Analysis on Non-newtonian Characteristics for Nano Magnetic Fluid

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 174 (2017) 1208 – 1214

13th Global Congress on Manufacturing and Management, GCMM 2016

Analysis on Non-Newtonian Characteristics for Nano Magnetic Fluid Shicai Feng*, Qidong Chen Mechanical Engineering School of Changshu institute of Technology, Suzhou of Jiangsu Province, China, 215500

Abstract Magnetic fluid is a colloidal solution which is composed of magnetic particles and carrier liquid and surface active agent. Theoretical analysis indicates that the magnetic fluid can be considered to be controlled by constitutive equation which different from Newtonian fluid. Experimental analysis indicates that the magnetic fluid in a magnetic field belongs to plastic pseudoplastic fluid in the non-Newtonian fluid, that is plastic shear thinning fluid which different from ordinary Newtonian fluids and nonNewtonian fluid, also is different from the usual two phase flow. So there is a certain guiding role in the application of dynamics analysis for magnetic fluid. 2016The TheAuthors. Authors. Published by Elsevier © 2017 © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management Keywords: Nano magnetic fluid; Non-Newtonian characteristics; Plastic shear thinning fluid

1.

Introduction

Classical Newtonian mechanics regards the shear stress of fluid in the flow as proportional to the shear rate, based on this, the famous Navier - Stokes equations can be got, and the basic equations of viscous Newtonian fluid movement is described. With the development of the production and science and technology, there are a lot of fluids which do not obey Newton's law of constant viscosity fluid in industrial production process and nature. That is the non-Newtonian fluid (viscosity changes with the shear rate and the shear stress, the shear rate is not in conformity with the law of Newton internal friction)1. Magnetic fluid is a kind of superparamagnetism magnetic materials which is sensitive to magnetic field and can flow, it is consist of nano scale magnetic particles and carrier liquid and surface active agent, it belongs to the colloid, also belongs to the two phase fluid of solid and liquid, it has a unique

* Corresponding author. Tel.: +0-086-512-5225-2011 fax: +0-086-512-5225-1596. E-mail address: [email protected]

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management

doi:10.1016/j.proeng.2017.01.285

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performance and basic characteristics, such as non-Newtonian fluid properties2. Until now, The research on mechanics of colloidal fluid is still blank, there are many problems need to be solved in the dynamics of two-phase flow and there is no mature theory for them3. In this paper, the magnetic characteristics of non-Newtonian fluid are analyzed. 2. The constitutive equations of non-Newtonian fluid The viscosity of non-Newtonian fluid changes with the shear rate. According to this definition , the nonNewtonian fluid can be divides into time independent fluid, time correlation fluid and viscoelastic fluid 4, as shown in table 1 : Table 1. The type of fluid name Fluid name

Type of fluid

Type of fluid Viscous fluid

Time independent fluid Plastic fluid Non-Newtonian fluid

Time correlation fluid Viscoelastic fluid

Type of fluid Pseudoplastic fluid Dilatant fluid Bingham fluid Plastic pseudoplastic fluid Plastic dilatants fluid

Thixotropy fluid Rheopexy fluid Linear viscoelasticity fluid

Volgt fluid Maxwell fluid Brugers fluid

Non-linear viscoelastic fluid

2.1 Time independent fluid The viscosity of fluid is related to temperature, pressure and shear rate, it has nothing to do with the shearing time and has a single value relationship between shear stress and shear rate. Time independent fluid constitutive equation can be represented as follow5:

W W y

aJ n

(1)

Among the formula 1, W y is yield stress. When W t W y , the fluid flow. When W  W y , the fluid does not flow. a is measurement for viscosity, with the a greater, the viscosity is larger. n is non-Newtonian effect coefficient,

with the n farther deviation 1, the non-newtonian characteristic is more significant. According to the difference for the yield stress W y and non-Newtonian effect coefficient n , the Non-Newtonian fluid can be divided into the following types and the corresponding relationship curve between shear stress W and shear rate J is shown in Fig. 1. When W y 0, n 1ˈW KJ , a is Newton fluid as shown in Fig. 1. When

Wy

0, n  1ˈW

aJ n , b is Pseudoplastic fluid as shown in Fig. 1.

When

Wy

0, n ! 1ˈW

KJ n , c

When

W y z 0, n 1ˈW  W y

KJ n , d

is Bingham fluid as shown in Fig. 1.

When

W y z 0, n  1ˈW  W y

KJ n , e

is Plastic pseudoplastic fluid as shown in Fig. 1.

