Modeling micropolar electrorheological fluids

• Autorzy: Eckart W. , Ruzicka M.
• Języki publikacji: EN

Abstrakty

EN

In general, electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to an electric field, the particles form structures which have essentially the direction of the electric field, resulting in a higher effective viscosity. Of considerable interest is the dependence of this effect on the direction of the electric field. Towards this end, we propose a micropolar theory including appropriate balance and constitutive equations for these suspensions essentially based on the works of Eringen. An appropriate non-dimensionalization is carried out which combines procedures of Eringen for micropolar fluids, on the one hand, and Eckart and Růžička for electrorheological fluids on the other. We then derive constitutive equations for the Cauchy stress and the couple stress and discuss the restrictions imposed on them by the second law of thermodynamics using scaling arguments. To illustrate the enhanced possibilities of micropolar electrorheology, a simple constitutive model which is linear in the strain rate is discussed in a study of a viscometric flow. We finally show that the velocity profile (hence the flow rate) may strongly depend on the direction of the electric field.

Słowa kluczowe

EN

micropolar theory; electrorheological fluids; entropy inequality; non-dimensionalization; constitutive theory; viscometric flow

PL

reologia; mechanika płynów

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2006
• Tom: Vol. 11, no 4
• Strony: 813--844
• Opis fizyczny: Bibliogr. 45 poz., wykr.

Twórcy

autor

Eckart W.

autor

Ruzicka M.

