摘要
电流变液是一种新型智能材料,在外加电场作用下呈现出屈服应力流体特性,自20世纪40年代以来,电流变液的研究曾一度处于低谷,但随着材料科学的发展,电流变液的潜在应用领域越来越广阔,近20年来电流变液的研究受到越来越多的关注。
本文首先从微观的角度,分析电流变链在Poiseuille流动中的受力以及变形,分析过程中推导了矩形截面管内Poiseuille流动速度分布的Galerkin近似解,并采用理论力学软索模型对电流变变链的受力进行分析,从而避免了点偶极子近似在粒子相距较近情况下引起的误差。分析结果可作为进一步讨论电流变液屈服应力以及临界电场强度的基础。
其次本文从运用的角度,在考虑电流变液屈服特性的前提下,分析了两种典型电流变器件(圆桶型电流变离合器和平板电流变阀)稳态以及瞬态动力学特性。对圆桶型电流变离合器动力学特性的分析发现,在离合器关闭时突加电场瞬间,流场中并未瞬时产生未屈服区,而存在滞后时间,且随外加电场强度的增大而减小;电流变液屈服应力方程中,参数以2.0为界,和时,离合器动力学特性具有显著区别。
论文第三部分对电流变液非零压力梯度平板剪切流动的稳定性进行了分析,提出流场对屈服应力达到饱和的概念;并得出平板壁面剪切运动以及电流变液屈服应力的提高,都将使流动稳定性增强的结论。
在论文第四部分中,对同心圆桶间宾汉流体螺旋T-C(Taylor-Couette)流动的稳定性进行分析,并采用有限体积法对失稳后的螺旋T-C流动,即螺旋T-V(Taylor-vortex)流动进行了数值模拟。研究发现对于螺旋T-C流动,屈服应力对流动稳定性具有双重影响;外桶旋转始终使流动趋于稳定;内桶轴向剪切运动能够增强流动对轴对称小扰动的抑制能力,但对非轴对称小扰动情况却不相同,即内桶轴向剪切运动仅对流动稳定性起有限增强作用;此外内、外桶半径比(0到1之间)增大,也将使流动趋于稳定。通过对螺旋T-V流动的数值模拟发现,屈服应力增大将使流场中Taylor涡减弱,且当屈服应力足够大时,螺旋T-V流动重新恢复螺旋T-C流动;内桶轴向剪切运动在使Taylor涡发生轴向迁移的同时也使其强度减弱。
Electrorheological fluid (ERF) is a new kind of "smart" material. When extra electric field is applied, it behaves just like a yield-stress fluid. The reports of research with ERF appeared sporadically since it was firstly reported in 1940's. But recently, with the development of materials science, the potential application region of ERF becomes more and more wide. And the number of investigations increased dramatically and researchers begin to pay more and more attentions to it.
In present dissertation, firstly an analytical study on the force and deformation of an ER single chain under Poiseuille flow is presented from the point of microscopic view. An approximate solution of the Poiseuille flow in a tube with rectangular cross is derived from Galerkin approach. The balance equation of moment for the ER chain is established to avoid using point-dipole model, which is not accurate enough in the case that dielectric particles are adjacent to each other. The result can be used in further study about the yield-stress and critical electric field strength.
Secondly, the steady and transient characteristics of concentric cylinder ER clutch and plane ER valve are studied with the consideration of yield. It can be found that when the extra electric field is suddenly applied, non-yield region in the clutch dose not generate synchronously. There is a retardation time which becomes shorter while the extra electric field becomes stronger. The demarcation point of, which is the parameter in ERF's yield stress equation, is 2.0. For, the dynamic characteristics of the clutch are remarkably different from those for.
Thirdly, the linear stability of plane shearing flow with non zero pressure gradient is studied. The conception of yield stress saturation is proposed. It can be found that the flow is stabilized by both plane shearing and the increment of yield stress.
The study about the linear stability of spiral Taylor-Couette flow is the fourth part of the dissertation. The numerical simulation of the Taylor-vortex
flow, which is the unstable pattern of the Taylor-Couette flow, is also achieved here. It can be found that yield stress plays a dual role in fluid stability and the rotation of the outer cylinder has stabilizing effect on the flow. The effect of the inner cylinder's sliding is slightly stabilizing on the disturbance of axisymmetric mode but destabilizing on the disturbance of non-axisymmetric mode. So the inner cylinder sliding just has a finite stabilizing effect on the spiral Taylor-Couette flow. Besides these, the increment of the radius ratio of the inner and outer cylinder also has stabilizing effect on the flow. It can be found from the analysis of the Taylor-vortex flow, that both the increment of yield stress and the sliding of the inner cylinder have the effect of weakening Taylor vortex. When the yield stress is high enough, the flow pattern will evolve from Taylor-vortex flow to Taylor-Couette flow and the Taylor vortex has a migration movement along the axial because of the existence of sliding.