When

W y z 0, n ! 1ˈW  W y

KJ n , f

is Dilatant fluid as shown in Fig. 1.

is Plastic dilatants fluid as shown in Fig. 1.

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Fig. 1 The corresponding relationship curve between shear stress and shear rate for non-Newton fluid

2.2 Time correlation fluid The viscosity of fluid is related to not only temperature, pressure and shear rate, but also associated with shear time, that is the single value relationship does not exist between shear stress and shear rate. So there is no simple constitutive equation for this fluid which should be described by the relationship curve between the viscosity and time. Time correlation fluid mainly include thixotropic fluid and rheopexy fluid. Thixotropic fluid refers to the fluid for whicht the viscosity decreases with the increase of the shear time under the constant shear stress action of fluid, when the stress is dismantled, the fluid viscosity gradually restore. Rheopexy fluid refers to the fluid for which the viscosity increases with the increase of shear time, when the stress is dismantled, the fluid viscosity gradually restore. 2.3 Viscoelastic fluid Viscoelastic fluid Refers to the fluid which not only has the properties of viscous fluid but also of elastic fluid. When the shear stress is put on the viscoelastic fluid, the shear deformation can be generated and the work has be done ,but the work is neither completely conserved as elastomer, nor completely dissipation like pure viscous fluid, it has the properties of both shear elastic and viscous, so For viscoelastic fluid, due to the viscous and elastic intertwine in shear flow, a variety of strange phenomenon can be found in them but not can be seen in the Newtonian fluid . 3. Characteristic test for magnetic non-Newtonian fluid According to the characteristics of non-Newtonian fluid, the experiment device as shown on Fig. 2 is designed, it is mainly composed of three parts: (1) Magnetic field device, the maximum 2.5 A current is generated by the DC constant current power supply through the electromagnetic coil, the range of magnetic field intensity is 0 ~ 220 mT, the induction intensity actual effect on the magnetic fluid is measured by SG - 42 digital Tesla meter. (2) Liquid storage vessel, used for serving measured liquid. (3) The devices of imposed shear stress and measuring, used to applying shear force to magnetic fluid and to measure the impressed torque for the yield stress of magnetic fluid. In the device, the arm length L of impressed torque is 0.284 m, the level tension can be got by calculating gram of added weight. When testing, the magnetic fluid is placed in the liquid storage vessel between the two electrical pure iron disc plate, the magnetic field strength between the rotating disc (designed diameter is 60 mm) and the fixed disc is changed by changing the current size in the coil. The relational guaph for analyzing the shear stress and torque is shown on Fig. 3. Let M torque and R disc radius and W shear stress of the magnetic fluid, integration is as follow:

M

R

R

0

0

³ Wds ˜ r ³ W ˜ 2Srdr ˜ r

R

2SW ³ r 2dr 0

2 3 SR W 3

(2)

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M

mg.L

(3)

By formula (2) and (3), formula (4) can be got as follow:

2 3 SR W 3

W

mgL

3mgL 2SR 3

Fig. 2 The experiment device of the characteristics of non-Newtonian fluid

Fig .3 The principle diagram of yield stress testing for the magnetic fluid

(4)

(5)

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When using the test device, the first thing is to consider the no-load torque without any magnetic fluid in the liquid storage dish, that is to overcome the static friction force between the vertical round bar and inwall of the magnetic flux guide through-hole. Because when the rotating disk and vertical round bar is affected by external force, the friction must be exist, so the friction. should be subtracted when the yield stress of magnetic fluid is measured. In addition, the arm lever of applied torque should be perpendicular to the direction of tensile force generated by scale weight whose applying minimum is 1 gram. The adjustable current(0 ~ 2.5 A) is generated by the DC power supply, the magnetic field strength between the rotating disk and fixed disk is read directly by the Tesla meter. Table 2 is the tested torque for no-load. Table 3 is the tested torque for added magnetic fluid . Table 4 is the measured values of yield stress for magnetic fluid. In the table, the current and magnetic field intensity and the quality of scale weight is read directly, the torque and yield stress are calculated through formula (2) and (4). Table 2. The tested torque for no-load Serial number Current˄A˅ Magneticfield intensity˄mT˅ Scale weight˄g˅ Torque˄Nm×10-3˅ Serial number Current˄A˅ Magneticfield intensity˄mT˅ Scale weight˄g˅ Torque˄Nm×10-3˅ Serial number Current˄A˅ Magneticfield intensity˄mT˅ Scale weight˄g˅ Torque˄Nm×10-3˅

