | Friction solid particles in magnetic fluids are usually regarded as macromolecules. Therefore, when discussing their magnetization from the viewpoint of molecular circulation, each solid phase particle can be replaced by a molecular current loop. The current loop receives force in the external magnetic field, which constitutes the magnetic body force in the magnetic fluid.
Cowley and Rosensweig [63] proposed the energy method. Their basic idea is to link the thermodynamic work with the mechanical work produced by the surface force to obtain the body force of the magnetic fluids, of which the results are comprehensive and universal. On the basis of the Langevin function [64] of the magnetization law of paramagnetic gas, the magnetization of magnetic fluids can be expressed as where M is the magnetization of magnetic fluids, m is the moment of particle,  is the Langevin parameter, s M is the saturation magnetization of magnetic fluids, ( ) L  is the Langevin function, 0 k is the Boltzman constant, 0 u is the permeability of vacuum, H is the magnetic field strength, and T is the temperature.
From Eqs. (2) and (3), it can be seen that the magnetization of magnetic fluids is a function of magnetic field strength and temperature.
Irrespective of the internal degrees of freedom, the motion equation of the incompressible magnetic fluids is where g is the acceleration of gravity, H  is the viscosity of magnetic fluids, and * p is the pressure. There are three assumptions as below: 1) The density of the magnetic fluid is a constant, f   const.
2) The flow of the magnetic fluid is potential flow, 0 V    .
3) The magnetization vector of the magnetic fluid is parallel to the external magnetic field, 0 Based on the hypotheses, the general form of Bernoulli equation of magnetic fluids is obtained: where v  is the velocity potential, and h is the distance between the magnetic fluid and the reference point.

Magnetic field calculation
Maxwell's equation is the theoretical basis for studying electromagnetic field [65]. The commonly used numerical methods for solving the problems of the electromagnetic field are the finite element method [66] and finite difference method [67]. Both of the two methods are based on meshing, but the meshing of the finite element method is more flexible and better adapt to the electromagnetic field with different distributions and tortuous shapes of the boundary. Therefore, more electromagnetic field problems are solved by the finite element method instead of finite difference method. When calculating the magnetic field in magnetic fluid sealing devices, the following five assumptions are usually made.
1) The magnetic fluid is in a state of saturation magnetization, and its permeability is approximately equal to the permeability of vacuum.
2) The hysteresis of soft magnetic materials is ignored, and soft magnetic materials are considered to be isotropic.
3) The permanent magnet is uniformly magnetized, and its uniformity is not affected by the external magnetic field.
4) The pole piece material and shaft material are both replaced by DT1 electrical pure iron. 5) All errors during processing and assembly are ignored.
On the basis of the above hypotheses, the way of calculating the magnetic field in magnetic fluid sealing devices can be obtained, as shown in Fig. 4.

Magnetic fluid sealing theory and application
The development of sealing technology is closely related to our modern society, such as industrial progress and transportation. Developing sealing technology takes both function and economy into consideration. Compared to other sealing methods, MFS offers an environmentally friendly and costeffective solution, which is used successfully in solving many sealing problems, such as small and medium diameter shafts vacuum [68] or gas [69] sealing problems at low or medium speeds. Table 4 is an overview of the characteristics of the six most widely used sealing methods.

Magnetic fluid static sealing
According to the shaft rotation speed, MFSs can be divided into static seal, low-speed seal, and high-speed seal. There is no relative movement between the sealed parts in the static seal. The research on the pressure resistance capacities of the static MFS is the basis for the study of the pressure resistance capacities of the rotary MFS and the reciprocating MFS. Only with an in-depth understanding of the pressure resistance capacity of the static MFSs can we discuss the influence of centrifugal force and temperature in the rotary MFSs, as well as various motion parameters in the reciprocating MFSs on the pressure resistance capacity of these MFSs. On the basis of the introduction in Ref. [88], only when the rotation speed exceeds 20 m/s, the influence of centrifugal force on the pressure resistance capacity of the MFS becomes apparent; yet, at the general rotation speed, the dynamic pressure resistance capacity of the MFS is approximately equal to the pressure resistance capacity of the static MFS. Roth [89] proposed a safe and simple operation for occluding intracranial aneurysms in patients. The operative technique employed two miniature permanent magnet probes that were placed against the outside of the aneurysmal neck, as shown in Fig. 5. Ferrofluid was injected into the carotid artery and flowed into the cerebral circulation towards the aneurysmal opening. Microspheres in liquid suspension were attracted from the circulation to the magnet probes, which accumulated in the orifice and formed an obstacle to the flow of blood into the aneurysm. Clinical experience of the patient confirmed the feasibility of a ferrofluid seal for treatment of thrombosis of intracranial berry aneurysms.