• Justinus-Kerner-Str. 1, 71636 Ludwigsburg, GERMANY,

Bibliografia

• Bloodworth R. (1994): Electrorheological fluids based on polyurethane dispersions. In: Electrorheological Fluids, ed. by R. Tao and G.D. Roy. World Scientific, Singapore, pp.67-83.
• Bloodworth R. and Wendt E. (1996): Materials for ER-fluids. - Int. J. Mod. Phys. B 23/24(10), pp.2951-2964.
• Brunn P.O. and Abu-Jdayil B. (1998): Fluids with transverse isotropy as models for electrorheological fluids. - Z. Angew. Math. Mech., vol.78, No.2, pp.97-107.
• Ceccio S.L. and Wineman A.S. (1994): Influence of orientation of electric field on shear flow of electrorheological fluids. J. Rheol., vol.38, No.3, pp.453-463.
• Chandna O.P. and Kaloni P.N. (1976): Steady plane flows of cosserat fluids. - Siam J. Appl. Math., vol.31, No.4, pp.686-698.
• Coleman B.D. and Noll W. (1963): The thermodynamics of elastic materials with heat conduction and viscosity. - Arch. Rat. Mech. Anal., vol.13, pp.167-178.
• Eckart W. (2000): Theoretische Untersuchungen von elektrorheologischen Flüssigkeiten bei homogenen und inhomogenen elektrischen Feldern. - PhD-thesis TU Darmstadt. Shaker, Aachen.
• Eckart W. (2000): Phenomenological modeling of electrorheological fluids with an extended Casson-model. - Continuum Mech. Thermodyn., vol.12, No.5, pp.341-362.
• Ericksen J.L. (1960): Theory of anisotropic fluids. - Trans. Soc. Rheol., vol.4, pp.29-39.
• Ericksen J.L. (1961): Conservation laws for liquid chrystals. - Trans. Soc. Rheol., vol.5, pp.23-34.
• Ericksen J.L. (1991): Liquid Crystals with variable degree of orientation. - Arch. Rat. Mech. Anal., vol.113, pp.97-120.
• Eringen A.C. (1966): Theory of micropolar fluids. - Journal of Mathematics and Mechanics, vol.16, No.1, pp.1-18.
• Eringen A.C. (1980): Theory of anisotropic micropolar fluids. - Int. J. Eng. Sci., vol.18, pp.5-17.
• Eringen A.C. (1997): A unified continuum theory of electrodynamics of liquid crystals. - Int. J. Eng. Sci., vol.35, No.12/13, pp.1137-1157.
• Eringen A.C. (1999): Microcontinuum Field Theories. - I/II New York: Springer.
• Eringen A.C. and Maugin G.A. (1989): Electrodynamics of Continua I/II. - New York: Springer.
• Grot R.A. (1976): Relativistic Continuum Physics: Electromagnetic Interactions. In: Continuum Physics (ed. by A.C. Eringen). - Academic Press, pp.130-221.
• Halsey T.C., Martin J.E. and Adolf D. (1992): Rheology of electrorheological fluids. - Phys. Rev. Letters, vol.68, pp.1519-1522.
• Happel J. and Brenner H. (1965): Low Reynolds Number Hydrodynamics. - Prentice Hall.
• Hutter K. (1975): On thermodynamics and thermostatics of viscous thermoelastic solids in the electromagnetic fields. - A Lagrangian Formulation. Arch. Rat. Mech. Anal., vol.58, pp.339-368.
• Hutter K. (1977): A thermodynamic theory of fluids and solids in the electromagnetic fields. - Arch. Rat. Mech. Anal., vol.64, pp.269-298.
• Hutter K. and van de Ven A.A.F. (1978): Field Matter Interactions in Thermoelastic Solids. - Lecture Notes in Physics. Springer Berlin Heidelberg.
• Jackson J.D. (1983): Klassische Elektrodynamik. - Berlin: Walter de Gruyter.
• Kafadar C.B. and Eringen A.C. (1971): Micropolar media - I. The classical theory. - Int. J. Eng. Sci., vol.9, pp.271-305.
• Kirwan Jr. A.D. (1986): Boundary Conditions for Micropolar Fluids. - Lett. Appl. Eng. Sci., vol.24, No.7, pp.1237-1242.
• Leslie F.M. (1968): Some constitutive equations for liquid Crystals. - Arch. Rat. Mech. Anal., vol.28, pp.265-283.
• Leslie F.M. (1979): On thermodynamics of polar fluids. - Arch. Rat. Mech. Anal., vol.70, No.189-202.
• Liu I.S. (1972): Method of Lagrange multipliers for exploitation of the entropy principle. - Arch. Rat. Mech. Anal., vol.46, pp.131-148.
• Liu I.S. (1996): On entropy flux-heat flux relation in thermodynamics with Lagrange multipliers. - Cont. Mech. Thermodyn., vol.8, pp.247-256.
• Liu I.S. (2002): Continuum Mechanics. - New York: Springer.
• Liu I.S. and Müller I. (1972): On the thermodynamics and thermostatics of fluids in electromagnetic fields. - Arch. Rat. Mech. Anal., vol.46, pp.149-176.
• Maugin G.A. and Eringen A.C. (1977): On the equations of the electrodynamics of deformable bodies of finite extent. - J. Mécanique, vol.16, pp.100-147.
• Müller I. (1985): Thermodynamics. - Pitman Publishing.
• Müller I. and Ruggeri T. (1993): Extended Thermodynamics. - New York: Springer.
• Nečas J. and Šilhavý M. (1991): Viscous multipolar fluids. - Quart. Appl. Math., vol.49, pp.247-265.
• Pao Y.H. (1978): Electromagnetic forces in deformable continua. - Mechanics Today (ed. by S. Nemat-Nasser), Pergamon Press, vol.4, No.209-306.
• Parthasarathy M. and Klingenberg D.J. (1996): Electrorheology: mechanisms and models. - Materials, Science and Engineering R, reports; vol.17, No.2, pp.57-103.
• Rajagopal K.R. and Růžička M. (1996): On the modeling of electrorheological materials. - Mech. Research Comm., vol.23, pp.401-407.
• Rajagopal K.R. and Wineman A.S. (1992): Flow of electrorheological materials. - Acta Mechanica, vol.91, pp.57-75.
• Růžička M. (1992): Mathematical and physical theory of multipolar viscoelasticity. - Bonner Mathematische Schriften, 233.
• Růžička M. (2000): Electrorheological Fluids: Modeling and Mathematical Theory. - Lecture Notes in Mathematics, 1748. Springer Berlin Heidelberg.
• Stokes V.K. (1984): Theories of Fluids with Microstructure. - Berlin, Heidelberg: Springer.
• Tanahashi T. and Okanaga H. (1989): Electromagnetic interaction on micropolar fluids. - JSME, Series II, vol.32, No.4, pp.508-515.
• Truesdell C. and Noll W. (1965): The Non-Linear Field Theories of Mechanics. - Handbuch der Physik, III/3. New York: Springer.
• Wunderlich T. (2000): Der Einfluß der Elektrodenoberfläche und der Strömungsform auf den elektrorheologischen Effekt. - PhD-thesis Univ. Erlangen-Nürnberg.