Abstract
We obtain criteria of stability of the unsteady motion of an incompressible Cosserat fluid in an arbitrary time-dependent domain, employing a general energy method due to J. Serrin. It is shown that the original motion is stable if R 2e ≦80 + 12800 C 0 or if λR e≦80 + 6400 C 0. The quantities R e and C 0 are the Reynolds number and Cosserat number, respectively, and -λ is the lower bound for the eigenvalues of the strain rate tensor D ij.
The theorems established for the stability criteria are universal in the sense that they do not depend either on the shape of the domain or on the distribution of the basic field variables. Finally an experimental scheme is proposed to determine the upper bound of the Cosserat number and consequently the characteristic length of a Cosserat fluid.
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Communicated by C. Truesdell
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Shahinpoor, M., Ahmadi, G. Stability of Cosserat fluid motions. Arch. Rational Mech. Anal. 47, 188–194 (1972). https://doi.org/10.1007/BF00250625
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DOI: https://doi.org/10.1007/BF00250625