Abstract
A generalization of the Lorentz reciprocal theorem is developed for the creeping flow of micropolar fluids in which the continuum equations involve both the velocity and the internal spin vector fields. In this case, the stress tensor is generally not symmetric and conservation laws for both linear and angular momentum are needed in order to describe the dynamics of the fluid continuum. This necessitates the introduction of constitutive equations for the antisymmetric part of the stress tensor and the so-called couple-stress in the medium as well. The reciprocal theorem, derived herein in the limit of negligible inertia and without external body forces and couples, provides a general integral relationship between the velocity, spin, stress and couple-stress fields of two otherwise unrelated micropolar flow fields occurring in the same fluid domain.
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© 1996 Springer Science+Business Media Dordrecht
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Brenner, H., Nadim, A. (1996). The Lorentz reciprocal theorem for micropolar fluids. In: Kuiken, H.K. (eds) The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0225-1_10
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DOI: https://doi.org/10.1007/978-94-009-0225-1_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6584-9
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