引文
Abu-Jdayil B., Brunn P.O., Effect of Electrode Morphology on the Slit Flow of an Electrorheological Fluid, J. Non-Newtonian Fluid Mech., 1996,63:45-61
Al-Mubaiyedh U. A., Sureshkumar R. and khomami B., Linear Stability of Viscoelastic Taylor-Couette Flow: Influence of Fluid Rheology and Energetics. J. Rheol. 2000, 44(5):1121-1138
Ali M.E., Weidman P.D., On the Stability of Circular Couette Flow with Radial Heating, J. Fluid Mech., 1990, 220:53-84
Ali M.E., Weidman P.D., On the Linear Stability of Cellular Spiral Couette Flow. Phys. Fluids A 1993, 5(5):1188-1199
Anderech D.C., Liu S. S., Swinney H.L., Flow Regimes in a Circular Couette System with Independently Rotating Cylinders. J. Fluid Mech. 1986, 164:155-183
Ashrafi N., Khayat R.E., A Low-Dimensional Approach to Nonlinear Plane-Couette Flow of Viscoelastic Fluids, Phys. Fluids, 2000, 12(2):345-365
Atkin R. J., Bullough W. A., Xiao Shi, Solution of the Constitutive Equations for the Flow of an Electrorheological Fluid on Radial Configurations, J. Rheol., 1991, 35 (7):1441-1461
Atkin R.J., Xiao Shi, Bullough W.A., Effect of Non-Uniform Field Distribution on Steady Flows of an Electrorheological Fluid, J. Non-Newtonian Fluid Mech. 1999, 86:119-132
Atkinson C., EI-Ali K., Some Boundary Value Problem for the Bingham Model. J. Non-Newtonian fluid Mech. 1992, 41:339-363
Atten P.,Zhu K.-Q.,The 5th International Conference on ER Fluids, MR Suspensions and Associated Technology, Sheffield, 1995
Batchelor G.K., The Stress System in a Suspension of Force-Free Particles, J. Fluid Mech., 1970, 41:545-570
Barenghi C. F., Jones C. A., Modulated Taylor-Couette Flow, J. Fluid Mech. 1989, 208:127-160
Barnes H. A., Walters K., Original Contributions The Yield Stress Myth?, Rheol. Acta, 1985, 24:323-326
Barenghi C.F., Jones C.A., Modulated Taylor-Couette Flow, J. Fluid Mech. 1989,208:127-160
Bercovier M., Engelman M., A Finite-Element Method for Incompressible Non-Newtonian Flows, J. Compt. Phys., 1980, 36:313-326
Beris A.N., Armstrong R.C., Brown R.A., Spectral/Finite Element Calculation of the Flow of a Maxwell Fluid Between Eccentric Cylinders, J. Non-Newtonian Fluid Mech., 1987, 22:129-167
Binyamin S., Totally Positive Differential Systems, Pacific J. Math., 1970.32(1):203-229
Bird R.B., Dai G.C., Yarusso B.J., The Rheological and Flow of Viscoplastic Materials, Rev. Chem. Eng., 1983,1:1-70
Block H., Kelly J.P., Electrorheological Fluids, GB Patent 2 170 510, 1986
Brooks D.A, High Performance Electrorheological Dampers, Inter. J. Modern Phys. B, 1999,13 Nos. 14,15&16:2127-2134
Bullough W.A., Johnson A.R, Tozer R, Makin J., Methodology, Performance and Problems in ER Clutch Based Positioning Mechanisms, Inter. J. Modern Phys. B, 1999,13 Nos. 14,15&16:2101-2108
Burgess S.L., Wilson S.D.R., Unsteady Shear Flow of a Viscoplastic Marterial, J. Non-Newtonian Fluid Mech., 1997, 72:87-100
Ceccio S.L., Wineman A.S., Influence of Orientation of Electric Field on Shear Flow of Electrorheological Fluids, J. Rheol., 1994,38(3),453-463
Chen T.J., Zhang X.S., Zitter. R.N.,Tao R., Deformation of an Electrorheological Chain under Flow. Journal of Applied Physics,1993, 74(2):942~944
Chen Y., Sprecher A.F., Conrad H., Electrostatic Particle-Particle Interactions in Electrorheological Fluids, J. Appl. Phys.1991, 70:6796-6803
