Closed shear thickening fluid squeeze film damper
By using a closed shear thickening liquid as the working fluid in the extruded oil film damper, and using its viscosity to change with the shear rate, the problem of poor vibration damping effect in the existing technology under high amplitude conditions is solved, and better vibration damping performance and structural simplification are achieved.
Patent Information
- Application Number
- CN202510023928.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-07
- Publication Date
- 2025-04-18
- Estimated Expiration
- 2045-01-07
AI Technical Summary
The existing extruded oil film dampers are difficult to meet the vibration damping requirements under high amplitude conditions, and the current and magnetorheological fluid devices are complex in structure and difficult to control, and have not yet been applied to the engineering.
The sealed shear thickening liquid is used as the working fluid. By filling the shear thickening liquid in the gap of the damper, and using the precession movement of the inner ring of the damper, its viscosity increases with the change of the shear rate, thereby generating a greater damping force.
It realizes an adaptive vibration damping effect without external excitation power supply, simplifies the device structure, reduces the design difficulty, and provides better vibration damping performance.
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Figure CN119844514A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of mechanical engineering vibration reduction, and in particular to a closed shear thickening liquid squeeze film damper. Background Art
[0002] In the process of high-speed operation of modern rotating machinery, rotor vibration is often inevitable due to the imbalance of the rotor and various complex excitation forces. Once the rotor amplitude exceeds the limit, it will cause friction with the stator components, seriously affecting the performance and safe and stable operation of the whole machine. In order to improve the working reliability of the rotating machinery rotor, the research and development of the rotor shaft vibration reduction device is very necessary.
[0003] Squeeze film damper is a vibration reduction device widely used in rotating machinery shaft systems such as aircraft engines. At present, squeeze film dampers all use lubricating oil with Newtonian fluid properties as the working medium to provide additional viscous damping to reduce the rotor amplitude and absorb vibration energy. Since the viscosity of Newtonian fluid remains constant with the shear rate, the damping force generated by the squeeze film damper often cannot meet the vibration reduction requirements under high amplitude conditions. In recent years, new materials such as electrorheological fluid and magnetorheological fluid have been applied to the development of squeeze film dampers. The rheological properties of these materials will change under the action of electric or magnetic fields, so the viscosity can be adapted to different vibration conditions by controlling the electric or magnetic field current, thereby improving the vibration reduction effect. However, since the electro- and magnetorheological fluid squeeze film dampers require external excitation power and additional electric or magnetic field devices during operation, the equipment structure is relatively complex, and the design of the control system is also very difficult, and has not yet been applied in engineering.
[0004] Shear thickening fluid is a stress field responsive intelligent material, and its viscosity is related to the shear rate. Under high-speed load, the viscosity of the fluid will increase rapidly, and the morphology will solidify; after the external load is removed, it can return to its initial state in a relatively short time. Compared with traditional viscous materials, shear thickening fluid can change its viscosity as the shear rate changes, and has adaptive characteristics. Compared with electrorheological fluid and magnetorheological fluid, it does not require an external excitation power supply when used, which reduces the design difficulty. It can be seen that the characteristics of shear thickening fluid are very suitable for the field of vibration control. Summary of the invention
[0005] According to the technical problem raised above, a closed shear thickening fluid squeeze film damper is provided.
[0006] The technical means adopted by the present invention are as follows:
[0007] A closed shear thickening liquid squeeze film damper comprises: a damper inner ring and a damper outer ring with a sealing sleeve outside the damper inner ring, the interior of the damper inner ring is connected to a rotor via a bearing, a gap is provided between the inner wall of the damper outer ring and the outer wall of the damper inner ring, the gap is filled with a working medium, and the working medium is a shear thickening liquid; a working medium filling structure is provided on the damper outer ring for realizing the injection and suction of the shear thickening liquid in the gap.
[0008] Furthermore, the damper is a circular ring structure, the inner surface of the outer ring of the damper is provided with an annular central groove connected with the gap along the circumferential direction, and the working fluid filling structure is connected with the central groove.
[0009] Furthermore, the working fluid filling structure comprises a liquid inlet through hole and a liquid outlet through hole, and the liquid inlet through hole and the liquid outlet through hole are symmetrically arranged on both radial sides of the damper outer ring and both penetrate the radial wall of the damper outer ring.
