LUBRICATION THEORY FOR A FIBER SUSPENSION .1. PRESSURE-DRIVEN FLOW INA PLANAR CHANNEL HAVING SLOWLY-VARYING CROSS-SECTION

The steady inertialess flow of a semi-dilute fibre suspension through a planar channel having slowly varying cross-section is considered. Fo r large enough fibre concentrations, flow separation occurs at the wal l near the widest part of the channel, and regions of asymptotically s tagnant fluid develop over a significant fraction of the channel. Thes e stagnant zones contain very thin sub-layers which are difficult to r esolve numerically. Lubrication theory breaks down when flow separatio n occurs. A new theory is developed which enables the stagnant regions to be removed from the numerical computation, with jump conditions th at stitch together the flowing regions on either side. The analysis pr edicts a region of very weak reversed flow near the wall and a stagnan t layer which, in the lubrication limit extends to the wall. The lubri cation results are compared with a full numerical solution. (C) 1997 E lsevier Science B.V.