Chida K., Sakaguchi S., Wagatsuma M., Kimura T., High-Speed Coating of Optical Fibres with Thermally Curable Silicone Resin Using a Pressurized Die, Electronic Lett., 1982, 18:713-715
Choi S.-B., Control Characteristics of ER Devices, Inter. J. Modern Phys. B, 1999,13 Nos. 14,15&16:2160-2167
Chossat P., looss G., The Couette-Taylor Problem,, Springer, 1994
Comparini E., A One-Dimensional Bingham Flow, J. Math. Anal. Appl., 1992, 169:127-139
Conrad H., Chen Y., Sprecher A.F., The Strength of ER Fluids, Int. J. Modern Physics. B, 1992, 6(15,16):2575-2594
Crochet M.J., Pilate G., Plane Flow of a Fluid of Second Grade through a Contraction,, J. Non-Newtonian Fluid Mech., 1976, 1:247-258
Crochet M.J., Davies A.R., Walters K., Numerical Simulation of Non-Newtonian Flow, Elsevier Amsterdam,1984
Davey A, On the Numerical Solution of Difficult Eigenvalue Problem, J. Comput Phys, 1977, 24:331-338
Davis S.H., The Stability of Time -Periodic Flows, Ann. Rev. Fluid Mech., 1976, 8:27-74
DiPrima, R.C., Swinney,H.L, Instability and Transition in Flow Between Concentric Rotating Cylinders In Hydrodynamic Instabilities and the Transition to Turbulence, Springer, 1981
Dorier C., Tichy J., Behavior of a Bingham-Like Viscous Fluid in Lubrication Flows, J. Non-Newtonian Fluid Mech., 1992, 45:291-310
Drazin, P.G,Reid W . H,流体动力稳定性,宇航出版社,1990
Duclos T. G. An Externally Tunable Hydraulic Mount Which Uses Electro - Rheological Fluid, SAE Noise and Vibration Conference and display, April 28-30,1987
Evans I.D., Letter to the Editor: On the Nature of the Yield Stress, J. Rheol. 1992, 36(7):1313-1317
Frigaard I. A., Howison S. D. and Sobey I. J., On the Stability of Poiseuille Flow of a Bingham Fluid, J. Fluid Mech. 1994, 263:133-150
Gans R.F., On the Flow of a Yield Strength Fluid through a Contraction, J. Non-Newtonian Fluid Mech., 1999, 81:183-195
Gulley G. L., Tao R., Static Shear of Electrorheological Fluids, Phys. Review E, 1993, 48:2744-2751
Gupta G.K., Hydrodaynamic Stability of the Plane Poiseuille Flow of an Electrorhological Fluid, Inter. J. Non-linear Mech., 1999, 34:589-602
Hall P., The Stability of Unsteady Cylinder flows, J. Fliud Mech., 1975,67:29-63
Hartnett J.P., Hu R.Y.Z., Technical Note: The Yield Stress an Engineering Reality, J. Rheol., 1989, 33:671-679
Howard S., Constitutive Equations for Electrorheological Fluids Based on the Chain Model, J. Phys. D: Appl. Phys., 2000, 33:1625-1633
Hu H.C., Kelly R. E., Effect of a Time-Periodic Axial Shear Flow upon the Onset of Taylor Vortices. Physical Review E , 1995, V51 No.4:3242-3251
Huang X., Phan-Thian N., Tanner R.I., Viscoelastic Flow between Eccentric Rotating Cylinders: Unstructured Control Volume Method, J. Non-Newtonian Fluid Mech. 1996, 64:71-92
Jang Y.J, Suh M. S., Yeo M.S., The Numerical Analysis of Channel Flows of ER Fluid. J. Intel. Material Sys. and Struc. 1996, l7:604-609
Junji F., Masamichi S., New Actuators Using ER Fluid and Their Applications to Force Display Devices in Virtual Reality and Medical Treatments, Inter. J. Modern Phys. B, 1999,13 Nos. 14,15&16:2151-2159
Joseph D.D, Stability of Fluid Motions, Springer,1976