[0010] Furthermore, the liquid inlet through hole is arranged at the lowest position of the damper gap, and the liquid outlet through hole is arranged at the highest position of the gap;
[0011] The outer ends of the liquid inlet through hole and the liquid outlet through hole are blocked by plugs, and sensors can be connected to the liquid inlet through hole and the liquid outlet through hole.
[0012] Furthermore, the bearing is a ball bearing, which includes a ball bearing inner ring, ball bearing balls and a ball bearing outer ring, the ball bearing inner ring is connected to the rotor, the ball bearing balls are connected between the ball bearing inner ring and the ball bearing outer ring, and the damper inner ring is installed on the ball bearing outer ring as a sleeve structure, and the ball bearing outer ring and the damper inner ring can move together through interference fit.
[0013] Furthermore, a slot is provided on the inner ring of the damper, a threaded hole is opened on the outer ring of the damper, and a stop bolt is connected in the threaded hole; when the damper is in operation, the inner ring of the damper only performs precession motion and no rotational motion, and the stop bolt fixed on the outer ring of the damper is inserted into the slot to stop the rotation of the inner ring of the damper.
[0014] Furthermore, a plurality of compensation grooves are formed in the central groove.
[0015] Furthermore, the volume of the shear thickening fluid filled in the gap is the total volume of the damper gap minus the volume of all compensation grooves.
[0016] Furthermore, at least one mounting groove is formed on the outer wall of the damper inner ring at both ends of the gap, and an O-ring is installed in the mounting groove to achieve a sealed connection between the damper inner ring and the damper outer ring.
[0017] Furthermore, the shear thickening liquid is prepared by mixing a dispersant and a dispersion medium, the dispersant is low-viscosity polyethylene glycol, and the dispersion medium is nano-silicon dioxide particles.
[0018] Compared with the prior art, the present invention has the following advantages:
[0019] 1. The closed shear thickening fluid squeeze film damper of the present invention does not require an external more complex working fluid circulation system device, reduces dependence on complex structures, and has a wider range of engineering applications.
[0020] 2. The working fluid of the closed shear thickening liquid squeeze film damper of the present invention has a shear thickening effect, that is, the viscosity of the working fluid increases with the increase of the precession radius, thereby being able to generate a greater damping force and having a better vibration reduction effect.
[0021] 3. The shear thickening fluid proposed in the present invention is a stress field responsive intelligent material that can change its viscosity according to the change of shear rate, and thus has adaptive characteristics. The shear thickening fluid squeeze film damper is annular, and is sealed at both ends with O-rings. A central groove structure is provided on the inner surface of the outer ring of the damper, and two symmetrically arranged through holes are designed in the groove for injecting and sucking out the shear thickening fluid into the gap of the damper. When the shear thickening fluid fills the gap between the inner ring and the outer ring of the damper, the liquid inlet and outlet holes are blocked to form a closed squeeze film damper, without the need for a complex oil supply and discharge circulation device that is compatible with traditional squeeze film dampers. The present invention can achieve that during the precession of the inner ring of the damper, the viscosity of the shear thickening fluid increases with the increase of the precession radius of the rotor, thereby generating a greater damping force, and has a better vibration reduction effect on the rotor than the squeeze film damper with traditional lubricating oil as the working fluid.
[0022] Based on the above reasons, the present invention can be widely promoted in the fields of vibration reduction and the like. BRIEF DESCRIPTION OF THE DRAWINGS
[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.
[0024] Figure 1 It is a longitudinal cross-sectional view of the closed shear thickening fluid damper of the present invention.
[0025] Figure 2 This is an axial center cross-sectional view of the damper of the present invention.
[0026] Figure 3 The present invention is attached Figure 1 A partial enlarged view of point C in the middle.
[0027] Figure 4 The present invention is attached Figure 2 A partial enlarged view of point D in the middle.
[0028] Figure 5 The present invention is attached Figure 2 A partial enlarged view of point E in the middle.
[0029] In the figure: 1. rotor; 2. inner ring of ball bearing; 3. ball of ball bearing; 4. outer ring of ball bearing; 5. inner ring of damper; 6. outer ring of damper; 7. liquid inlet hole; 8. anti-rotation bolt; 9. liquid outlet hole; 10. first O-ring; 11. second O-ring; 12. center groove; 13. compensation groove. DETAILED DESCRIPTION
[0030] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.
[0031] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0032] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.
[0033] Unless otherwise specifically stated, the relative arrangement, numerical expressions and numerical values of the parts and steps set forth in these embodiments do not limit the scope of the present invention. Meanwhile, it should be clear that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to those of ordinary skill in the relevant art may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be considered as a part of the specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, and therefore, once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.
