DAMPED OSCILLATIONS IN A BINGHAM PLASTIC FLUID

Stokes' second problem, the propagation and damping of waves into a semi-infinite fluid generated by harmonic oscillations of a flat pate on the surface, is solved for the simple Bingham Theological constitutive model. The solution reveals the existence of “windows” in the distance-time-stress space in which shearing is possible whereas outside these restricted regions no shearing can occur. Within these restricted regions the wave forms developed are exponentially damped, traveling waves which propagate from the excitation plane into the fluid and disappear along definitely prescribed boundaries determined by the yield condition. The most significant consequence of the existence of these “windows” of shear is that even very small yield stresses will radically modify the induced velocity wave patterns from that which would be expected based upon the classical Newtonian fluid solution of Stokes' second problem. At least in this physical setting, it is not necessary for shear to occur globally for motion to occur anywhere, as has been postulated in some recent studies of complex motions. Thus, the motion is consistent with a simple Bingham model which does possess a yield stress.