Klingenberg D.J., Frank V.S., Zukoski C.F. The Small Shear Rate Response of electrorheological Suspension 1 Simulation in the point-Dipole limit, J. Chem. Phys., 1991, 94 No. 9:6171-6175
Lipscomb G.G., Denn M.M., Flow of Bingham Fluids in Complex Geometries, J. Non-Newtonian Fluid Mech., 1984, 14:337-346
李兆敏,蔡国琰,非牛顿流体力学,石油大学出版社,1998年4月。
Lueptow R.M., Docter A., Min K., Stability of Axial Flow in an Annulus with a Rotating Inner Cylinder. Phys. Fluids A, 1992, 4(11): 2446-2455
Lukkarinen A., Kaski K., Computational Studies of Compressed and Sheared Electrorheological Fluid, J. Appl. D., Appl. Phys., 1996,29:2729-2732
Luo X.-L, A Control Volume Approach fot Integral Viscoelastic Models and Its Application to Contraction Flow of Polymer Melts, J. Non-Newtonian Fluid Mech., 1996, 64:173-189
Marques F., Lopez J. M., Taylor-Couette Flow with Axial Oscillations of the Inner Cylinder: Floquet Analysis of the Basic Flow. J. Fluid Mech. 1997, 348: 153-175
Mei C.C., Yuh M., Slow Flow of a Bingham Fluid in a Shallow Channel of Finite Width, J. Fluid Mech., 2001, 431:135-159
Meseguer A., Marques F., On the Competition between Centrifugal and Shear Instability in Spiral Couette flow, J. Fluid Mech. 2000, 402:33-56
Missirlis K.A., Assimacopoulos D., Mitsoulis E., A Finite Vilume Approach in the Simulation of Viscoelastic Expansion Flows, J. Non-Newtonian Fluid Mech.,1998, 78:91-118
Moser R.D., Moin P., Leonard A., A Spectral Numerical Method for the Navier-Stokes Equations with Applications to Taylor-Couette Flow. J. Comp. Phys. 1983, 52:524-544
Mott J.E, Joseph D.D., Stability of Parallel Flow between Concentric Cylinders, Phys. Fluids, 1968, 11:2065-2073
Murray B.T., Mcfadden G.B., Coriell S.R., Stabilization of Taylor-Couette Flow Due to Time-Periodic Outer Cylinder Oscillation, Phys. Fluids A, 1990, 2:2147-2156
Nguyen Q.D., Boger D.V., Measuring the Flow Propertied of Yield Stress Fluids, Annu. Rev. Fluid Mech.,1992,24:47-88
NG B.S., Reid W.H., The Compound Matrix Method for Ordinary Differential Systems, J. Comp. Phys., 1985, 58:209-228
Ollis D.F., Pelizzetti E., Serpone N., Photocatalyzed Destruction of Water/Contaminants, Environ. Sci. Technol., 1991,25:1523-1529
Oliveira P.J., Pinho F.T., Pinto G.A., Numerical Simulation of Non-Linear Elastic Flows with a General Collocated Finite-Volume Method, J. Non-Newtonian Fluid Mech., 1998, 79:1-43
Orszag S.A., Galerkin Approximations to Flows within Slabs, Spheres, and Cylinders, Phys. Rev. Lett., 1971a, 26:1100-1103
Orszag S.A., Accurate Solution of the Orr-Sommerfeld Stability Equation, J. Fluid Mech. 1971b, 50:689-703
Papanastasiou T.C., Flows of Materials with Yield, J. Rheol., 1987, 31(5):385-404
彭杰,电流变器件中电流变液的流动及动力学问题研究,清华大学硕士论文,1999
Perera M.G.N., Walters K., Long-Range Memory Effects in Flows Involving Abrupt Changes in Geometry, Part ⅠFlows Associated with L-Shape and T-Shape Geometries. J. Non-Newtonian Fluid Mech., 1977, 2:49-81
Perera M.G.N., Walters K., Long-Range Memory Effects in Flows Involving Abrupt Changes in Geometry, Part ⅡThe Expansion-Contraction-Expansion Problem, J. Non-Newtonian Fluid Mech., 1977, 2:191-204
Petek,N.K An Electronically Controlled Shock Absorber Using Electrorheological Fluid, SAE TECHNICAL PAPER SERIES 920275, 1992, February:24-28