[0034] In the description of the present invention, it is necessary to understand that the directions or positional relationships indicated by directional words such as "front, back, up, down, left, right", "lateral, vertical, perpendicular, horizontal" and "top, bottom" are usually based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description. Unless otherwise specified, these directional words do not indicate or imply that the device or element referred to must have a specific direction or be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the scope of protection of the present invention: the directional words "inside and outside" refer to the inside and outside relative to the contours of each component itself.
[0035] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below their position devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.
[0036] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. If not otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.
[0037] The purpose of the present invention is to provide a closed squeeze film damper based on the Newtonian fluid squeeze film damper, in which the working medium can produce a shear thickening effect, and the structure is simpler and the damping and vibration reduction effect is better.
[0038] The invention discloses a closed type shear thickening liquid squeeze film damper, which is a closed type squeeze film damper with shear thickening liquid as the working fluid, and is used to reduce the vibration amplitude of the rotor. The main structure includes: a damper outer ring 5, a damper inner ring 6, a liquid inlet through hole 7, a stop bolt 8, a liquid outlet through hole 9, a first O-ring 10, a second O-ring 11, a center groove 12, and a compensation groove 13. The inside of the damper inner ring 5 is connected to the rotor 1 through a ball bearing, and the damper outer ring 6 is sealed on the outside of the damper inner ring 5. There is a gap between the inner wall of the damper outer ring 6 and the outer wall of the damper inner ring 5, and the gap is filled with a working fluid. The working fluid in the damper gap is a pre-prepared shear thickening liquid. O-rings are used to seal the two ends of the damper gap (at both ends along the width direction of the damper) to ensure the airtightness of the damper gap.
[0039] The ball bearing includes a ball bearing inner ring 2, ball bearing balls 3 and a ball bearing outer ring 4. The ball bearing inner ring 2 is connected to the rotor 1. The ball bearing balls 3 are connected between the ball bearing inner ring 2 and the ball bearing outer ring 4. The damper inner ring 5 is installed on the ball bearing outer ring 4 as a sleeve structure. The ball bearing outer ring 4 and the damper inner ring 5 can move together through interference fit.
[0040] The damper is an annular structure as a whole. An annular center groove 12 connected to the gap is provided at the axial center position of the inner surface of the damper outer ring 6. The center groove 12 is provided with a liquid inlet hole 7 and a liquid outlet hole 9 for injecting and sucking out the shear thickening liquid into the gap. The liquid inlet hole 7 and the liquid outlet hole 9 are symmetrically arranged on both radial sides of the damper outer ring 6, and both penetrate the radial wall of the damper outer ring 6. The first O-ring 10 and the second O-ring 11 are respectively sealed at both ends of the damper gap. When the shear thickening liquid is injected into the damper gap cavity through the liquid inlet hole 7 and the liquid outlet hole 9, the two holes are blocked to form a closed shear thickening liquid squeeze film damper. That is, when the shear thickening liquid fills the gap between the inner and outer rings of the damper, the two holes are sealed to form a closed squeeze film damper, thereby eliminating the oil supply circulation system device of the traditional squeeze film damper.
[0041] The damper inner ring 5 is provided with a slot, and in the axial direction, the slot is located outside the second O-ring 11. The damper outer ring 6 is provided with a threaded hole, and a rotation-stopping bolt 8 is connected in the threaded hole. During the operation of the damper, the damper inner ring 5 only performs precession motion, but not rotational motion; this structure realizes the rotation stop of the damper inner ring 5 by the rotation-stopping bolt 8 fixed on the damper outer ring 6.
[0042] It should be noted that the attached Figure 1 The inner and outer ring structures of the squeeze film damper in the figure are simplified structures. In actual application, the structures of the inner and outer rings of the damper are different, but the structures of the gap areas between the inner and outer rings of the damper are basically the same.
[0043] The outer walls at both ends of the damper inner ring 5 are provided with mounting grooves, and the mounting grooves of the first O-ring 10 and the second O-ring 11 are arranged on the damper inner ring 5 in an axially sealed manner. According to the structural dimensions and sealing requirements of the actual application, multiple seals can be arranged on the damper inner ring 5 to ensure the sealing effect.