Ferrofluid plugs, which facilitated blood flow stasis in arteries during surgery, have been proposed as an alternative to present methods that caused arterial wall damage. Perry and Jones [90] investigated theoretically and experimentally for hydrostatic loading of ferrofluid using liquid and air pressure. Figure 6 depicts the employed experimental apparatus. The apparatus consisted of a vertical long glass tube open at both ends. The glass tube produced an area of intense magnetic field, which was mounted between two electromagnet poles. Ferrofluid was injected into the gap space, and another liquid, which was immiscible with the ferrofluid, was injected from the top of the glass tube. They found that the modified Bernoulli equation to account for ferrofluid-magnetic field coupling adequately predicted the sealing capacity of the hydrostatic plug when the ferrofluid surfaces were in stable equilibrium. So ferrofluids could be successfully used as an axial hydrostatic pressure seal against several immiscible liquids.
Polevikov [91] solved capillary hydrostatic problem numerically. The problem with an essentially nonconnected free surface concerned the axisymmetric equilibrium shapes of the static MFS under the action  of an external pressure drop. He investigated the effect of the magnetic flux shape concentrator on the critical pressure drop in the class of hyperbolic profiles, and found the dependence of the critical pressure drop on the magnetic field strength, the fluid magnetization, the gap width, as well as the magnetic fluid slug volume. Li et al. [92] discussed the design principle of ferric nitride MFS device and its working process, based on the absorption principle of magnetic fluids by magnetic field. They analyzed the pressure-bearing capacity of the designed static MFS theoretically and verified it experimentally by conducting a series of sealing tests. A safety valve was successfully constructed by MFS using the ferric nitride magnetic fluid and passed a series of tests involving the opening pressure stability test, controllability test, and sealing performance test. The test results showed that it could operate smoothly for a duration above 10,000 h. Two years later, Li et al. [93] prepared magnetic fluids in a gas-liquid reactor by plasma activation and ionization at atmospheric pressure. They explored a sealing device with iron-nitride magnetic fluid, through controlling of discharge parameters. The sealing hours of the safety valve met the customers' requirements | https://mc03.manuscriptcentral.com/friction on sample machine, which was about 10,000 h. In some special fields such as chemical industry and pharmaceutical industry, requirements of largediameter flange sealing [94][95][96] are strict. He et al. [97] successfully developed a novel technique for static sealing the flanges, of which diameters were larger than 600 mm by using magnetic fluids for the first time. They measured various factors including the pressure resistance capacity and the leak rate in static sealing of the large flange. Its pressure resistance capacity followed exactly the rules of the small flanges, and its leak rate was zero. Li et al. [98] complemented the study of static MFS for large flanges. They reasoned the differential pressure formula to calculate the burst pressure of the MFS in large diameter flanges and put forward a way to prolong the life of the MFS. The fact is that the static MFS was successfully used for almost four years, which demonstrated that the presented MFS was reliable. Li and Yang [99] designed the static MFS structures, whose diameter was larger than 390 mm, and the sealing gaps were 1.1, 1.5, 2, and 2.5 mm, as shown in Fig. 7. They obtained the pressure resistance capacities of the proposed structure under different sealing gaps by experiments. The experimental results illustrated that the maximum pressure resistance capacities of these sealing structures were 20%, 13%, 8%, and 4% of that of the traditional structure. Besides, the pressure resistance capacities of the sealing structures were not sensitive to the change of temperature in the range of 20-120 °C.
