Threshold between Smooth and Wavy Laminar Sheet Flow

Abstract

A numerical and experimental investigation of roughness effects on thin laminar fluid films is described. The flow considered is pressure driven in an essentially two-dimensional channel between a flat wall and a wavy one. Conclusions, based on finite-element method solutions of the applicable equations of motion and substantiated by experimental findings, lead to the definition of a comprehensive friction index. This generalized friction coefficient appears to properly sense the microinertial influence of surface irregularities on the flow and allows the design of a “sensitivity parameter” for quantifying the threshold between hydrodynamically smooth and hydrodynamically wavy laminar sheet flow. Among relevant technical areas, this matter is of importance in hydrodynamic lubrication where it may determine the limit of the applicability of the classical Reynolds equation.