Symmetry relations in viscoplastic drag laws
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Kamrin_Symmetry relations.pdf
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Author(s)
Goddard, J. D.
Kamrin, Kenneth N.
Date Issued
November 2014
Journal
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher
Royal Society
Citation
Kamrin, K., and J. D. Goddard. “Symmetry Relations in Viscoplastic Drag Laws.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2172 (October 8, 2014): 20140434–20140434.
Version
Original manuscript
Abstract
The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of nonlinear viscoplastic fluids. This follows from Edelen's nonlinear generalization of the Onsager relation for the special case of strongly dissipative rheology, where constitutive equations are derivable from his dissipation potential. For flow domains with strong dissipation in the interior and on a portion of the boundary, this implies strong dissipation on the remaining portion of the boundary, with strongly dissipative traction–velocity response given by a dissipation potential. This leads to a nonlinear generalization of Stokes resistance formulae for a wide class of viscoplastic fluid problems. We consider the application to nonlinear Darcy flow and to the effective slip for viscoplastic flow over textured surfaces.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1098/rspa.2014.0434