Polevikov and Tobiska [100] deduced a mathematical model for studying the MFS stability under the action of an external pressure drop in the static condition. Besides, they computed the shape of the free surface under the influence of magnetic particles diffusion by a numerical algorithm. When particle concentration achieved its maximum for larger fluid volume due to the dense packing of particles, numerical experiments for different sets of parameters demonstrated that the influence of the particles diffusion on the burst pressure could not be neglected. In the past, scholars researched the MFSs of small gap. Li et al. [101] designed the static MFS and set up the experimental rig to meet the requirements of the large gap MFS in aerospace, aviation, metallurgy, etc. The relationships among the burst pressure and the injected volume of magnetic fluids, seal gap, magnetization, and temperature were obtained. The theoretical analyses and tests indicated that MFS with large diameter and large gap sustained a definite pressure, which met the requirements of practical problems. In 2012, He et al. [102] calculated the distribution of the magnetic field in the seal gap and the pressure resistance capacity theoretically for the same equipment mentioned above. The previous literatures mostly focused on numerical analyses of MFSs with few pole pieces and the value of critical pressure in one-stage MFS, lacking of numerical simulation and experimental validation about the static pressure of multi-stage MFSs. Zhang et al. [61] analyzed larger number of sealing stages by numerical simulation and experimental investigation. They found that the seal capacity was improved significantly by increasing the number of the pole teeth, but the sealing pressure did not increase linearly with the growing number of pole teeth.

Magnetic fluid rotary sealing
Magnetic fluid sealing technology has been studied for more than half a century, and has been successfully industrialized and commercialized. Most of the research and applications are related to rotary MFSs. At present, the rotary MFSs are relatively mature for sealing vacuum and gas. The main difficulties lie in sealing liquid [103], large diameter sealing [104], large gap sealing [105], and high-speed sealing [106]. In Section 3.2, the main literatures on theoretical, simulation, and experimental research of rotary MFSs in the past forty years are introduced in chronological order.  [114] adopted iterative computation in numerical algorithm to obtain the boundary surface configurations of MFSs. Bonvouloir [115] found that the ratio of magnetic force to centrifugal force, a dimensionless number, was not a good predictor of high-speed seal failure. Instead of this dimensionless number, Reynolds number was proved to be a better predictor of seal failure. Therefore, he proposed an empirically derived model based on Reynolds number to predict seal failure. Kim et al. [116] studied the basic characteristics of MFSs applied to the lubricant retainer. The lubricant oil seal set showed a good pressure resistance of 618 kPa under a rotational speed of 1,800 r/min, which consisted of Nd-permanent magnets (4 Wb/m 2 ) and six stages of pole piece in seal housing. Li [41] explored the feasibility of rotary MFSs used in thin film dense wavelength division multiplexing filter manufacturing. He considered large diameter, high-speed, motion control, and tight tolerance for rotating accuracy, which were the technical challenges in this application, and proved that MFSs could provide satisfactory performance in this new promising application. Sekine et al. [117] developed an MFS used in an axial-flow blood pump to solve underlying problems such as complexity of a supporting system and abrasive wear. Sealing pressures were measured at motor speed up to 8,000 r/min, when the seal was immersed into water or bovine blood. And the measuring result was about 200 mmHg. Liu et al. [107] established a new MFS, of which the structural parameters were optimized by a simulation apparatus. Figure 8 shows a new type of MFS, which decreased the velocity difference and the magnetic flux leakage at the interface. One of the major alterations accompanying this novel MFS was the introduction of a soft iron bushing with high permeability on the shaft. Besides, the magnetic circuit was comprised of the magnet, pole pieces, the magnetic fluid, and the soft iron bushing. Since the permeability of the soft iron bushing was similar to that of the pole piece, and the soft iron bushing was aligned with the pole piece, the magnetic flux leakage at the interface could be effectively decreased, which meant that this structural change was helpful  for maintaining the interface stable. Another main change was the addition of the aluminum shields next to the bushing and the pole pieces. A small gap was formed in front of the magnetic seal by this arrangement. In this case, the velocity difference of the two liquids became very low to maintain a definitely positive effect on the interface stability. Zhao et al. [118] analyzed the factors, which influenced the MFS capacity by numerical computations. They found that when the shaft diameter was large, the gravity should be considered, and the centrifugal force had an influence on the MFS capacity. Szydło and Matuszewski [119] carried out the tests for specially selected profiles of sealing lips and hydrophobic magnetic fluids at various linear velocities in a sealing unit. Although the tests were preliminary, their results showed