Giant slip lengths of a simple fluid at vibrating solid interfaces

TL;DR

This paper analytically investigates how slip boundary conditions at solid-fluid interfaces influence the damping and friction forces in vibrating systems, revealing giant slip lengths that impact nano-electromechanical device design.

Contribution

It provides a theoretical framework for understanding slip effects in fluid-structure interactions, extending previous experimental findings to more general geometries and conditions.

Findings

Giant slip lengths can lead to overdamped regimes in vibrating fluid systems.

Theoretical results confirm the robustness of slip effects across different geometries.

Implications for NEMS design due to enhanced fluidic effects at small scales.

Abstract

It has been shown recently [PRL 102, 254503 (2009)] that in the plane-plane configuration a mechanical resonator vibrating close to a rigid wall in a simple fluid can be overdamped to a frozen regime. Here, by solving analytically the Navier Stokes equations with partial slip boundary conditions at the solid fluid interface, we develop a theoretical approach justifying and extending these earlier findings. We show in particular that in the perfect slip regime the above mentioned results are, in the plane-plane configuration, very general and robust with respect to lever geometry considerations. We compare the results with those obtained previously for the sphere moving perpendicularly and close to a plane in a simple fluid and discuss in more details the differences concerning the dependence of the friction forces with the gap distance separating the moving object (i.e., plane or sphere) from the fixed plane. Finally, we show that the submicron fluidic effect reported in the reference above, and discussed further in the present work, can have dramatic implications in the design of nano-electromechanical systems (NEMS).