WANG Biao, XIAO Zhong-min. General Constitutive Equation of an ER Suspension Based on the Internal Variable Theory[J]. Applied Mathematics and Mechanics, 2001, 22(2): 167-181.
 Citation: WANG Biao, XIAO Zhong-min. General Constitutive Equation of an ER Suspension Based on the Internal Variable Theory[J]. Applied Mathematics and Mechanics, 2001, 22(2): 167-181.

# General Constitutive Equation of an ER Suspension Based on the Internal Variable Theory

• Rev Recd Date: 2000-11-05
• Publish Date: 2001-02-15
• A microstructural constitutive theory of ER suspensions was formulated in this investigation. The framework was based on the internal variable theory and the mechanism analysis. The ER suspension consists of fine particles with high dielectric constant and the supporting fluid. Under the action of the electric field, the polarized particles will aggregate together to form the chain-like structures along the direction of the electric field. As the size and orientation of the particle aggregates are volatile, and they adjust according to the applied electric field and strain rate, the energy conservation equation and the force equilibrium equation were thus established to determine the orientation and size of the aggregates. Following that, a three-dimensional, explicit form of the constitutive equation was derived based on the interaction energy and the dissipation function of the system. The response of the system under the action of a simple shearing load was considered and discussed in detail. It is found that the shear-thinning viscosity of an ER suspension is well approximated by the power-law ∝(Mn)-0.82.
•  [1] Tao R.Electric-field-induced phase transition in electrorheological fluids[J].Phys Rev E,1993,47:423-426. [2] Parthasarathy M,Klingenberg D J.Electrorheology:Mechanisms and Models[J].Materials Science and Engineering,1996,R17:57-103. [3] Halsey T C,Martin J E,Adolf D.Rheology of electrorheological fluid[J].Phys Rev Lett,1992,68(10):1519-1522. [4] Halsey T C.The structure and dynamics of electrorheological fluids[A].In:R Tao Ed.Proceedings of the Conference on Electrorheological Fluids[C].Singapore:World Scientific,1992,37-52. [5] Rosensweig R E.On the magnetorheology and electrorheology as states of unsymmetric stress[J].J Rheol,1995,39(1):179-192. [6] Klingenberg D J,Zukoski C F.Studies on the steady-shear behavior of electrorheological suspensions[J].Langmuir,1990,6:15-21. [7] Bonnecaze R T,Brady J F.Dynamic simulation of an electrorheological fluids[J].J Chem Phys,1992,96(3):2183-2202. [8] Bonnecaze R T,Brady J F.Yield stresses in electrorheological fluids[J].J Rheol,1992,36(1):73-115. [9] Ginder J M,Ceccio S L.The effect of electrical transients on the shear stresses in electrorheological fluids[J].J Rheol,1995,39(1):211-234. [10] Conrad H,Chen Y,Sprecher A F.The strength of electrorheological fluids[A].In:R Tao Ed.Proceedings of the Conference on Electrorheological Fluids[C].Singapore:World Scientific,1992,195-218. [11] Bossis G,Lemaire E,Volkova O.Yield stress in magnetorheological and electrorheological fluids:A comparison between microscopic and macroscopic structural models[J].J Rheol,1997,,41(3):687-704. [12] Martin J E,Odinek J.Aggregation,fragmentation,and the nonlinear dynamics of electrorheological fluids in oscillatory shear[J].Phys Rev Lett,1995,75(15):2827-2830. [13] Jordan M,Schwendt A,Hill D A,et al.Zeolite-based electrorheological fluids:Testing,modeling and instrumental artifacts[J].J Rheol,1997,41(1):75-92. [14] Rice J R.Inelastic constitutive relations for solids:An internal-variable theory and its application to metal plasticity[J].J Mech Phys Solids,1971,19:433-455. [15] Ziegler H.Introduction to Thermomechanics[M].the second,revised edition.Amsterdam:North-Holland Publishing Company,1983. [16] Landau L D,Lifshitz E M.Pitaevskii.Electrodynamics of Continuous Media[M].the second edition.Chapters 1 and 2.Oxford:Pergamon Press,1984. [17] Eringen A C,Maugin G A.Electrodynamics and ContinuaⅠ,Ⅱ[M].New York:Springer-Verlag,1990. [18] Bossis G,Clercx H,Grasselli Y,et al.Theoretical analysis of field induced structures in ER and MR fluids[A].In:R Tao,G D Roy Eds.Electrorheological Fluids[C].Singapore:World Scientific,1993,153-171. [19] Happel J,Brenner H.Low Reynolds Number Hydrodynamics[M].Chapter 9,Dordrecht:Martinus Nijhoff Publishers,1986. [20] Ginder J M,Davis L C.Viscoelasticity of electrorheological fluids:Role of electrostatic interactions[A].In:R Tao,G D Roy Eds.Electrorheological Fluids[C].Singapore:World Scientific,1993,267-282. [21] Shulman Z P,Kordonsky V I,Zaltsgendler E A,et al.Structure,physical properties and dynamics of magnetorheological suspensions[J].Int J Multiphase Flow,1986,12(6):935-955. [22] Takimoto Jun-Ichi.Computer simulation of model electrorheological fluids[A].In:R Tao Ed.Proceedings of the Conference on Electrorheological Fluids[C].Singapore:World Scientific,1992,53-58. [23] Kim S,Karrila S J.Microhydrodynamics:Principles and Selected Applications[M].Part Ⅱ,Butterworth-Heinemann Series in Chemical Engineering,Boston:Butterworth-Heinemann,1991.

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