that the studies about applications of MFSs working in liquid environment should continue. Krakov and Nikiforov [120] studied the distribution of the magnetic particle concentration in the magnetic fluid rotating shaft seal. They discovered that the shaft rotation caused not only a meridional flow of magnetic fluids, but an azimuthal flow as well. Hydraulic and pneumatic micro-actuators showed promising properties for generating high force densities at microscale. The fabrication of powerful seals with low leakage was one of the major technological difficulties in the development of these actuators. De Volder and Reynaerts [108] proposed a novel seal technology for linear fluidic microactuators, which combined a clearance seal with a ferrofluid seal. They tested these actuators, of which the outside diameter was 2 mm, and the length was 13 mm, using pressurized water and air. The actuator was able to generate both pulling and pushing forces depending on whether the pressure was exerted to the pressure Ports 1 or 2. Figure 9 depicts the actuator configuration. Integrating these seals into miniaturized fluidic actuators provided forces up to 0.65 N and strokes up to 10 mm at a driving pressure of 1.4 MPa.
To overcome mechanical sealing defects for underwater robotic vehicles (URVs), Kim et al. [121] proposed a new kind of MFS, which separated liquid from gas by adjusting the pressure inside the air chamber of the MFS. They developed a new computational method by using the finite element method for the estimation of the maximum pressure resistance of MFS. The comparison results between the experiment and the numerical calculation showed good agreement, except in the case of low rotational speed of the shaft. When the MFS was dismantled, no leakage was observed, which meant that the proposed MFS could be a good substitution against liquid for URVs. In 2010, French scholars, Ravaud et al. [122] presented three-dimensional study of centering effect and static capacity of a ferrofluid seal. They also put forward a method based on a potential energy criterion to study the seal shape. Meanwhile, the calculation of the magnetic pressure of the ferrofluid seal was theoretically established. Their study results were meaningful for the design or manufacturing of ironless loudspeaker structures and ironless bearings. Four years later, Pinho et al. [123] investigated damping induced by ferrofluid seals in ironless loudspeakers. The ironless loudspeaker is shown in Fig. 10, where the moving part guided by two ferrofluid seals along z-axis was a magnetic rigid cylinder. They described the model for determining the viscous damping coefficient of the ferrofluid seal in the ironless loudspeaker, based on a combination of frequency, shear rate, local viscosity, and function of magnetic field.
Matuszewski [124] defined the ways of experiments conducted on multi-stage rotating MFS operating in permanent contact with utility water. The special test procedures were aimed to define the main characteristics of MFSs, which were elaborated and practically used. These characteristics were working life of the seal, critical pressure, and critical motion velocity. Matuszewski [125] concluded that multi-stage MFSs could be efficiently used to seal rotary shafts in water with a limited number of cycles and a finite range of motion velocity. Schinteie et al. [126] carried out a complex study of the magnetic behavior of concentrated ferrofluids applied in rotary seals. To avoid the aggregation of magnetic nanoparticles, especially in the non-uniform and intense magnetic field specific to the sealing stages, they designed ferrofluids with both good colloidal stability and high magnetization. Sodium centrifugal pumps employed mechanical seals and conventional oil-cooled bearings to seal the gas and support the rotor. Accidents of oil ingress into sodium still occurred despite engineering safety features incorporated into the previous design. Therefore, a design variant that eliminated the need for oil in seals and top bearings was a promising option. Sreedhar et al. [109] discussed the feasibility of implementing a combination of the magnetic bearing and the ferrofluid seal, which could achieve this goal. Cai and Xing [127] analyzed the mechanism of the increase in starting friction torque of rotary MFS, based on the changes in the microstructure and viscosity of magnetic fluids. They concluded that the sealing structure, the type of magnetic fluids, as well as the working condition involving magnetic field gradient, temperature, and shaft velocity were the main factors influencing the starting friction torque. Liu [128] focused on a secondary flow in the narrow gap of a magnetic fluid shaft seal. By using a spectral finite difference method with a new mapped function, he evaluated the circumferential speed and the secondary flow of magnetic fluids with variation in magnetic fluid plug shape. Yang and Li [110] proposed a new type of stepped MFSs with stepped labyrinth seals and multiple magnetic sources to improve the pressure capacity of MFSs with a large sealing gap. Figure 11 exhibits the converging and diverging stepped MFSs. The difference between the converging stepped MFS and the diverging stepped MFS lied in the leakage direction of the sealed medium. Different from the traditional MFSs, the proposed MFSs had multiple magnetic sources and stepped shafts. The experimental results showed that the stepped MFSs performed better than the universal MFSs with the same basic parameters.
