Theoretical predictions of the streaming potential generated by two-phase flow in a polygonal capillary are presented. The capillary walls are wetted by the continuous water phase, in which is suspended a long non-conducting oil drop. It is assumed that when fluid flows along the capillary a thin film of fluid is created between the drop and the capillary walls, which allows ions in the charge cloud adjacent to the wall to be convected. Current returns via conduction along the menisci of wetting fluid in the corners of the polygonal capillary. These menisci have finite cross-sectional area even when fluid is at rest, so that streaming potentials are predicted to grow linearly with the applied pressure gradient. (C) 2010 Elsevier Inc. All rights reserved.