[0044] The shear thickening fluid is prepared by mixing low-viscosity polyethylene glycol as a dispersant and nano-silica particles as a dispersion medium. When applying the present invention, it is necessary to prepare a nano-silica shear thickening fluid of optimal concentration according to the working characteristics of the damper. The viscosity of the prepared shear thickening fluid has the characteristic of increasing with the increase of shear rate, and can have different viscosity values under different extrusion speeds of the inner ring of the damper, thereby generating different damping forces, and has adaptive characteristics. According to the rotor's demand for the damping force provided by the shear thickening fluid damper, the optimal concentration of the nano-silica particle dispersant can be determined by means of simulation and experiments to ensure that the prepared shear thickening fluid meets the viscosity characteristics of the damper under the designed working conditions and achieves an ideal vibration reduction effect.
[0045] There are two through holes on the center groove 12 of the damper outer ring 6, one of which is a liquid inlet through hole 7 and the other is a liquid outlet through hole 9. When installing the shear thickening liquid squeeze film damper, the liquid inlet through hole 7 is arranged at the lowest position of the damper gap, and the liquid outlet through hole 9 is arranged at the highest position of the gap. Its main function is to ensure that the shear thickening liquid can smoothly fill the damper gap cavity, and the volume of the injected shear thickening liquid can be controlled by the flow rate of the two through holes. The shear thickening liquid working medium in the damper gap can be replaced through the liquid inlet through hole 7 and the liquid outlet through hole 9 as needed.
[0046] After a proper amount of shear thickening liquid is injected into the gap between the liquid inlet through hole 7 and the liquid outlet through hole 9, plugs may be used to block the gap, thereby forming a closed squeeze film damper.
[0047] Attached Figure 2 and attached Figure 3 The specific positions of the inlet through hole 7 and the outlet through hole 9 can be adjusted according to the actual application structure. If it is necessary to detect the change of parameters such as pressure or temperature during the operation of the damper, the inlet through hole 7 and the outlet through hole 9 can be connected to the corresponding sensor.
[0048] Specifically, the above-mentioned liquid inlet through hole 7 and liquid outlet through hole 9 may not be blocked by a plug after the damper gap is filled with shear thickening liquid. In order to understand the changes in parameters such as liquid film pressure and temperature during the operation of the damper, the liquid inlet through hole 7 and liquid outlet through hole 9 can be used as measurement holes for connecting corresponding sensors. That is, if the monitoring of parameters such as pressure and temperature in the gap of the damper during operation is considered, the above-mentioned liquid inlet through hole 7 and liquid outlet through hole 9 can be connected to a suitable sensor. At this time, the amount of shear thickening liquid injected into the damper gap needs to consider the gap between the through hole and the sensor.
[0049] When the damper needs to replace the shear thickening liquid in the gap, the liquid inlet hole 7 and the liquid outlet hole 9 can be reopened. Air can be injected into the gap first to ensure that the shear thickening liquid is completely discharged, and then new shear thickening liquid can be refilled.
[0050] Considering the high-speed precession motion of the damper inner ring 5, the shear thickening liquid in the gap undergoes certain cavitation and thermal expansion in a confined space, and three compensation grooves 13 of a certain volume are evenly arranged in the central groove 12. The total volume of the three compensation grooves 13 can be calculated based on the volume expansion rate of the shear thickening liquid and the given cavitation ratio. Therefore, the volume of the compensation groove 13 is not considered in the initial volume of the shear thickening liquid added to the gap. The total volume of the compensation groove 13 can be calculated based on the stable temperature and cavitation ratio of the damper during operation. Figure 3 , Attachment Figure 4 The volume of the shear thickening fluid added to the gap is the total volume of the damper gap minus the volume of all compensation grooves. In the process of injecting the shear thickening fluid into the gap, the volume of the shear thickening fluid injected into the gap is determined by the volume difference of the shear thickening fluid of the two through holes.
[0051] The physical properties of the shear thickening fluid are measured, and a certain value of the cavitation ratio in the gap is given to estimate the stable temperature during the operation of the damper, determine the expansion volume of the shear thickening fluid at the highest temperature, and distribute this expansion volume to the volume of each compensation groove 13 in the central groove 12.
[0052] During the operation of the closed shear thickening fluid squeeze film damper, the damper inner ring 5 is restricted from rotating and can only precess. The continuous precession of the inner ring 5 shears and squeezes the shear thickening fluid in the gap, causing the shear thickening fluid to produce different damping forces, thereby reducing the vibration amplitude of the rotor system. The continuous precession of the damper inner ring 5 causes the shear thickening fluid, which is squeezed and sheared, to increase in viscosity as the shear rate increases, thereby producing a greater damping effect. The faster the precession speed of the damper inner ring 5 changes, the greater the shear rate of the shear thickening fluid, and the greater the damping effect it produces.
