AN EXACT NONSTATIONARY SOLUTION OF SIMPLE SHEAR-FLOW IN A BINGHAM FLUID

The flow of Bingham fluids can have yield surfaces that separate unyielded regions from yielded regions. The analytical solution for the Bingham flow equation that contains a moving yield surface is presented. An initially homogeneous simple shear flow in the semi-infinite bulk bounded by a planar boundary is assumed, and consideration is given to what disturbance occurs upon the reduction of the applied shear stress on the boundary after time t = 0. The solution is of the 'similarity' type in which all length scales grow as approximately t1/2 and the unyielded region in particular grows from the boundary such that its thickness is proportional to t1/2.