Piau J.M., Flow of a Yield Stress Fluid in a Long Domain. Application to Flow on an Inclined Plane, J. Rheol., 1996,40(4):711-723
Philips R.J., Armstrong R.C., Brown R.A, A Constitutive Equation for Concentrated Suspensions that Accounts for Shear-Induced Particle Migration, Phys. Fluids A, 1992, 4(1):30-40
Rajagopal K.R., Wineman A., Flow of Electrorheological Materials, Acta Mechnica, 1992, 91:57-75
Rajagopal K.R., Wineman A., a Constitutive Equation for Non-linear Electrorheological Solids, Acta Mechanica, 1999, 135:219-228
Ray R.N., Samad A., Chaudhury K., Hydromagnetic Stability of Plane Poiseuille Flow of Oldroyd Fluid, Acta Mechanica 2000,143:155-164
Sadeghi V.M., Higgins B.G., Stability of Sliding Couette-Poiseuille Flow in an Annulus Subject to Axisymmetric and Asymmetric Disturbances, Phys. Fluids A, 1991,3:2092-2104
Schurz J., The Yield Stress an Empirical Reality, Rheol. Acta, 1990, 29(2):170-171
Schurz J., Letter to the Editor: A Yield Value in a True Solution? J. Rheol., 1992, 36(7):1319-1323
Sekimoto Ken, An Exact Non-Stationary Solution of Simple Shear Flow in a Bingham Fluid, J. Non-Newtonian Fluid Mech., 1991, 39:107-113
Sekimoto Ken, Motion of the Yield Surface in a Bingham Fluid with a Simple Shear Flow Geometry, J. Non-Newtonian Fluid Mech., 1993, 46:219-227
Slavtchev S., Miladinova S., Kalitzova-Kurteva P. Unsteady Film Flow of Power-Law Liquids on a Rotating Disk, J. Non-Newtonian Fluid Mech., 1996,66:117-125
Spasche R.M., Pattern Formation in Viscous Flows: the Taylor-Couette Problem and Rayleigh-Benard Convection. Basel; Boston;Berlin;Birkhauser,1999
Sproston J.L, Rigby S.G., Williams E.W., Stanway R, A Numerical Simulation of Electrorheological Fluids in Oscillatory Compressive Squeeze-Flow, J. Phys. D: Appl. Phys., 1994, 27:338-343
孙德军,童秉纲,尹协远,Orr-Sommerfeld方程数值解法中的复数广义矩阵特征值问题,力学学报,1995,27(5):631-635
Takeshi Tomiuga, Koji Okamoto, Haruki Madarame, Visualization Study on Chain Structure in Electrorheological Fluids, Inter. J. Modern Phys. B, 1999,13 Nos. 14,15&16:1783-1790
Tam W.Y., Yi G.H., Wen W.J., Ma H.R, Loy M.M.T., Sheng P., New Electrorheological Fluid: Theory and Experiment, Phys. Review Lett., 1997, 78(15):2987-2990
Tang X., Li W.H.,Wang X.J.,Zhang P.Q., Structure Evolution of Electrorheological Fluids under Flow Conditions, Int. J. Modern Physics B, 1999, 13 Nos.14,15&16:1806-1813
Tanner R.I., Bush M.B., Phan-Thien N., A Boundary Element Investigation of Extrude Swell, J. Non-Newtonian Fluid Mech., 1985, 18:143-162
Tao R, Sun J.M.,, Three-Dimension Structure of Induced ER Solid, Phys. Rev. Letters, 1991, 67(3):398-401
Tao R., Sun J.M., Ground State of ER Fluids form Monte Carlo Simulation, Phys. Rev. A, 1991, 44(10):6181-6184
Tao R., Jiang Qi, Simulation of Structure Formation in an Electrorheological Fluid, Phys. Review Lett., 1994, 73(1):205-208
Taylor A.J., Wilson S.D.R., Conduit Flow of an Incompressible , Yield-Stress Fluid, J. Rheol., 1997,41(1):93-101
Thurston G.B., Gaertner, Viscoelasticity of Electrorheological Fluids during Oscillatory Flow in a Rectangular Channel, J. Rheol., 1991, 35(7):1327-1343
Tian Y., Meng Y.G., Wen S.Z., ER Fluid Based on Zeolite and Silicone Oil with High Strength, Materials Letters, 2001,50(2-3):120-123
