On the Navier boundary condition for viscous fluids in rough domains

Abstract

In this paper we review some recent results concerning the study of the asymptotic behavior of viscous fluids in rough domains assuming Navier boundary conditions on the rough boundary. Our main interest is to study the relation between both the adherence and the Navier boundary conditions in the case of a boundary with weak rugosities. We show that the roughness acts on the fluid as a friction term. In particular, if the roughness is sufficiently strong, Navier condition implies adherence condition. This generalizes previous results of other authors.

Microwave absorption by nanoresonator vibrations tuned with surface modification

“…Additional results concerning non-Newtonian fluids have also suggested the presence of non-standard effects that can be interpreted as a violation of the no-slip condition at the solid-liquid boundary and are responsible for lowered energy dissipation into the fluid [18]. This violation of the no-slip boundary condition has been confirmed by several experiments [27][28][29][30][31][32] and furthermore, has been also shown to take place in highfrequency oscillatory regimes associated with nanoscale dimensions [33,34]. In this study we develop a theoretical framework to explore the possibility of engineering the vibrational damping of a nanomechanical resonator based solely on the modification of its surface properties and furthermore, to quantify the microwave absorption in a nanoresonator suspended in a thin film of fluid.…”

Effective slip law for general viscous flows over an oscillating surface

“…They generalized their previous results from the study of Gérard‐Varet and Masmoudi , give error estimates for this homogenized no‐slip boundary condition of Navier type, and find a more accurate effective boundary condition of Navier type. For the asymptotic behavior of viscous fluid satisfying Navier's condition on a slightly rough boundary, we refer to recent articles . Finally, the wall law for very rough surface was investigated in .…”