Slow flow of a Bingham fluid in a gap of slowly varying width

The slow Poiseuille flow of a Bingham fluid in an infinitely long gap of slowly varying width is considered. A consistent analytical theory is developed using a lubrication scaling without deviating from the Bingham model. It is shown that for sufficiently small gap width variations there is a rigid plug zone around the center of the gap. A numerical treatment of the problem is also presented using the method of augmented Lagrangian.Science, Faculty ofMathematics, Department ofGraduat