Abstract
The flow of a suspension of rigid rods in a wedge of small angle is considered. In the lubrication limit when the angular width of the channel is small but the rod concentration is high it is found that wedges of fluid (here called stagnant zones) in the interior of the channel become asymptotically static. The small scale structure within these zones is determined, and matched asymptotic expansions are used to provide jump conditions across them. These results are found to show good agreement with exact solutions for wedge flows even when the angular half-width of the wedge is not small (up to 30°, say). Analogous jump conditions are devised for stagnant zones in general planar lubrication flows of rigid rod suspensions.
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