[0053] Specifically, during the operation of the squeeze film damper of the enclosed shear thickening fluid, the shear rate of the squeezed shear thickening fluid increases along the precession direction, and the viscosity of the shear thickening fluid increases, thereby producing a stronger damping effect. And as the precession speed of the damper inner ring 5 increases, the shear rate of the shear thickening fluid increases, and the damping effect it produces becomes stronger. That is, the adapted shear thickening fluid can automatically adapt to the working conditions of the damper to change the viscosity value, thereby adjusting the magnitude of the damping force generated and reducing the vibration amplitude of the rotor system.
[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A closed shear thickening fluid squeeze film damper, characterized in that: include: A damper inner ring (5) and a damper outer ring (6) with a sealing sleeve outside the damper inner ring (5); the interior of the damper inner ring (5) is connected to the rotor (1) via a bearing; a gap is provided between the inner wall of the damper outer ring (6) and the outer wall of the damper inner ring (5); the gap is filled with a working medium, which is a shear thickening liquid; and a working medium filling structure is provided on the damper outer ring (6) for realizing the injection and suction of the shear thickening liquid in the gap.
2. The closed shear thickening fluid squeeze film damper according to claim 1, characterized in that: The damper is a circular ring structure, the inner surface of the damper outer ring (6) is provided with an annular central groove (12) in the circumferential direction and communicated with the gap, and the working medium filling structure is in communication with the central groove (12).
3. The closed shear thickening fluid squeeze film damper according to claim 2, characterized in that: The working fluid filling structure comprises a liquid inlet through hole (7) and a liquid outlet through hole (9), wherein the liquid inlet through hole (7) and the liquid outlet through hole (9) are symmetrically arranged on both radial sides of the damper outer ring (6) and both penetrate the radial wall of the damper outer ring (6).
4. The closed shear thickening fluid squeeze film damper according to claim 3, characterized in that: The liquid inlet through hole (7) is arranged at the lowest position of the damper gap, and the liquid outlet through hole (9) is arranged at the highest position of the gap; The outer ends of the liquid inlet through hole (7) and the liquid outlet through hole (9) are blocked by plugs, and sensors can also be connected to the liquid inlet through hole (7) and the liquid outlet through hole (9).
5. The closed shear thickening fluid squeeze film damper according to claim 1, characterized in that: The bearing is a ball bearing, and the ball bearing comprises a ball bearing inner ring (2), ball bearing balls (3) and a ball bearing outer ring (4); the ball bearing inner ring (2) is connected to the rotor (1); the ball bearing balls (3) are connected between the ball bearing inner ring (2) and the ball bearing outer ring (4); the damper inner ring (5) is installed on the ball bearing outer ring (4) as a sleeve structure, and the ball bearing outer ring (4) and the damper inner ring (5) move together through interference fit.
6. The closed shear thickening fluid squeeze film damper according to claim 1, characterized in that: The damper inner ring (5) is provided with a slot, the damper outer ring (6) is provided with a threaded hole, and a stop bolt (8) is connected in the threaded hole; during operation of the damper, the damper inner ring (5) only performs precession motion without rotational motion, and the stop bolt (8) fixed on the damper outer ring (6) is inserted into the slot to stop the rotation of the damper inner ring (5).
7. The closed shear thickening fluid squeeze film damper according to claim 2, characterized in that: A plurality of compensation grooves (13) are provided in the central groove (12).
8. The closed shear thickening fluid squeeze film damper according to claim 7, characterized in that: The volume of the shear thickening fluid filled in the gap is the total volume of the damper gap minus the volume of all compensation grooves (13).
9. The closed shear thickening fluid squeeze film damper according to claim 1, characterized in that: The outer walls of the damper inner ring (5) at both ends of the gap are each provided with at least one mounting groove, and an O-ring is installed in the mounting groove to achieve a sealed connection between the damper inner ring (5) and the damper outer ring (6).
10. The closed shear thickening fluid squeeze film damper according to claim 1, characterized in that: The shear thickening liquid is prepared by mixing a dispersant and a dispersion medium, wherein the dispersant is low-viscosity polyethylene glycol and the dispersion medium is nano silicon dioxide particles.
Citation Information
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