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Title:Second-gradient fluids: A theory for incompressible flows at small length scales
Author(s):Fried, Eliot; Gurtin, Morton E.
Abstract:Using a nonstandard version of the principle of virtual power, we develop a gradient theory for incompressible flows at small length scales. In addition to 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. As an application, we reconsider the classical problem of plane Poiseuille flow for generalized adherence and slip conditions.
Issue Date:2005-04
Publisher:Department of Theoretical and Applied Mechanics (UIUC)
Series/Report:TAM Reports 1064, (2005)
Genre:Technical Report
Publication Status:published or submitted for publication
Peer Reviewed:is peer reviewed
Date Available in IDEALS:2007-03-09
Is Version Of:Published as Eliot Fried and Morton E. Gurtin, Tractions, Balances, and Boundary Conditions for Nonsimple Materials with Application to Liquid Flow at Small-Length Scales. Archive for Rational Mechanics and Analysis, Vol. 182, No. 3, 2006, pp. 513-554. DOI: 10.1007/s00205-006-0015-7. Copyright 2006 Springer.

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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