1 0 2.3 8 22.27 8 0.7 63.9 92 256.05 15 1.4 142.2 106 295.02

2 0.1 7.3 17 47.31 9 0.8 72.4 96 267.09 16 1.5 158.2 107 297.80

3 0.2 14.3 36 100.20 10 0.9 87.5 101 181.11 17 1.6 165.6 107 297.80

4 0.3 23.7 53 147.51 11 1.0 93.9 103 283.89 18 1.7 179.7 109 303.37

5 0.4 33.0 69 192.04 12 1.1 109.4 103 286.67 19 1.8 183.6 110 306.15

6 0.5 40.8 78 217.09 13 1.2 117.8 104 289.45 20 1.9 194.0 111 308.94

7 0.6 52.0 86 239.36 14 1.3 133.3 104 289.45 21 2.0 202.4 111 308.94

2 0.1 12.5 18 50.19 9 0.8 94.2 99 275.53 16 1.5 176.5 110 306.15

3 0.2 24.5 38 105.76 10 0.9 106.5 103 286.67 17 1.6 188.3 111 308.94

4 0.3 35.4 54 150.29 11 1.0 119.0 105 292.24 18 1.7 199.9 113 314.50

5 0.4 47.0 71 197.61 12 1.1 130.2 105 292.24 19 1.8 211.2 115 320.07

6 0.5 58.7 79 219.87 13 1.2 141.6 106 295.02 20 1.9 222.4 115 320.07

7 0.6 71.4 88 244.92 14 1.3 153.7 107 297.80 21 2.0 233.6 116 322.85

5 0.4 98.44 12 1.1 98.44 19 1.8 246.09

6 0.5 49.22 13 1.2 98.44 20 1.9 196.87

7 0.6 98.44 14 1.3 147.65 21 2.0 246.09

Table 3ˊ The tested torque for added magnetic fluid Serial number Current˄A˅ Magneticfield intensity˄mT˅ Scale weight˄g˅ Torque˄Nm×10-3˅ Serial number Current˄A˅ Magneticfield intensity˄mT˅ Scale weight˄g˅ Torque˄Nm×10-3˅ Serial number Current˄A˅ Magneticfield intensity˄mT˅ Scale weight˄g˅ Torque˄Nm×10-3˅

1 0 3.1 9 25.50 8 0.7 83.1 94 261.62 15 1.4 165.2 110 306.15

Table 4ˊ The measured values of yield stress for magnetic fluid Serial number Current˄A˅ Yield stress of magnetic fluid˄Pa˅ Serial number Current˄A˅ Yield stress of magnetic fluid˄Pa˅ Serial number Current˄A˅ Yield stress of magnetic fluid˄Pa˅

