Flow of a Bingham fluid in a non symmetric inclined channel

The flow of a Bingham fluid in a tilted channel of non uniform width is considered. The upper wall of the channel is assumed to be flat but not parallel to the bottom one and the flow is driven only by the gravity. A lubrication approximation is considered and an analytical solution is determined. We find conditions ensuring the appearance of the plug at a certain distance from the channel inlet. We also give an explicit formula for the pressure drop along the channel. Some numerical simulations are worked out for different values of the Bingham number and for different slopes of the upper wall.