University of Illinois Urbana-Champaign

Second-gradient fluids: A theory for incompressible flows at small length scales

Fried, Eliot; Gurtin, Morton E.

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https://hdl.handle.net/2142/322

Description

Title
Second-gradient fluids: A theory for incompressible flows at small length scales
Author(s)
  • Fried, Eliot
  • Gurtin, Morton E.
Issue Date
2005-04
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.
Publisher
Department of Theoretical and Applied Mechanics (UIUC)
Series/Report Name or Number
TAM Reports 1064, (2005)
ISSN
0073-5264
Type of Resource
text
Language
en
Permalink
http://hdl.handle.net/2142/322

Owning Collections

Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
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.