MFSs have attracted attention as potential candidates for blood pump seals owing to their interesting properties. Tomioka and Miyanaga [129] discussed the seal capacity including the sealing durability and  sealing pressure under blood sealing. According to the viewpoint of biological compatibility, they performed hemolysis tests for blood sealed by magnetic fluids. They found that hemolysis of blood sealed with the organic-solvent MFSs was maintained below 0.5%. Li et al. [130] focused on the influence of magnetoviscous effects and viscosity on the performance of MFSs in water condition. They prepared three engine oil-based magnetic fluids of different viscosities as well as similar saturation magnetization values, and designed a multi-stage MFS structure. From the experimental results, it could draw a conclusion that the viscosity of the magnetic fluid was a decisive factor for its seal ability in water condition. They also demonstrated that the observed difference in critical pressure values was mainly caused by the magnetoviscous effect at relatively low rotational speeds. Wang et al. [111] developed an improved MFS adding gas isolation device to avoid direct contact between magnetic fluids and the sealed liquids, which improved the performance of MFS for sealing liquid medium. As shown in Fig. 12, compared to original structure, the improved structure of MFS added two parts, the breathing ring and the gas vent. Through the gas vent, the space between the sealed liquids and magnetic fluids was connected to compressed gas. The pressure of compressed gas was equal to the pressure at the end of the sealed liquids, but lower than the critical pressure at the end of the MFS. In this way, the issue of MFS for sealing liquid medium was converted to MFS for sealing gas medium successfully.
In contrast to traditional hydrodynamic and hydrostatic bearings, Hu et al. [131] introduced a kind of liquid-gas mixed supporting structure based on a ferrofluid seal. Such a design had the advantage of adjustable supporting forces, independent of relative movement or any other external facilities, which provided the underlying applications for low-velocity and precision mechanisms. In order to improve the service life of the magnetic fluid rotary seal, van der Wal et al. [132] presented a magnetic fluid rotary seal with a replenishment system, which renewed the magnetic fluid in the sealing ring, while sealing capacity was maintained. They validated that the service life of the magnetic fluid rotary seal was theoretically unlimited by replacing the degraded magnetic fluid in the seal at a sufficient rate. Yang et al. [133] designed a converging MFS with double magnetic sources to improve the pressure resistance capacity of MFSs with small clearance. The experimental and theoretical results showed that the pressure resistance capacity of the converging MFS did not decrease with the increasing clearance or dropping number of pole teeth. And the pressure resistance capacity of the converging MFS was better than that of the step less MFS. Li et al. [112] proposed a meliorative MFS structure to improve the durability and pressure resistance capacity for sealing liquid. Furthermore, they optimized the structural parameters to maximize the magnetic induction intensity in the sealing gap. According to the optimized results, they designed an MFS test device at the same time.
The test results demonstrated that the durability and pressure resistance capacity of the proposed MFS structure were better than those of the traditional MFS structures, particularly for a large gap structure. In this study, a circular pole piece was devised as a radial magnetizing permanent magnet ring, as shown in Fig. 13. As a result, the critical sealing pressure of the new structure was 2 to 3 times that of the traditional structure.