1 0 49.22 8 0.7 98.44 15 1.4 196.87

2 0.1 49.22 9 0.8 147.65 16 1.5 196.87

3 0.2 98.44 10 0.9 98.44 17 1.6 196.87

4 0.3 49.22 11 1.0 147.65 18 1.7 196.87

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4. Analysis on Characteristics for Nano Non-Newtonian Magnetic Fluid Magnetic fluid is a kind of colloid solution which is composed of magnetic particles and carrier liquid and surface active agent, obviously it is composed of heterogeneous and is different from the Newtonian fluid such as water and mechanical oil, it is also different from multiphase flow. Because the viscosity of Newtonian fluid is constant and the multiphase flow contains multiphase, but the steady magnetic fluid contains nano-scale magnetic particles, so it can inevitably lead to magnetic fluid to have a variety of effects of nanometer materials, especially under the action of applied magnetic field, the special effects can be shown, and magnetic fluid is called "the third fluid". There is a complex motion to the magnetic particles in the magnetic fluid, from a macro perspective, because of the different apparent viscosity for the magnetic fluid in different outside magnetic field strength 6, the magnetic fluid can be considered to be controlled by constitutive equation which different from Newtonian fluid , so it must be a non-Newtonian fluid which do not obey the law of Newton's constant viscosity, its constitutive relations is significantly different. From the testing, the magnetic fluid can maintain long-term stability and the magnetic particles are distributed evenly in the fluid, the viscosity has nothing to do with time, therefore the magnetic fluid does not belong to the time correlation non-Newtonian fluid, it has no property of elastic fluid, therefore it also does not belong to the viscoelastic non-Newtonian fluid. According to these, the magnetic fluid should belong to time independence non-Newtonian fluid. From the type of non-Newtonian fluid, it can be seen that there are two kinds of fluid for time independence, one is viscous fluid, another is plastic fluid, the difference for them is whether there is t yield stress. From the testing data in table 2 ~ table 4, when there are no liquid in the liquid storage vessel, the strength of the magnetic field varies from 2.3 mT to 202.4 mT, the required torque will vary from 0.025605 Nm to 0.30894 Nm. When there are magnetic liquid in the liquid storage vessel, the strength of the magnetic field varies from 3.1 mT to 322.85 mT, the required torque will vary from 0.0255 Nm to 0.32285 Nm, the corresponding yield stress of magnetic fluid changes from 98.44 Pa to 246.09 Pa, this shows that there is a yield stress in magnetic fluid under the action of additional magnetic field, it also shows that the magnetic fluid under the action of the applied magnetic field does not belong to pure viscous fluid but belongs to the plastic fluid. There are three kinds of plastic fluid, one is pseudoplastic fluid (shear thinning fluid), another is the dilatant fluid (shear thickening fluid), and the last is Bingham fluid. Because the viscosity of magnetic fluid under the action of additional magnetic field was variable with the variation of the strength of magnetic field and shear rate, therefore the magnetic fluid is not Bingham fluid. For magnetic fluid, under the action of applied magnetic field, the magnetic particles are magnetized by magnetization of magnetic field, the magnetized magnetic dipole chains are arranged in the direction of magnetization7, in this case, when the shear rate is improved, the chain structure will be destroyed and the shear stress will be decreased, so the magnetic fluid belongs to pseudoplastic non-Newtonian fluid. From the perspective of the type of two phase flow, magnetic fluid belongs to the solid-liquid two phase fluid because of solid magnetic particles8. In fact, any phase scale in the usual two phase flow or a multiphase flow is larger than the nanoscale magnetic particles in magnetic fluid, such as the solid phase in gas-solid and liquid-solid two phase flow, the bubble and droplets in gas-liquid and liquid-liquid two phase flow, they can reach micron grade above, so the magnetic fluid are different from the usual two phase flow. 5. Conclusion (1)The magnetic fluid in a magnetic field belongs to plastic pseudoplastic fluid in the non-Newtonian fluid, that is plastic shear thinning fluid which different from ordinary Newtonian fluids and non-Newtonian fluid, also is different from the usual two phase flow. (2) Under the action of the outer magnetic field, the magnetic particles in magnetic fluid is directional alignment, a certain resistance to external force effect is generated, the increase of the viscosity of magnetic fluid is shown, the stronger the magnetic field, the greater the viscosity. Under the action of outside magnetic field, the magnetic particles in the magnetic fluid is magnetized, the magnetized vector is consistent with the direction of external magnetic field, at the same time, because the rotation of the magnetic particles is driven by the vortex of carrier fluid, if the vector direction of carrier fluid vortex does not parallel with the direction of external magnetic field, the magnetic particles will be subject to the action of the magnetic torque, the torque will prevent the rotation of the

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magnetic particles, these will result in increases of rotational velocity contrast between carrier liquid and magnetic particles, that is the increase of two phase friction, on the macroscopic, it shows the increase of the viscosity of magnetic fluid. These are the main reasons of magnetic fluid as non-Newtonian fluid. References [1] S. C. Feng, Research on interfacial stability affected by relative speed between magnetic fluid and sealed liquid, China university of mining and technology, 2004 [2] S.H. Xu, Z. H. Wu, Influence of non-Newtonian properties of magnetofluid on the motion of the voice coil, Audio Engineering, 40(2016)23 ୉27. [3] S. C. Feng, S. j. Liu, T. G. Liu, Researching on present situation and development of nano-magnetic fluid in mechanical seal, Lubrication engineering, 163(2004)127-131 [4] J. G. Qian, Research on dynamic interface stability in magnetic fluid sealing liquid. China oniversity of mining and technology, 2009 [5] S. F. Han, Constitutive equation of non-newtonian fluid and theory of calculation analysis. Beijing: Science press, 2000 [6] R. E. Rosensweig, Magnetic fluids. International science and technology, 6ୄ1966୅48-53 [7] R. C. Ye, S. J. Liu, H. Gao, Development and problems of the preparation of magnetic fluids. Materials for Mechanical Engineering, 3(2003)33~34 [8] Y. Mitamura, T. Yano, W. Nakamura, A magnetic fluid seal for rotary blood pumps: Behaviors of magnetic fluids in a magnetic fluid seal, Bio-Medical Materials and Engineering, 23(2013)63–74