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

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.published or submitted for publicationis peer reviewe