Cheng et al. [134] reported the experimental investigation and analysis of the effect of rheological characteristics on the starting torque of the MFS. They measured the viscosities and shear rates of magnetic fluids under specific magnetic field, as well as the variation of the starting torque for diester-based MFS and perfluoropolyether-based MFS. It is found that the magnetic fluid with higher viscosity generated higher starting torque correspondingly, but the variation tendency of the starting torque was the same. Since www.Springer.com/journal/40544 | Friction Fig. 13 Schematic diagram of proposed sealing structure. Reproduced with permission with Ref. [112], © Elsevier B.V. 2021.
shear thinning and particle agglomeration were the major microscopic mechanisms leading to the change of the starting torque, it is concluded that the critical factor influencing the starting torque of the MFS was the rheological behavior.

Magnetic fluid reciprocating sealing
Magnetic fluid reciprocating sealing technology is a new dynamic sealing technology. Since the magnetic fluid reciprocating sealing can be combined with the rotary sealing to realize the sealing of the reciprocating and rotating compound movement, this kind of sealing technology attracts more and more people's attention. Magnetic fluid reciprocating sealing technology originated in the early 1980s. Compared with the number of studies conducted on magnetic fluid rotary seals, the number of studies on magnetic fluid reciprocating seals are much fewer. The scholars mainly investigated magnetic fluid reciprocating sealing from three aspects. The first is structural optimization design, which improves the sealing properties, such as sealing life and capacity. The second is theoretical analysis, such as the anti-pressure equation and the influence of motion velocity. The third is experimental verification to evaluate the sealing performance.
Goldowsky [135] proposed a novel linear MFS and provided relevant test data. Figure 14 is a schematic diagram of a single-stage linear MFS, which was suitable for the heart engine. The fastigiated pole piece surrounding the shaft was the key to its operation. An axial magnetic field gradient was built up towards the magnet, which effectively trapped ferrofluid film adhering to the shaft during axial movement. The length of the upper pole piece was equal or greater than the stroke of the shaft. The washer-shaped pole piece on the bottom severed as a magnetic flux return path. The beginning sharp edge of the fastigiated pole piece maintained the sealing pressure. This seal could solve main difficulties in the development of a miniature isotope-driven Stirling engine employed as a power source for an artificial heart by applying magnetic fluids.
Miyake and Takahashi [136] studied characteristics of a linear magnetic fluid vacuum seal with rotation by experiments. This seal principle prevented seal breakage caused by the shaft linear movement. And the behavior of magnetic fluids on the same motion was obtained by using a two dimensional linear seal model. Evsin et al. [137] developed the seal structures of reciprocating MFSs with gas dynamic resistances and damper volumes. The gas dynamic processes in the multi-stage seal system were analyzed, and the operating conditions of reciprocating MFSs were obtained. Its operation was affected by the seal deformation and the carry-over, the former being the main factor. Based on the anti-pressure formula of the reciprocating MFS from general Navier-Stokes equation, Li et al. [138] studied the motion mechanism of magnetic fluids in the reciprocating seal gap. They estimated the magnetic field distribution in sealed structure and got the maximum static anti-pressure | https://mc03.manuscriptcentral.com/friction to verify the correctness of the anti-pressure formula. Finally, the influence of stroke and speed on the sealing anti-pressure was investigated. After this work, Li et al. [139] concentrated on the regular pattern of the magnetic fluid flow, the loss quantity caused by the shaft with reciprocating motion, the sealing failure reason, and the new structure design. Two years later, Li et al. [140] set up a new experimental facility, which was composed of a step-by-step motor, pin roller screw, microscope, camera, permanent magnet, reciprocating motion shaft, pole pieces, and the magnetic fluid in the seal gap. By using the image processing and optical technology of the experimental facility, they investigated the flow of magnetic fluids in the seal gap when the reciprocating shaft moved with different strokes and velocities. In order to solve the main failure reasons of magnetic fluid reciprocating seals, they designed a new structure for these seals, and the application indicated that the new structure was very effective in some occasions. As shown in Fig. 15, the structure combined elastic rings and teeth, which employed transition fit between ring and shaft. Since the magnetic fluid introduced under the pole teeth was more stable, the micro leakage rate was reduced. The structure worked well in the reciprocating vacuum pump, of which the stroke was up to 200 mm, and the seal age reached 5,800 h.
