Abstract
Electrorheological (ER) fluids are a class of materials whose rheological properties transform from liquid-like to solid-like upon the application of an external electric field. We consider the simplest model of ER fluids: a collection of identical dielectric solid spheres dispersed in a liquid. By transforming the problem to one of effective dielectric constant optimization, it is shown that the ground state of the ER fluid and its various electrical and rheological properties may be calculated from first principles through the Bergman-Milton representation. In particular, we obtain the upper bounds on the dielectric constant, the shear modulus, and the static yield stress of the ER fluid in its high field (solid) state.
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References
W. M. Winslow, J. Appl. Phys. 20, 1137 (1949).
R. Tao and J. M. Sun, Phys. Rev. Lett. 67, 398 (1991); R. Tao and J. M. Sun, Phys. Rev. A 44, R6181 (1991).
D. J. Bergman, in “Solid State Physics,” vol. 46, edited by H. Ehrenreich and D. Turnbull, Academic Press, 1992, p.147; G. W. Milton, Appl. Phys. A 26, 1207 (1981); G. W. Milton, J. Appl. Phys. 52, 5286 (1981).
V. Heine, in “Solid State Physics,” vol. 35, edited by H. Ehrenreich, F. Seitz and D. Turnbull, Academic Press, 1980, p.1.
G. Bossis, H. Clercx, Y. Grasselli and E. Lemaice, in “Electrorheological Fluids,” edited by R. Tao and G. D. Roy, World Scientific, 1994, p.153; H. Clercx and Bossis, Phys. Rev. E 48, 2721 (1993).
L. C. Davis, Appl. Phys. Lett. 60, 319 (1992); L. C. Davis, J. Appl. Phys. 72, 1334 (1992); L. C. Davis, J. Appl. Phys. 73, 680 (1993).
K. M. Blackwood et al. in “Electrorheological Fluids,” edited by R. Tao and G. D. Roy, World Scientific, 1994, p. 3; Y. H. Shih and H. Conrad, ibid, p. 294.
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Sheng, P., Ma, H. (1998). Upper Bounds on Electrorheological Properties. In: Golden, K.M., Grimmett, G.R., James, R.D., Milton, G.W., Sen, P.N. (eds) Mathematics of Multiscale Materials. The IMA Volumes in Mathematics and its Applications, vol 99. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1728-2_14
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DOI: https://doi.org/10.1007/978-1-4612-1728-2_14
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