Tichy J A., Hydrodynamic Lubrication Theory for the Bingham Plastic Flow Model, J. Rheol., 1991, 85:477-496
Tichy J A., Behaviour of a Squeeze Film Damper with an Electrorheological Fluid, Tribology Transactions, 1993,36:127-133
Toll S., Manson J.-A.E., Dynamics of a Planar Concentrated Fiber Suspension with Non-Hydrodynamic Interaction, J. Rheol., 1994,38(4):985-997
Vovey G.H., Stanmore B.R., Use of The Parallel-Plate Plastometer for The Characterisation of Viscous Fluid with a Yield Stress, J. Non-Newtonian Fluid Mech. 1981,8:249-260
Vladimir O., Dissipation of Energy in a Concentric ER clutch and Its Refined Quasi-Static Model, Inter. J. Modern Phys. B, 1999,13 Nos. 14,15&16:2109-2118
Wang Y., Letter to the Editor: Comment on "Conduit Flow of an Incompressible, Yield-Stress Fluid"[J. Rheol. 41,93-101(1997)], J. Rheol., 1997, 41(6):1387-1390
Walton I.C., Bittleston S.H., The Axial Flow of a Bingham Plastic in a Narrow Eccentric Annulus, J. Fluid Mech., 1991,222:39-60
Wen W.J., Men S.Q., Lu K.Q., Structure-Induced Nonlinear Dielectric Propertied in Electrorheological Fluids, Phys, Review E, 1997, 55(3):3015-3020
Weisberg A.Y., Kevrekidis I.G., Smits A.J., Delaying Transition in Taylor-Couette Flow with Axial Motion of the Inner Cylinder, J. Fluid Mech., 1997,348:141-151
魏宸官,电流变技术-机理、材料、工程应用,北京理工大学出版社,2000
White F.M. Viscous Fluid Flow. McGraw-Hill Book Company 1974
Whittle M., Atkin R.J., Bullough W.A., Fluid Dynamic Limitation on the Performance of an Electrorheological Clutch, J. Non-Newtonian Fluid Mech., 1995, 57:61-81
Whittle M., Atkin R.J., Bullough W.A., Dynamic of an Electrorheological Value, Int. J. Modern Phy. B, 1996, 10 Nos. 23 & 24:2933-2950
Whittle M., Atkin R.J., Bullough W.A., Dynamics of a Radial Electrorheological Clutch, Inter. J. Modern Phys. B, 1999,13 Nos. 14,15&16:2119-2126
Whittle M., Firoozian R., Peel D.J., Bullough W.A., Decompositions of the Pressure Response in a Valve Controlled ER System, J. Intelligent Mater. Syst. Str., 1994,5:105-111
Wilkinson J.H., Cantab M.A.,SC. D.,The Algebraic Engenvalue Problem, Oxford University Press,1965
Williams E.W., Rigby S.G. Sproston J.L., Stanway R., Electrorheological Fluids Applied to an Automotive Engine Mount, J. Non-Newtonian Fluid Mech., 1993, 47:221-238
Wilson S. D.R., Squeezing Flow of a Bingham Material, J. Non-Newtonian Fluid Mech. , 1993,47:211-219
吴承伟,李勇,陈浩然,电流变智能Smart轴承稳态性能分析,大连理工大学学报,1995,36(4):402-407
Xue S.C., Phan-Thien N., Tanner R.I., Numerical Study of Secondary Flows of Viscoelatic Fluid in Strainght Pipes by a Implicit Finite Volume Method, J. Non-Newtonian Fluid Mech.,1995, 59:191-213
Yasufumi Otsubo, Kazuya Edamura, Creep Behavior of Electrorheological Fluids, J. Rheol. 1994, 38(6):1721-1733
Yasufumi Otsubo, Masahiro Sekine, Shingo Katayama, Electrorheological Properties of Silica Suspensions, J. Rheol., 1992,36(3):479-497
赵爱红,张培强,庄礼贤,电流变液在工程中的应用,机械,1997,24(5):47-50
周鲁卫,叶聚丰,唐颐,电流变液的研究进展及应用前景,物理,1994, 4:212-218
ZHU K.Q., A Study on the Superconvergence of Multhopp's Discretization in Vortex-Lattice Methods, Fluid Dynamics Research, 1992, 9:73-79
朱克勤,Tao R.,电流变液和电流变效应。力学进展,1994, 24:154-162
Zhang Z., Zhu K.Q., Characteristics of Electroeheological Fluid Flow in Journal Bearings, Chin. Phys. Lett., 2002,19(2):273-275