title: Symmetry relations in viscoplastic drag laws.
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 ofstrongly dissipativerheology, 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.
authors.affiliation: Department of Mechanical Engineering , Massachusetts Institute of Technology , Cambridge, MA, USA.
authors.forename: K
authors.initials: K
authors.lastname: Kamrin
authors.affiliation: Department of Mechanical and Aerospace Engineering , University of California , San Diego, CA, USA.
authors.forename: J D
authors.initials: JD
authors.lastname: Goddard
keywords: drag relations; low-Reynolds flow; non-Newtonian flows; viscoplasticity