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Long slender drops in a simple shear flow

Published online by Cambridge University Press:  19 April 2006

E. J. Hinch  and
A. Acrivos
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge University, England
A. Acrivos
Affiliation:
Chemical Engineering, Stanford University, U.S.A.
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Abstract

We study theoretically the slow viscous motion of a long slender drop placed in a simple shear flow, the drop having a low viscosity compared with that of the suspending fluid. As a simplifying approximation, the cross-section of the drop is taken to be circular. An equilibrium shape with the drop nearly aligned with the flow is found for all shear rates, although the equilibrium is only stable to small disturbances for shear rates below some critical value. The stable equilibria just below the critical shear rate are found to be accessible only if the shear rate is increased slowly.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 2 , 29 May 1980 , pp. 305 - 328
Copyright
© 1980 Cambridge University Press

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References

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