It can be seen from Ref. [111] that Wang et al. had already obtained anti-pressure formula of MFSs using for reciprocating shafts from general Navier-Stokes equation, and set up an experiment rig to verify the validity of the formula. After that, Li et al. [141] concluded that the major reasons of the MFS failure were the deformation of magnetic fluid film in the seal gap and the leakage of magnetic fluids due to the reciprocating motion of the shaft. The magnetic fluid-sealed feedthroughs were widely applied in high and ultra-high vacuum equipment, which was employed in semiconductor fabrication and robotics industry. The operating conditions of MFSs during reciprocating motion were so different from those during rotating motion that using conventional structures for reciprocating motion seals would result in poor results. Ochoński [142] gave a brief introduction to magnetic fluid sealing technology, behavior of magnetic fluids, principle of sealing, and seal failure mechanism for the linear motion of the shaft. Meanwhile, some novel structures of vacuum linear feedthroughs with MFSs were presented, which had practical applications. Mizutani et al. [143] proposed the MFS for linear motion system with a gravity compensator. It was feasible to prevent magnetic fluids from leaking out of the seal clearance. Figure 16 shows the structure of the new MFS, of which the gap between pole pieces and a magnet was filled with a resin to prevent magnetic fluids from moving into the gap. The two pole pieces shaped tapered tip holding the magnetic fluid to maintain the performance of the seal, which was put near the piston produced by non-magnetic material and coated with the oil repellent layer. They evaluated the performance of the presented MFS. And the results confirmed that the proposed MFS was suitable for using in linear motion seals, and the oil repellent layer on the piston surface could greatly enhance the sealing performance.
Chen et al. [144] described the equation for evaluating the seal capacity of reciprocating MFSs and obtained the thickness of magnetic fluids on the surface of reciprocating shaft in theory. They used experimental method to quantitatively depict the relationship From a large number of studies mentioned above, we summarized practical applications, advantages, and disadvantages of magnetic fluid static sealing, magnetic fluid rotary sealing, and magnetic fluid reciprocating sealing, as shown in Table 6.

Conclusions and perspective
We have presented a general summary of mature and emerging MFSs, covering their novel designs, theoretical analyses, and diverse applications. Because of their advantages such as zero leakage, long service life, and low wear, MFSs have been widely used as a gas seal. Since magnetic fluids are able to create hermetic sealing for hazardous gases, magnetic fluid sealing is very important in preserving the environment [145]. With rapid developments in medicine, chemistry, nuclear power [146], and other industries, stirrers [147], reactors [148], and other related components have more stringent requirements in terms of sealing. Therefore, MFSs with unique properties play a pivotal role in ensuring effective sealing under high-risk environments.
However, in liquid environment, MFSs are generally unstable due to material-related and structural challenges. It is difficult to ensure their high-pressure resistance and long durability, on account of the complex chemical and physical processes involved in the liquid seal. Therefore, the research of MFSs in the field of liquid sealing majorly focuses on the following three directions: (1) Based on the Kelvin-Helmholtz instability theory [149][150][151], the factors affecting the instability of the liquid-liquid interface are studied.
(2) In order to reduce the instability of the liquidliquid interface, the design of the seal structures is optimized.
(3) From the perspective of material science [152][153][154], it is significant to prepare hydrophobic magnetic fluids with high saturation magnetization intensity. Hitherto, magnetic fluids including iron particles coated with silica have been used for long service life oil seal, without magnetic characteristic degeneration induced by oxidation. If the service life can be extended, magnetic fluid sealing technology has potential and promise in several marine applications like propeller shafts of boats [155] and medical applications like sealing blood in rotary blood pumps [156].
