MOTION OF THE YIELD SURFACE IN A BINGHAM FLUID WITH A SIMPLE-SHEAR FLOW GEOMETRY

Non-steady flow of a Bingham fluid is analyzed for a simple-shear flow geometry. It is asserted that when a yield surface undergoes a latera l motion, the spatial gradient of shear stress in the lateral directio n is continuous across the yield surface. Using this property, the equ ation of motion of a Bingham fluid was transformed into a form of the moving boundary problem in which appropriate boundary conditions are s upplemented at the yield surface. This problem is compared with the co -called Stefan problem of crystallization. We find that, in a Bingham fluid, the lateral motion of the yield surface is determined by a spat io-temporally non-local mechanism, while, in the Stefan problem, the m otion of the crystallization front is determined merely by a spatially non-local mechanism.