Tractions, Balances, and Boundary Conditions for Nonsimple Materials with Application to Liquid Flow at Small-Length Scales |
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Authors: | Eliot Fried Morton E Gurtin |
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Institution: | (1) Department of Mechanical and Aerospace Engineering, University of Washington in St. Louis, St. Louis, MO 63130-4899, USA;(2) Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3190, USA |
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Abstract: | Using a nonstandard version of the principle of virtual power, we develop general balance equations and boundary conditions
for second-grade materials. Our results apply to both solids and fluids as they are independent of constitutive equations.
As an application of our results, we discuss flows of incompressible fluids at small-length scales. In addition to giving
a generalization of the Navier–Stokes equations involving higher-order spatial derivatives, our theory provides conditions
on free and fixed boundaries. The free boundary conditions involve the curvature of the free surface; among the conditions
for a fixed boundary are generalized adherence and slip conditions, each of which involves a material length scale. We reconsider
the classical problem of plane Poiseuille flow for generalized adherence and slip conditions. |
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