With the rapid development of aerospace and military industry, higher safety and reliability seals are demanded in these fields, such as tank panoramic mirror [157], radar waveguide component [158], and guided-missile launcher [159], especially in high-speed conditions. At present, the application of magnetic fluid sealing technology in low-speed or medium-speed conditions has gradually matured, but the development of magnetic fluid high-speed sealing has not made a breakthrough. Temperature rise is a key factor affecting the high-speed sealing performance of MFSs. For the sake of solving the problem of high-speed sealing, adding the cooling structure and improving the heat transfer performance of magnetic fluids are two major ways that we can adopt. In the future, research on the cooling structure optimization and convective heat transfer characteristics of magnetic fluids will promote the application of MFSs under high-speed working conditions. Besides, in some sealing applications for precision and high-end equipment, such as robot joints [160][161][162] and radio frequency sputtering units [163], the resistance torque of the sealing structure should remain in a stable range, and the starting resistance torque is expected to be small in any conditions. However, the starting resistance torque varies with the environment and standing time, which may cause the sealed equipment fail, and thus further research on the starting resistance torque is necessary. Large diameter shafts are widely used in various heavy equipment, such as high-power motors [164], shield machines [165], and propeller shafts of ships [166]. Due to the large diameter of the shafts, the radial runout of the shafts also increases, which will cause friction and wear between the shafts and the pole teeth, and even damage the sealing structure. Therefore, a large sealing gap must be left between the sealed shaft and the pole teeth. Nevertheless, when the sealing gap becomes bigger, the sealing ability of the MFS will be significantly reduced. Hence, how to improve the sealing ability of the large gap MFS, such as pressure resistance, still needs further research.
Because of the weak pressure resistance capability of MFSs, once the instantaneous pressure fluctuation exceeds the limit pressure value of the MFS, the MFS fails. The leakage of the sealing medium causes economic losses and even does serious harm to the human body and the environment. In order to meet the requirements of no leakage and withstand pressure fluctuations in the sealing conditions of some modern mechanical equipment such as reactors, more and more new combined sealing structures have been proposed. MFSs are combined with other forms of seals to achieve the effect of complementary advantages. At present, many scholars have made great efforts in the studies of combined seals.
There are many studies concentrated on the sealing surface in other sealing forms, such as surface texture [167] and surface treatment [168]. Relevant studies have proved that in these seals, the sealing performance can be significantly improved by changing the sealing surfaces. It is a pity that the current research of MFSs rarely considers the influence of the sealing surface. The change of the sealing surface brings about many unexpected changes, e.g., the wettability [169] and contact angle [170] of magnetic fluids, so surface interaction is a promising direction for the subsequent research of magnetic fluid sealing.
The magnetic fluid is one of the most important components in the MFS, so the characteristics of the magnetic fluid have a great influence on the MFS. The study of the characteristics of magnetic fluids has guiding significance for the applications of MFSs. Some magnetic fluids with special properties can be applied in special sealing occasions, e.g, radiation resistance magnetic fluids [171] using to aerospace and biomedicine sealing technology, non-toxic magnetic fluids [172] for human blood sealing, and low-temperature resistance magnetic fluids [173] for equipment sealing in extremely cold areas.
Addressing the issues mentioned above, our team has made important progress in the following four aspects. First, we have invented the nuclear radiationresistant magnetic fluid rotary sealing technology. The design theory of nuclear radiation-resistant rotary MFS and the pole piece integrated structure has been established. Second, we have developed the highand low-temperature resistant magnetic fluid rotary sealing technology. The failure mechanism of rotary MFSs under high-and low-temperature conditions (within the range of −55-80 °C in the military national standard) has been revealed. Third, we have created the high-pressure resistant magnetic fluid rotary sealing technology, built up the design theory of high-pressure resistant rotary MFSs, and designed their structures. Finally, we have constructed the large radial runout magnetic fluid rotary sealing technology. The design theory of the rotary MFS with large radial runout has been proposed, and a new www.Springer.com/journal/40544 | Friction structure of the rotary MFS, which can adapt to the large radial runout of the rotating shaft, has been presented.
Future endeavors could be focused on the liquid sealing, high-speed sealing, large gap sealing, starting resistance torque, combination seals, sealing surfaces, and characteristics of magnetic fluids. In addition, attention could be paid to bringing these research achievements into new situation, e.g., the high-risk environment. In summary, with more efforts devoted to the study of MFSs, the goals of improvement in their performance, making their application area wider, etc., will be achieved. We believe that MFS can accomplish more exciting goals in the future, and our review will inspire research fellows who are exploring or just touching this field.