Junction between a 3-D Stokes flow and a 2-D thin film with pressure boundary conditions

✍ Scribed by G. Bayada; M. Chambat

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 830 KB
• Volume: 12
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670120403

✦ Synopsis

Abstract

A 3‐D Stokes equation modelling the flow in the inlet region of a lubricated device is studied. Boundary conditions on both the pressure and the velocity are considered. The geometry induces that the flow region is divided into two parts: the first one is a thin gap with height ϵ__h__, where a change of scale is performed, and the second one is a cavity whose dimensions are large with respect to ϵ. Two equivalent variational formulations are proposed and lead to accurate a priori estimates. The resulting asymptotic equation for the pressure in the thin gap is the currently used Reynolds equation, whose boundary conditions are obtained via the junction with the 3‐D cavity. Both hydrostatic and hydrodynamic cases are considered.