Onsager principle and electrorheological fluid dynamics

Ping Sheng, Jianwei Zhang, Chun Liu

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We present the formulation of a two-phase, electrical-hydrodynamic model for the description of electrorheological fluid dynamics, based on the Onsager principle of minimum energy dissipation. By considering the energetics of (induced) dipole-dipole interaction between the solid particles in terms of a field variable n(x→), we employ the Onsager principle to derive the relevant coupled hydrodynamic equations, together with a continuity equation for n(x→). Numerical solution of the relevant equations yields predictions that display very realistic behaviors as seen experimentally. In particular, we show that while the predicted results have features that resemble Bingham fluids, there can be important differences. For example, the yield stress obtained by extrapolating the shear rate to zero is 30-40% lower than that obtained from the maximum of the stress-strain relation. Moreover, for the conventional electrode configuration where the field is perpendicular to the shearing direction, there is very clear shearing-thinning effect that has been seen experimentally.

Original languageEnglish (US)
Pages (from-to)131-143
Number of pages13
JournalProgress of Theoretical Physics
Issue number175 SUPPLEMENT
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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